THE OM COMPOSER’S BOOK Volume One
Collection Musique/Sciences Collection Musique/Sciences directed by Jean-Michel Bardez & Moreno Andreatta The The Musique/Sciences series Musique/Sciences series contributes to our understanding of the relationship between two activities that have shared intimate links since ancient times: musical and scientific thought. The often-cited often-cited Quadrivium (music, Quadrivium (music, astronomy, geometry, and arithmetic) reminds us that, in an age imbued with the spirit of the Gods, it was not uncommon to think of these two modes of thought as twins. During the twentieth century, music and science developed new links, establishing relationships with mathematics and opening new lines of musical research using information technology. Modeling, in its theoretical, analytical and compositional aspects, is more than ever at the center of a rich musicological debate whose philosophical implications enrich both musical and scientific knowledge. The pleasure of listening is not diminished when it is more active, more aware of certain generating ideas—au ideas—au contraire .
Published works G´erard erar d Assayag, Assaya g, Fran¸cois cois Nicolas, Guerino Mazzola (dir.), Penser la musique avec les math´ mat h´emati ema tique quess ? , 2006 Andr´e Riotte, Marcel Mesnage, Formalismes Formali smes et mod`eles , eles , 2 vol., 2006
Forthcoming Moreno Andreatta, Jean-Michel Bardez, John Rahn (dir.), Autour de la la Set Theory Guerino Mazzola, La Mazzola, La v´ erit´ eri t´e du beau dans d ans la musique musi que Franck Jedrzejewski, Mathematical Jedrzejewski, Mathematical Theory of Music
THE OM COMPOSER’S BOOK Volume One
Edited by Carlos Agon, G´ erard erard Assayag Assayag and Jean Bresson
Preface by Miller Puckette
Collection Collection Musique/Sciences
Editorial Board Carlos Agon, Ircam/CNRS, Paris G´ erard erard Assayag, Ircam/CNRS, Ircam/CN RS, Paris Marc Chemillier, University of Caen Ian Cross, University of Cambridge Philippe Philipp e Depalle, McGill University, Montr´eal eal Xavier Hascher, University of Strasbourg Alain Poirier, National Conservatory of Music and Dancing, Paris Miller Puckette, University of California, San Diego Hugues Vinet, Ircam/CNRS, Paris Editorial Editorial Coordination Coordination Claire Marquet Page Layout Carlos Agon and Jean Bresson Texts translated by Justice Olsson Cover Design Belleville
Tous droits droit s de traduction, traduct ion, d’adaptation d’adapt ation et de reprod r eproduction uction par tous proc´ed´ ed´ es es r´ eserv´ eserv´es es p our tous pays. Le code de la propri´ et´ et´ e intellectuelle du 1er juillet 1992 n’autorise, aux termes de l’article L. 122-5, 2e et 3e a), d’une part, « que les copies ou reproductions repro ductions strictement stricte ment r´eserv´ees ees a ` l’usage du copiste et non destin´ dest in´ees ees ` a une utilisation collective » et, d’autre part, « que les analyses et les courtes citations dans un but d’exemple et d’illustration ». « Toute repr´ r epr´esentation esentation ou reproduction repro duction int´ egrale egrale ou partielle, partiel le, faite sans le consentement de l’auteur ou ayant cause, est illicite » (article L.122-4). L.1 22-4). Cette repr´esentation ou reproduction par quelque pro c´ ed´ ed´ e que ce soit constituerait donc une contrefa¸ con sanctionn´ sanction n´ ee ee par les articles article s L. 335-2 et suivants sui vants du Co de de la propri´ pr opri´et´ et´ e intellectuelle. intell ectuelle. ISBN 2-7521-0027-2 et 2-84426176-0 c 2006 by Editions DELATOUR FRANCE/Ircam-Centre Pompidou www.editions-delatour.com www.ircam.fr
Contents Preface Introduction
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Writing a Homage to Marin Mersenne: Tombeau de Marin Mersenne for Theorbo and Synthesiser (General Midi) Michel Amoric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Electronics in Kaija Saariaho’s Opera, L’Amour de loin Marc Battier and Gilbert Nouno . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Vuza Canons into the Museum Georges Bloch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 TimeSculpt in OpenMusic Karim Haddad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 The Genesis of Mauro Lanza’s Aschenblume and the Role of Computer Aided Composition Software in the Formalisation of Musical Process Juan Camilo Hern´ andez S´anchez . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Generating Melodic, Harmonic and Rhythmic Processes in ”K...”, an Opera by Philippe Manoury Serge Lemouton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Composing the Qualitative, on Encore’s Composition Jean-Luc Herv´ e and Fr´ e d´eric Voisin . . . . . . . . . . . . . . . . . . . . . . . . 99 Navigation of Structured Material in “second horizon ” for Piano and Orchestra (2002) Johannes Kretz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 When the Computer Enables Freedom from the Machine (On an Outline of the Work H´ er´ edo-Ribotes) Fabien L´evy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Some Applications of OpenMusic in Connection with the Program Modalys Paola Livorsi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Fractals and Writing, Six Fractal Contemplations Mikhail Malt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Algorithmic Strategies in A Collection of Caprices Paul Nauert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Sculpted Implosions : Some Algorithms in a Waterscape of Musique Concr` ete Ketty Nez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 STRETTE H`ector Parra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Klangspiegel Lu´ıs Antunes Pena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Kalejdoskop for Clarinet, Viola and Piano ¨ Orjan Sandred . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Flexible Time Flow, Set-Theory and Constraints Kilian Sprotte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 To Touch the Inner Sound, Before it Becomes Music; to Dream About Dreams, Before they Become Real Elaine Thomazi-Freitas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Appendix. OpenMusic
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Preface The field of computer music can be thought of as having two fundamental branches, one concerned with the manipulation of musical sounds, and the other concerned with symbolic representations of music. The two are iconized by Max Mathews’s MUSIC program and Lejaren Hiller’s ILIAC Suite, both of 1957, although both have important antecedents. The two branches might provisionally be given the names “Computer Generated Music” (Denis Baggi’s term for it) and “Computer Aided Composition”—or CGM and CAC for short. (In France the latter is called “Composition Aid´ee par Ordinateur”. The corresponding English acronym, “CAC”, is less than mellifluous and someday we should settle on a better one.) As a field, CAC has flown a very different trajectory from CGM. While in the United States the great strides between 1957 and 1980 were on the CGM side, in Europe during the same period we saw work by Xenakis (starting as early as 1962), Koenig (Project 1, 1964), and many others that, taken together, can be seen as the first proof that CAC could be widely useful in creating new music. Meanwhile in the United States, many people, myself included, thought of CAC as a topic of computer science research, not likely ever to give rise to tools useful to musicians. Interest in CAC has grown in the USA in the intervening years, but excepting the brilliant example of David Cope, work in the USA on this topic has lagged behind that in Europe. Today CGM is ubiquitous and CAC appears futuristic. An entire generation of composers and other musicians has learned to use the computer to synthesize and process musical sound. It can be argued that the computer has been the one addition to the classical orchestra since the advent of percussion early in the twentieth century. This is a great achievement. CGM is now generally accepted, and the status of a musician in the Mathews tradition essentially depends on how good his or her output sounds, in the same way as that of an orchestral string or wind player. CGM has become a normal, respectable, middle-class occupation. The development of CAC, on the other hand, has seen a deepening realization that the problems of the field are much more difficult than they may have appeared at first. In hindsight, this should have been obvious to everyone all along: CGM is in effect building instruments (which were previously made of wood and the like), but CAC is in effect making the computer carry out thought processes previously carried out in human brains. Clearly, a piece of wood is easier to understand than even a small portion of a human brain. Ultimately, CAC researchers will have to settle for much less than a full understanding of even a single musical phenomenon. The best that can be hoped for is partial solutions to oversimplified versions of the real problems. Computational Complexity From my point of view, having come to computer music in the year 1979, the comparative situations of the two branches in the year 2006 come as a surprise. To the user of a 16-bit DEC PDP-11 computer, the manipulation of musical symbols looked trivial compared to the hard practical problems posed by the sheer size of the problem of sound synthesis. ix
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A five-second, one-channel soundfile was a large object in 1979, and the realization of a piece of computer music lasting ten minutes could easily require a solid week of computer time. Back then I was exceedingly lucky even to have that possibility. Now, in 2006, three IRCAM pieces from the 1980s can be run simultaneously in real time on a computer small and light enough that it could easily be thrown several rows into the audience. The symbol manipulators, on the other hand, whose programs once only took a few thousand arithmetic operations and a one- or two-inch stack of punched cards to run, now take their place as the heaviest computer users in all of music. The growth in complexity of CAC algorithms appears to have outrun the ability of computers to run them. The Markov chains of the early days (a few hundred arithmetic operations per note, say) have given way to combinatorial search and optimization problems requiring as many trillions of calculations as the user can afford to wait for. The imagination of composers and researchers in CAC far outstrips the supply of available computation power. In general, the cost of CGM per audio sample has not remained constant, but has not grown quickly. The best CGM of the seventies, thirty years ago say, probably cost less than ten thousand arithmetic operations per sample of output. The speedup in computing in the intervening years has allowed us the luxury of running the classic CGM algorithms in real time, thus changing the nature of the pursuit fundamentally. The algorithms themselves have grown somewhat more complex as well, but the universal preference for real-time synthesis and processing has put a lid on that growth. CAC has not become real-time at all. Since it appeals to the composer in us (whereas CGM appeals to the performer in us), it seems reasonable to expect that CAC software will continue to absorb all the computing resources that can possibly be brought to bear on it. Anything allowed to grow will naturally do so. Programmers and users About 1970, when I started using the computer—there was only one in my town— there was no distinction between computer users and computer programmers. It only occasionally happened that someone used a program that someone else had written. For the most part, each program was written for its own particular, special purpose. Over the following decade, however, this began to change for two reasons. First, people learned to write large, flexible programs (troff being my favorite example) powerful enough that different users could turn a given program to very different purposes. Second, and more subtly, the possibilities for combining different bits of software together began to multiply. An important step was the invention of the Unix operating system, which unified all I/O through one very simple and clean abstraction. This permitted users to direct one program’s output to another program’s input, frequently without the need even to choose a name for the data passing between the programs. This made it possible for a relatively simple program such as “tr” to be put to all sorts of different uses. Try it on a headerless soundfile, for instance, to put a classical music lover’s teeth on edge, in a way I doubt the program’s original designer had imagined. A parallel development was underway in the computer music community. Here the roots of the idea reach all the way back to about 1958 when Max Mathews’s MUSIC N programs began to offer reconfigurable unit generators , which the user configured in a network to generate musical sounds, predating and anticipating the modular synthesizers built by Moog and others in the 1960s. By the mid 1980s many researchers were thinking
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about trying to turn this notion of reconfigurability to use in passing data of other formats than audio signals. Programs themselves (such as MUSIC, Max/MSP, or OpenMusic) have become complicated and difficult to develop, but once the paradigm for making interconnections has been worked out, they are comparatively easy to extend. Users can contribute extensions and benefit from each other’s work, without having to worry about the tricky stuff such as GUIs or file formats. In another sense, however, a patch is itself a program, and the job of connecting simple functions together to make larger ones can be thought of as programming. In this sense, the trend toward patch-based software can be seen as shifting the level on which the user programs the computer away from the C or Lisp code itself and into the “language” of patches. It may be that this is fundamentally a better level at which to operate a computer, than either that of code or that of the user of a large, monolithic program such as a database application. Art music and the computer In Europe and its former colonies such as the U.S., composers, since early in the twentieth century, have paid much attention to problems of symbol manipulation and combinatorics. This idea found an early expression in Shoenberg’s 12-tone harmony, continued through the serialism typified by Webern and later Boulez, and may have culminated in the various mathematics-inspired approaches of Xenakis. The affinity of composers such as Xenakis and Koenig for computers seems to grow naturally from their symbol-based and/or quantitative approaches to musical composition. It is no accident that computers were used in experimental classical composition, whereas more tradition-bound musics such as Jazz stayed far away from the computer room. And researchers in CAC repaid the compliment by paying close attention to sets and permutations, and less so to melodic contour, for example. To this day, the field of CAC looks primarily to the classical ‘art music’ tradition as a source of working assumptions and problems. Since computers are well adapted to symbolic and quantitative manipulation, it is not surprising that ‘art’ composers have often turned to the computer, sometimes merely for assistance, and sometimes for inspiration. The strange field called ‘computer science’ (which has little to do with writing or using computer programs) is often invoked as well. Certain metaphors from computer science, such as hierarchies and networks, machine learning, and database operations, often can be explicitly mapped to musical processes, and this is useful to some of the more formally procedural composers. I think these formalistic tendencies are now giving way to a more intuitive approach among ‘art’ composers. Whether or not that is true, there is certainly more crosstalk today between ‘art’ composers and musicians of other idioms. This is reflected in a general movement in CAC away from formal and mathematical tools, in favor of more intimate modes of interaction with the computer, even up to direct manipulation of data structures by composers. So for instance when early CAC researchers wrote computer programs whose output might be an entire piece of music, today we see developments such as Open Music which, in their graphical orientation and patching metaphor, encourage the composer to proceed by experimentation and intuition instead of by formal planning and specification.
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The field of CAC in general is moving away from mathematical and computer science constructs, and toward a more useful and powerful working relationship with the rest of the composition process. A greater fluidity of interchange between the problem-solving or material-generating functionality of a program such as OM, and the higher-level, partly intuitive thought processes that must reside in the human brain makes the entire field of CAC more accessible and more widely useful than ever before. Software and Computer Aided Composition In CAC, the variety of approaches and the flexibility of applications have grown as time has passed. Back when computer programs used stacks of cards as input and output, it was natural to think of “composition” as an atomic computer job: in go the program and some parameters, and out comes music. As computing became interactive, a much more powerful mode of working emerged, in which the computer might be called on hundreds or thousands of times to solve specific problems, such as voicing a chord or quantizing a rhythm. Lisp, which is widely used in AI circles, was an early favorite among CAC researchers. In return, the AI community, especially around MIT and Stanford, has long taken a strong interest in music. The history of CAC software is dominated by large Lisp-based systems. Perhaps the most important advance in the field of CAC was Patchwork by Mikhael Laurson, a direct ancestor of OM. Patchwork (which Laurson still develops) presents the user with a patching GUI, in which the semantic is that each object, to produce its output, asks the objects upstream of it to compute their outputs, recursively. This demand-driven dataflow model is also used in OM, although the nature of the function calls has been greatly generalized compared to those of Patchwork. Central to the success of both Patchwork and OM is the presence in each of tightly integrated music notation display packages. A transparent connection is maintained between the displayed score and the (user-accessible) data underneath, allowing for easy transitions between the two media. This greatly enhances the ability of the user to tightly integrate the algorithmic part of the work (on the data structures) with the intuitive aspect (in the composer’s mind, transmitted via the notation). Initially, the notation GUI functions as an invitation to composers to try the software. After the composer is attracted, the notation package serves as his or her personal interpreter to the language of Lisp. That the developers of Patchwork and OM have actively sought to involve composers in the earliest stages of the design of the software is itself another decisive reason for their success. Few centers, anywhere in the world, have ever managed to match IRCAM’s simultaneous ability to attract world-class music production projects and to support researchers in the field of computer music. Even though state support for IRCAM has eroded since the golden age of the 4X and the ISPW, the creators of OM maintain this spirit, of which the present book is an important manifestation. OM is almost certainly now the world’s dominant platform for doing CAC research and practice, despite the presence of several other approaches (including one, by Karlheinz Essl, that runs within Max). Is this because OM’s design is the best, or is it that OM has benefitted from the presence at IRCAM of so many willing composers, such as the ones represented in this book? The two rival explanations are impossible to extricate from one another.
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This doesn’t imply that all interesting research in CAC is being done in OM. David Cope’s work seems to me the most interesting CAC research from a theoretical standpoint. His particular software solutions belong to the class of “automatic composition” programs and are hence less adaptable to the needs of the main body of composers today than systems such as OM. I hope someday to see his ideas brought out in more modular form. Promising areas of current and future research An excellent trend is underway, and has been for at least several years, in that composers of computer music today no longer immerse themselves in one primary software package to realize works. The possibility of passing between one world and another (such as Max and OM, for example) would not have occurred to many researchers or composers in the days when mastery of any one idiom could take years of study and work. But as computer music software in general has become more open and more modular, the opportunities for interchange of data have increased, and at the same time the initial cost (primarily in time) of using a new software package has gone down. Many new and interesting sparks should fly from the collisions between the vastly different software packages that now can be brought together. Related to this, perhaps even a case of the trend toward interoperation, is the growing involvement of CAC in manipulating sounds directly (not through the mediation of a score). Such work lies simultaneously within CGM and CAC, and in one possible future the distinction between the two will simply disappear. This is in high contrast to the early days of CAC in which the output was a stack of punched cards, or even to the situation only ten years ago, in which Patchwork users needed MIDI hardware to hear their musical ideas. (CGM people like me scoff at the practice of using MIDI to synthesize music.) The world of sounds is much richer than the world of musical note heads and stems. The latter will always be a useful organizing and mnemonic device, but the former is what actual music is made of. In more general terms, I look forward to an increased concern in CAC about continuously variable quantities, such as parameters of analysis or specification of sound (as well as the function of time that represents a recorded sound itself). In the future, computer music in general will have to deal with high-dimensional objects such as would specify a timbre. The dimensionality of a set such as the “set of all possible sounds” is probably not even well defined. New techniques will be needed to describe and manipulate such quantities. I’m also very excited about the recent work in OM on generalizing constraint problems to optimization problems. The cool thing about treating compositional problems as optimizations instead of constraints is that you can juggle the weights of the terms of the function and watch, incrementally, as the machine tries to optimize the ever-changing function. This can be used to find solutions to standard constraint problems, by adding and dropping component constraints and watching how the solution changes. It’s almost never interesting to see ALL the solutions of a constraint problem anyway; most of the time there’s either no solution or else there are lots that you’d be equally happy with. Next, I would like to see some of the techniques now only available in OM become usable some day within real-time environments. This is clearly a huge undertaking, since the style of programming currently used in real-time applications is so different from that
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in OM. But there would be much gained if this became possible. In the meantime it’s possible to send messages back and forth between OM and some lower-latency process that takes care of real-time performance. But in the ideal, the connection between the real-time and the compositional environments would be much more based on sharing data and functions, rather than just communication protocols. Another word for real-time composition is “improvisation”, and in this view George Lewis was doing CAC research when he developed Voyager in the 1980s, and Salvatore Martirano was apparently also doing CAC with the SalMar in the 1970s. Improvisation is not only important in its own right, but also as the primary means by which composers and performers have extended instrumental language, probably long before music wes ever written down. Improvising with computers will lead us to a greater mastery of the computer as a musical instrument in composed settings as well as improvised ones, and I think CAC will play an important role in this development. One more area. I’ve mentioned David Cope’s automatic composition project, and although I can’t say I understand his methods very well, it’s clear that his use of natural language recognition tools (in particular, “augmented networks” has somehow captured something essential in the way classical musical forms work. No other research I’m aware of has ever gained any real purchase on the questions of how musical motion, tension and resolution, and musical themes work; and no other software algorithms I have seen can make music that develops (in the classical sense) over the time scale of an entire piece in the way Cope’s can. There is clearly something vitally important in this work, and other researchers (myself not excepted) should be making a greater effort to learn its lessons. Read this book Perhaps I have named the frontiers well and perhaps not (only time will tell), but at least as far as the present is concerned, this volume contains the best summary of current work in the field that I know of. That each chapter of the book concerns the composition of a real piece of music reassures us that the methods described here can indeed be brought to musical fruition. And while, by the design of the book, composers using software other than OM aren’t represented here, perhaps two thirds or three quarters of the entire field creeps in at one spot or another. OM has established itself as the most important locus of convergence of researchers and composers working on, or in, CAC; and, well, here they are. This book should prove useful not only to those wishing to learn how to use OM in its present state (at least at the moment before OM develops further or is replaced by something else) but also in the longer term as a repository of ideas, many of them having roots in the past, even in non-computer-music, and many of which will reappear in different musical and software contexts in the future. This is how music works, after all—a musical idea is important in the way it speaks to the rest of the world of musical ideas. It’s not the individual notes that count: it’s their interrelationships.
Miller Puckette February 20, 2006
Introduction This book brings together accounts about the way various composers approach the computer when composing. More specifically, each chapter of this book gives an example of computer-aided composition (CAC). While it is true that the composers presented here have widely differing styles, they share a common denominator: they all use OpenMusic software when composing. OpenMusic is a visual programming language for computeraided composition designed and developed by the Musical Representation team at Ircam. It was born out of years of research and experiment in the use of symbolic representations of musical structures and their application in composition. After all these years of practice, we would like to sum up the current situation in computer-aided composition. However, rather than publish a series of theoretical texts, we thought it would be preferable to let the composers speak for themselves. Each article included in this book describes one or more pieces that have already been played. Consequently, the book will talk about musical results rather than experiments. Using the description of computer programs for composition, the reader can focus his or her attention on various questions: music formalization; the specification and organisation of musical material (structure and form); external causes (perceptual, speculative, aesthetic etc). This book will make it possible to compare a large number of different approaches, types of artistic development, and above all composition styles. Moreover, it will allow us to hear the viewpoint of a valuable number of composers concerning the potential of the computer in composing a musical work. The ways in which each composer approaches the computer are unique, on several levels. First of all, in their degree of mastery of the computer: there are composers for whom the computer is a kind of magic hat: they can pull anything out of it. At the opposite end of the scale are composers who have a reasonable understanding of what can and must be done, and what belongs more to the realm of science-fiction. Secondly, there are those who never discuss the musical relevance of the computer, and those who have totally integrated the computer into their aesthetics and creative strategy. Concerning CAC, the huge diversity of aesthetic models cohabiting among today’s composers makes it almost seem as if there has to be a computer system for each composer. Starting from these special relationships between composers and the computer, the aim of this book therefore is to serve as a source of reflection about computer-aided composition. The practice of computer-aided composition is both old and new. In 1957, L. Hiller along with L. Issacson and R. Baker created the first piece of music ”composed” on computer: Illiac Suite for String Quartet . Shortly before that, at the end of the Fifties, the invention of the transistor led to the second generation of computers, the direct ascendants of the computers of today. With a little boldness, we could explain that precocious birth of CAC by saying that it represented a big challenge for the artificial intelligence of the time. If we twist Minsky’s definition of AI somewhat, we could imagine computer-aided composition at that time as follows: Making computer programs do musical composition, that is a task better carried out by human composers, because it demands very high-level mental pro1
Introduction
cesses such as perceptual learning, memory organisation and critical reasoning. This view of CAC might be fascinating to the computer scientist, but would not at all be met with approval by composers, for reasons that are obvious. Those early experiences — which can be summed up in three stages: selection of the material, random combination, and then selection of the result — have no aesthetic value for most composers today. Cooperation between computer scientists and composers has gone far beyond a state of affairs where the programmer simply imposes computer tools on the composer, or where the programmer simply carries out the composer’s instructions. There is no sense in considering the composer as an end user; firstly, ease of use and timesaving are not his main concerns, and secondly, it is difficult or impossible for the composer to entrust his creative action to somebody else. In our approach to computer-aided composition, we do not see the composer or the music as something to be modelled, but rather we instigate and then study compositions in an effort to gain a better understanding of the role of computer processing and concepts in music. Thus we are proposing a shift in the problem/solution paradigm, so beloved of programmers, towards an idea/exploration approach, in which computer tools will make it possible to either carry out or to modify the composer’s intentions, depending on the possibilities open to him. ”Modern” computer-aided composition, in the form in which it began to emerge in the Eighties, was influenced by various factors: the availability of personal computers; technical progress in graphic user interfaces; emerging standards such as MIDI in 1983; and technical progress in programming languages, in our view the most single important factor. Using a programming language means that the composer has to think deeply about the very process of formalisation. It also means that he is not working with some black box offering only a limited number of choices. Programming languages open up an enormous range of possibilities to the composer – providing he is willing to make the effort in formulating and designing his project. However, it should be noted that certain computer practices do not count for much in composition. They are merely tools that do not greatly influence the composer’s aesthetics. By contrast, there are others that, with a little boldness, allow us to learn something of the role of programming in composing. Let us imagine a composer-programmer, for whom the computer is an absolutely necessary ingredient when composing. Naturally, this does not have to be the case: there are people who can compose without using a computer. But for those who do use a computer, a programming language for composers is only the first step towards a ”more intelligent” way of using the computer in musical creation. In other words, using a programming language in no way guarantees a quality result. And finally, it is not easy to settle on a relevant aspect of composition in order to formalise it in computer terms. Experience has tended to show that tasks which appear elementary to the composer can be extremely complex in computer terms, impossible even. Similarly, information complexity is not at all the same thing as musical complexity or richness. Using computer aided composition software for simple and repetitive tasks is not an aspect that should be neglected. An excellent example of this way of using the computer can be found in Lemouton’s article “Generating melodic, harmonic and rhythmic processes in K..., an opera by Philippe Manoury”. Philippe Manoury is well known in the computer music domain for his innovations and his research regarding real-time processes, but he also uses postserial techniques in his writing. Some of those post-serial rules can easily be automated. 2
The very simple OpenMusic patches shown in the article were used to generate musical material which was then printed in several bound notebooks, which served as melody, chord and rhythm ”reservoirs” into which the composer was able to dip while writing the score. Various other perhaps more important ways in which the computer was used in composing the opera, concerning synthesis, spatializing, as well as real-time systems, are not dealt with in the present article. Computer music software, in the way we conceive it, can in no way handle all aspects of a composition. In most cases, OpenMusic is used for some special aspects of the composition (rhythmical, melodic, harmonic etc). Similarly, the results proposed by the computer are often corrected or modified by hand, when they are not rejected outright. Levy in his article “When the computer enables freedom from the machine (on an outline of the work H´er´edo-Ribotes )”, puts forward musical situations, illustrated with examples, in which, in his view, OpenMusic is relevant (calculating ”prime spectra”, ”iterated harmonic transposition”, Tanner vectorial representation etc). In dealing with other tasks, by contrast, e.g. quantization, the composer prefers to take advantage of the slowness of pen and ink and manual calculation, even though there is a programme which would render the task less laborious. In this article, the author deals with two aspects of OpenMusic. The first is epistemological, with a view to demonstrating that computer music techniques, far from getting the composer locked into considerations of an exclusively technical nature, allow him to set himself free of them. The second aspect is of an aesthetic nature, where Fabien Levy attempts a succinct description of the artistic thinking behind computer procedures used in his composition. Generally speaking, OpenMusic was designed to enable the composer to set up the programmes needed in preparing complex material, structured by a set of rules expressed in a coherent way. We approach the computer-aided composition from three angles: formalisation, modelling and experimentation. Musical formalisation is the phase that precedes the conception and the writing of one or more pieces. It serves as a musical language for the composer. In our view, we can approach the source that is to be formalised in two ways: the first is based entirely on purely musical issues, and serves to decide which computer tools will be the most suitable for a given task; the other approach consists in transferring information or knowledge from an extramusical domain (which may be of a scientific, social, religious, literary or other nature) towards the musical domain. As for the relevance of a given formalisation approach, this will depend in the first instance on the musical issues requiring formalisation. In the second instance, it will depend upon the correspondences that exist between the extramusical entities and sufficiently significant musical structures. It should be noted that formal logic does not necessarily imply the use or the presence of musical coherence. If a correspondence of this type is to be used in a musical composition, it needs to be supported via musical conceptualisation and thought. An example of the first type of formalisation is to be found in the article “Timesculpt in OpenMusic”. In this text, Karim Haddad’s chief preoccupation is musical time. It contains various compositional strategies for manipulating duration. Haddad introduces the notion of a ”time block” as a symbolic representation for a duration. Time blocks are displayed as bars, but they only exist during the composition phase. The composer has built up a time block algebra based on tree structures, using OpenMusic rhythmic symbolic representations (he also contributed considerably to its development). Various operations (rotations, homotheties/scalings, inversions, filtering etc) are applied to the 3
Introduction
time blocks in order to generate the rhythmic material of his composition. Thanks to this formalisation, Karim Haddad can create time blocks that are manually constructed or generated by sound analyses. Each of the selected results is then simplified into traditional music notation for performance. A formalisation example taking as its source an extramusical domain is to be found in “Navigation of Structured Material in Second Horizon for Piano and Orchestra”. In order to create organic musical gestures in this piece, Kretz bases it on the simulation of physical movement. Using MAX software, he formalised the movement of a ball in a closed room, subject to factors such as gravity and friction. Various trajectories were then imported into OpenMusic to be used as writing parameters. The translation of spatial positions into the harmonic domain did not yield satisfactory results as far as the composer was concerned; however the various spatial envelopes did influence the final form of the work. Johannes Kretz makes particular use of techniques resulting from constraint programming in order to create musical structures using musical gestures as their source, in turn derived from the movements of a ball. His domain of variables is a pool of chords generated by an imposed 12-tone series. Another constraint method, this time applied to orchestration, opens up unexplored and promising fields of research. Formalisation generated by mathematics is more difficult to classify than the two preceding categories. The question of whether music is a mathematical discipline is not dealt with directly in this book. Nevertheless, it cannot be denied that numbers are an important source of inspiration in composition. The golden mean, the Fibonacci series, or magical squares are all frequently used examples. In “Writing a Homage to Marin Mersenne: Tombeau de Marin Mersenne for Theorbo and Synthesiser”, the composer Michel Amoric uses OpenMusic to calculate global spectral analyses of instrumental sounds, based on Mersenne numbers. Other composition techniques round out this homage to Mersenne: the use of short extracts or fragments from 18th century pieces, and the implementation, in the form of constraints, of rules proposed by Mersenne in his book Harmonie Universelle . In his article “Fractals and Writing”, Malt demonstrates how he applies the mathematical notion of fractals when constructing a ”self-similar” form that serves as an overall guide to his piece Six Fractal Contemplations . This is made up of six short pieces for solo instruments (trumpet, flute, viola, voice, guitar and clarinet) and CD. According to the performance order of each piece, the composer sets up a curve based on the evolution of each instrument’s register centres. This curve shows a global aspect of the work, but it also determines the way each piece evolves. This is where the notion of self-similarity comes in: the evolution of each piece is the same as the evolution of the sequence of the six pieces. For this purpose, Mikhail Malt used ”fractal proliferation” via IFS (Iterated Function System), a collection of functions that he developed in OpenMusic for the manipulation and the creation of recursive linear systems. This system most notably makes it possible to build fractal objects. The IFS system is described in detail in this article, as well as its underlying mathematical theory. Concerning modelling, the composer has to create a formal device which, by providing at least a partial description of the characteristics of a composition process, makes it possible to simulate the compositional process in an experimental way for purposes of verifying, observing or even generating similar processes. In OpenMusic, the modelling 4
result of a piece is represented by a computer program component known as a patch 1 The various articles in this book use two main modelling types, known as constructive and declarative. The constructive approach goes via an algorithm or a programme that specifies the stages to be followed in constructing a musical piece. Usually, these programmes display several parameters or entry fields which the composer may vary with each execution. OpenMusic is essentially a functional language, and can be seen as a function library for implementing musical operations. Functional programming appears to be well suited to composers. It is a programming style that answers the need to set up multidimensional objects, and to apply operations for purposes of modifying them, or creating new objects. In OpenMusic, there are functions that are dedicated to intervals; to harmonic processing; to chord, motif and more complex musical object interpolation. The functional approach appears to be particularly relevant to composers who attach great importance to the interaction between musical material and the processes that modify that material. In her article “Sculpted Implosions : Some Algorithms in a Waterspace of Musique Concr` ete”, Nez describes, in detail, compositional techniques that she uses in controlling pitch and rhythm. She describes various pitch control techniques, among them the morphing of a note’s harmonic series; contour formation for a chord sequence, and the various types of interpolation between two chords. In the rhythmic domain, she explains the various algorithms for constructing time curves, and even more interestingly, the composer explains how she combines these time curves with the generated chord sequences. These different OpenMusic techniques are already an integral part of Ketty Nez’s instrumental writing. The fact that they were implemented into OpenMusic made it possible for the composer to explore new creative fields. For example, the harmonic and rhythmic results were converted into filtering parameters which were then applied to prerecorded sounds. Another example of material transformation processing can be found in “Kaija Saariaho’s L’Amour de loin ”. Nouno and Battier summarize the process as follows: the sound material is made up of sampled spoken voice extracts from the libretto, as well as instrumental sounds. These samples are analysed using resonance model techniques. The filtering phase consists of combining electronic components generated by a predefined harmonic structure with a timbre generated by resonance model analysis. The electronic part is first written in the form of a score. The electronic sounds are based on harmonic structures specific to each character in the opera. Finally, the sounds that thus created are mixed in real-time using the spatializer developed at the Ircam. In the declarative approach, instead of the composer providing a recipe for the construction of a musical entity, he defines the principal features of the required object. Then, by means of a combinatorial search mechanism, the computer proposes one or several objects that satisfy the specified requirements. Constraint programming is the most commonly used computer-aided composition programming paradigm in this approach. A constraint is quite simply a logical relationship concerning a set of variables (unknown problem variables in a given domain). It provides partial information about permitted values, thus ”constraining” the values within a certain range. Together, variables, do-
1
In most of the articles, the patch figures accompany the composer’s discourse. Understanding a patch by looking at an image is not an easy task. It is not an absolute must in order to understand the articles, however any reader not familiar with OpenMusic and who wishes to gain a rough idea of the language can refer to the appendix at the end of this book as well as the recommended reading.
5
Introduction
mains and constraints make up a CSP (Constraint Satisfaction Problem ). Once the CSP has been written in OpenMusic, it is passed on to a solver, which finds the values that satisfy the constraints to be applied in a musical structure. ¨ In “Kalejdoskop for clarinet, viola and piano” by Orjan Sandred, the rhythmical constraints are used in two ways: either the rhythmical entities are the result of a CSP, or they are the words of a constraint problem that concatenates them according to certain rules. The first two sections of the piece are three voice containing rhythmic structures. The three voices are linked by note attack constraints. Each note attack in the first voice in particular has its equivalent in the second voice. The same ”inclusion” constraint is imposed on the second and third voices. Other constraint types apply globally, for example, in a given voice, short notes are favoured in the first bars whereas long notes are favoured in the closing bars, to create a ritardando feeling. In this article, the reader will discover a great variety of rhythmical and harmonic constraints, but even more importantly, the composer lays out his own viewpoint as to the musical relevance of these rules. In “The Genesis of Mauro Lanza’s Aschenblume and the Role of Computer Aided Composition Software in the Formalisation of Musical Process”, Juan Camilo Hernandez demonstrates an analogous use of constraints. One of the main themes of his article is a hierarchical rhythmical language that generates rhythmic motifs. Using the division modulo of a rhythmic motif, Mauro Lanza obtains sub-motifs that coincide with the original motif. Note density in a sub-motif is controlled by a system of constraints. The composer uses Mikael Laurson’s Pmc Engine library. The article also contains shrewd and delicate analyses of other aspects: creating a harmonic field for purposes of making the sound of the composition homogenous; using melodic envelopes to control sound processing; time stretching of each of the work’s sections. The use of a given modelling type, constructive or declarative, can give rise to expressions in one form that will not be favoured in the other. The choice of one or the other form will therefore depend on how easily the model may be adapted to a given musical situation. Nevertheless, within a single composition, it may be necessary to use both approaches. In “Flexible Time Flow, Set-Theory and Constraints”, Kilian Sprotte uses both functional programming and constraint programming in order to create rhythmic and harmonic musical structures. Generally speaking, his approach here consists in defining algorithms so as to generate a set of musical objects (constructive approach), as well as selecting and organising a subset that satisfies certain rules or constraints (declarative approach). Models can be a source of inspiration to the composer. In “Vuza canons into the museum”, Georges Bloch takes as his basis a model proposed in OpenMusic for the construction of“regular complementary rhythmic canons of maximal category”. Although there is an algorithm to calculate musical objects, it should not be thought that the composer will simply use it systematically on a ”no questions asked” basis. Georges Bloch’s in-depth study of these canonic structures revealed features of certain objects that, in the model, had remained hidden. For example, by coupling certain voices, he obtained canons that maintain regularity and complementarity properties. Moreover, Georges Bloch proposed operations that occur between canons, for example, modulation between two canons. Even though the operation gives a result that goes beyond the bounds of the model’s properties, from a perceptual viewpoint, the structure thus created is in tune with the composer’s intention. In the composition’s final canon, Georges Bloch employs harmonic constraints that destroy the perception of the canon form and so create 6
the feeling of a texture. One of the principal functions of a model lies in the way it can be used to formulate hypotheses and then simulate them. In this context, experimentation becomes absolutely essential. Once the model is implemented, it is unlikely that the composer will remain within the bounds of a given set of parameters. In contrast to other approaches (algorithmic music, for example), in the way we deal with computer-aided composition, material generated by processing will be reworked by the composer according to other criteria, most of them aesthetic. The composer does not know beforehand what the final result will be like. Material generated by a model is considered to be potential material only, and it is up to the composer to decide where to stop the model. A model generates a family of results that can be progressively extended; it can thus be viewed as an equivalence class of compositions. In this context, two identical results that do not come from the same model are not equal, because they do not have the same evolutionary possibilities. The score describes the work in notes, but it is the model that gives it meaning. Among other things, it determines whether a trend will move towards or away from complexity, as well as the specificity of the work’s constructions. To take an example on the level of form, there are compositions that start out from the global and then ”fill-in” on the local scale, or vice versa, there are pieces in which it is the assemblage of the local sections that will bring the whole into the light. In A Collection of Caprices , Paul Nauert uses a strategy that he calls ”top-down”. The composer decides that his piece will comprise 11 sections, with long and short sections alternating. Then he composes them. The OMTimepack library, implemented by the composer, provides tools for generating durations according to a specific statistical profile. Once the rhythmic sketch of the piece has been completed, the composer inserts the pitches. To do this, he uses pitch equivalence classes that create a uniformity dynamic within each section, while creating contrasts between different sections. The opposite approach, ”Down-top”, is to be found in the article “Composing the qualitative, on Encore ’s composition” by Jean-Luc Herv´e and Fr´ed´eric Voisin. Encore is a piece for 18 musicians, electronics and two Disklaviers. The MIDI Disklavier scores were created using OpenMusic. An important phase was the realisation of simple composition gesture ”prototypes”: mounting runs, descending runs and repeated notes. These elementary gestures were then given reciprocal articulations, and placed in the OpenMusic maquette editor (see appendix). In this way, changing a gesture inside a maquette can have an impact on the way other gestures are updated, both downstream and upstream. The entire cadenza is made up of a succession of 10 boxes corresponding to the 10 phrases of the cadenza. Each box is itself a maquette, containing the phrase’s entire gesture sequence. These sophisticated, high-level representations of musical structures and knowledge, in conjunction with the OpenMusic computer language, have made it possible for us to bring together in one book a broad community of composers as well as various original forms of musical thought so characteristic of the information technology environment. Reading through the various articles, it becomes obvious that the composer is able not only to represent (and perform) the final score, but can also take care of all the various levels of formal elaboration, and where applicable, algorithmic generators. Works that are created in this way partly contain their own structural analysis. Such a symbolic approach to computer-aided composition has undoubted relevance for the composer. Among other things, modelling a piece makes it possible to do the following: substitute 7
Introduction
one compositional notion for another at varying levels of abstraction; reduce the amount of information necessary for describing a musical object; have access to a veritable symbolic function, i.e. one that can be read, written and memorised; take advantage of the symbolic nature of information technology so as to be able to gain increased control over the computer. Finally, this symbolic approach to computer-aided composition promotes and stimulates relationships between music and other artistic domains. Music, painting and poetry for example, are linked together in Hector Parra’s Strette . In his article, the composer set up a direct link between the vocal component in his composition and the features of Paul Celan’s poem Engf uhrung . In a parallel way, links are proposed between ¨ music and painting, taking as a motif the Chˆ ateau Noir by C´ezanne. Various patches are used in formalising the way Hector Parra designs and creates relationships between colour, rhythm and pitch. This computer formalisation of high-level musical structures (notes, chords, voices, etc) may give the impression that the physical reality of music i.e. the sound, is neglected. Indeed, the process of modelling sound phenomena using formal concepts that are on a higher level of abstraction than are the signal models remains for the moment a utopian project. What is even more problematical is the way those two levels of musical representation, the signal and the symbolic, relate. This is a scientific obstacle that has yet to be overcome. Nevertheless, this obstacle has not prevented composers from establishing formal links between sound and the written symbol. In the present book are to be found artistic propositions whose aim is to build a bridge between the two worlds, one that will allow a two-way exchange: extracting information from signals, and controlling sound signal synthesis. Klangspiegel by Luis Antunes Pena is a composition based on the manipulation of data generated by sound analysis. The data are transformed in OpenMusic and is then synthesised, producing a ”virtual image” of the original sound. The analysis is also used in another way, on the macro time level. By means of the combinatory power of the computer, the data generated by analysis are made to respond to symbol manipulation (for the most part, in and between the rhythmic and harmonic domains). The results thus obtained, synthesis of the sound and instrumental writing, are considered by the composer to be a dual representation of the original sound. Confronting these two images or representations is the composer’s chief preoccupation in this work. In “Some applications of OpenMusic in connection with the program Modalys”, Paola Livorsi explains how she uses OpenMusic to control sound synthesis parameters that are then employed by the program Modalys . Multiple synthesis parameters are prepared in OpenMusic, among them access envelopes, and sound and resonance duration values. Apart from performing a task that would be difficult and imprecise if done by hand, OpenMusic made it possible to control the parameters in a dynamic way, throughout the sound’s entire duration. Paola Livorsi also introduces random variations in order to enrich synthesis of the sounds. There are numerous instances in the book where composers have had to ”program” their own composition tools for personal use. The programmes thus created have been integrated into OpenMusic in the form of libraries. So a library can be said to be an open version of what was originally a personal composition tool. In her article “To Touch the Inner Sound, Before it Becomes Music; to Dream About Dreams, Before they Become Real” Elaine Thomazi-Freitas explains how she used the om-tristan library (created by the composer Tristan Murail) in the frequency domain. Using spectral analysis data, 8
Elaine Thomazi-Freitas extracts rhythmic and harmonic figures and manipulates them in order to generate the musical content of her composition Derri`ere la Pens´ee . Thus, OpenMusic is software in continuous development. Day by day, it becomes richer thanks to the special programs created by composers. Can it be said that software brings into being composer-programmers, or, rather that programming is a necessary and unavoidable practice when using the computer to create music? The first of those two notions seems far too pretentious to us, and so we prefer to believe in the second. However, in compiling the present texts, we do not lay claim to demonstrating such a hypothesis. The idea of the present book is to constitute a source of reflection, not from one but from several viewpoints. As far as music is concerned, the texts may serve as a potential tool for any composer looking to explore the many links between compositional thought and use of the computer. Moreover, in the hands of a ”working musicologist” the computer tools described in the book may become the starting point for new directions in systematic musicology, i.e. for purposes of proposing and studying formal models that contain clues to the creative processes leading up to a work of music. Last but not least, this research could also be useful to the community of music lovers interested in gaining a better understanding of certain aspects of current musical exploration. From the viewpoint of computer science, this book can be viewed as a highly practical research tool. Using the developments presented here, the computer scientist could extrapolate certain ideas to other activities and fields such as AI or Human-Computer Interaction, in which programming languages are used. It is our hope that this type of study might make it possible to better grasp certain concepts in computer science, and thus be able to assess their expressive potential. The present book is a first step towards an approach to current study of computer aided composition. It will be followed by other volumes, always with a view to showing a living and vibrant domain that remains as yet largely unexplored. We cannot individually thank all the people who took part in preparing this project for publication, but we hope that each and everyone will consider this as an expression of our profoundest gratitude.
Carlos Agon
9
Writing a Homage to Marin Mersenne: Tombeau de Marin Mersenne for Theorbo and Synthesiser (General Midi) - Michel Amoric Abstract. This piece is a homage to Marin Mersenne fascination with the problems of consonance, acoustics or organology, that are of particular interest to us today. OM was crucial in writing this Tombeau de Mersenne. In particular, OM was used to calculate, from Mersenne numbers, the spectral analysis of instrumental samples, the defragmentation of old scores or the implementation of rules presented in Harmonie Universelle. Once the OM score realised, I separated the lute part from that of the synthesiser. ***
1
Introduction
Medieval D´ eplorations, Dump, and Motets, Renaissance Lachrimæ, Funeral Tears, and Laments, or the Baroque Tombeaux 1 . . . , were all forms that composers adopted to commemorate both their peers and their patrons.
Figure 1. Marin Mersenne, Oiz´ e 1588 – Paris 1648 (print room, BNF)
1
It is important to notice during this period that the tombeaux, written for the lute, theorbo, harpsichord or viol, represented the quintessence of music of the time, particularly in 17th century France.
11
Michel Amoric
If this tradition was somewhat neglected during the 19 th Century, it was once again embraced by composers in the 20 th century2 . This Tombeau of Marin Mersenne , is an elegiac homage to one of the precursors to the relationship between science and music.
2
INVENTIO ... Using OpenMusic
The material for this piece was specifically chosen for its correlation to Marin Mersenne’s works on the question of music:
• Mersenne numbers, applied to certain musical parameters : a homage to Mersenne the mathematician. • Samples of instrumental sounds : a homage to Mersenne the organologist. • Fragments of pieces from the 17 th century, and rules on 17th century composition: a homage to Mersenne the musicographer. • Constraints in writing presented in Harmonie Universelle : a homage to Mersenne the theoretician.
2.1
Mersenne numbers, (M = xn − 1)
Number systems have often been used by composers 3 to code certain parameters of their work in the hope that by resorting to mathematical abstraction they would break with the mould of their time. (Assayag, 2000) As mysticism played a central role in developing the relationship between figures and art, it seemed to me particularly appropriate to write a Tombeau de Mersenne . Furthermore, I applied Mersenne numbers to the domains of scale heights, height intervals and duration. Let us remember that the properties of Mersenne numbers are prime when the exposit n is also prime (M = xn − 1). (The reverse being untrue). Writing in base 2, is thus fairly simple. (There are only 1, using a n) Example : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221. . . )4 . 2
This can be seen as of 1917, with Maurice Ravel as well as G. Migot, M. Dupr´ e, M. Delage, A. Jolivet, M. Kagel, E. Satie, F. Schmitt, P. Dukas, B. Bartok, M. de Falla, M. Ohana, O. Messiaen, G. Piern´ e, J. Rodrigo, Ropartz, F. Schmitt, G. Amy, A. Boucourechliev, M. Constant, B. Jolas, A. Louvier, O. Messiaen, I. Xenakis, and let us not forget : I. Stravinsky (In memoriam Dylan Thomas 1954) or P. Boulez (with his Rituel in memoriam Bruno Maderna , 1974, or Explosante fixe 1973 for the death of Igor Stravinsky). 3 Various means were employed to objectify sacred numbers (1, 3, 7 . . . ) : geometric constructions (symmetry, golden numbers. . . ), poetic or rhetorical models. . . this numerical identification was particularly useful in facilitating either the memorisation or recognition of works in the fashion of ”Oratio Numerosa”. 4 It is easy to show that if the number n = 2 p − 1 is prime, then p must also be prime. In 1644 Mersenne advanced that n is prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 et 257 but not prime for the 44 other prime numbers inferior to 257. It was later proved that Mersenne was wrong, concerning 5 of the prime numbers inferior or equal to 257 (two were accepted that do not lead to a prime number (67 et 257) and 3 were excluded that do : 61, 89 et 107). Let us note that 49 000 participants connected onto the web in a world-wide competition to find new and even bigger Mersenne numbers.
12
Writing a Homage to Marin Mersenne...
Figure 2. Implementation using OM of Mersenne’s formula applied to calculating a chromatic
range mode
With Mersenne numbers, I was able to establish series of harmony, frequency and duration. Produced by using OM’s Z n library, Mersenne numbers in modulo 12 provide a mode of six intervals : 2, 1, 1, 2, 2, 4, that I treated exactly as they appear, or grouped according to authentus and plagis modes.
2.2
Instrumetal sound samples
Analysed using the sonogram Audiosculpt , the data of the spectrum of lute sounds were exported to OM by using the Repmus library. We were able to thus obtain patterns of 6 to 30 notes representing the acoustic behaviour of instrumental sounds. The first part to the piece largely uses these patterns, in a superimposed, contracted or dilated fashion. 13
Michel Amoric
Figure 3. A circular representation of interval relations in a dodecaphonic range according to
M. Mersenne, in Harmonie Universelle, vol. II, livre second, des dissonances , p. 136
Figure 4. Usage of the Z n library to construct harmonies of which the height intervals were
chosen using Mersenne numbers
2.3
Selection of fragments and the total of height from a series of 17th century pieces
Several tombeaux for a lute solo, by contemporaries of Marin Mersenne, were captured in FINALE , then imported into OM. These “quotation fragments” were directly reproduced or else underwent a rhythmical and melodic hybridisation (by adopting the rhythm of one section and applying it to the heights of another). In addition, the total heights and their statistical distribution taken 14
Writing a Homage to Marin Mersenne...
from the repertoire pieces were used as a “reservoir” for height in the second and third parts.
Figure 5. Representation of the total heights of four
«
tombeaux
»
for the 17th century lute,
providing a statistical estimation
2.4
Various writing constraints, proposed by Mersenne in his Harmonie Universelle
As all treatises of this period, Mersenne outlines in his Harmonie Universelle, (Mersenne, 1636) a succession of constraints such as:
• not repeating a same interval more than three times, • the succession of two fifths or parallel octaves 5 , • not using the melodic triton, • favouring contrary movements, • alternating consonance-dissonance 6 , • privileging proximities7 ... The Situation library enabled us to incorporate these constraints and apply them to numerous passages in the second part of the piece, linked to Mersenne numbers.
3
DISPOSITIO . . . & OM models
The score of the piece is composed of 21 elements, divided into three parts. This division echoes rhetorical literary or musical figures used in the 16 th century. 5
“One must not place two or several types of consonance in succession, particularly when they are perfect, let the parts progress with similar movements, or changes of harmony. ” 6 “One must place an imperfect consonance during or after a perfect one where possible ; or if one follows a set of two perfect consonance, they must different in type ”. 7 “One must pass wherever possible to the consonance of the nearest degree and consequently one must pass from a minor third to a unison, and a major sixth to an octave; this can be heard in passages made up of contrary movements ”.
15
Michel Amoric
Figure 6. A patch that demonstrates Mersenne’s various writing constraints, applied to a
Mersenne numbers series
The first part of the piece is composed of nine sections, based on spectral analysis as described above. These sections were then transposed, contracted, dilated isolated or superimposed. The second part includes pseudo-canons constructed using Mersenne numbers. A section of periodic chords were devised from general harmonic fields of tombeaux . The third part is characterised by an ostinato of periodic chords produced from a series of Mersenne numbers and then controlled by algorithms of interpolation. These events, based on fragments of 17th century texts, ornament the entire piece. Once created, I divided the score into two, with one part devoted to Midi sounds and the other to instrumental sounds (see figure 7).
4
ELOCUTIO . . . Using the OM model
The combination of the sound of the lute, both complex and versatile (which represents the 18th century tradition and common taste, as can be imagined), with that of syn16
Writing a Homage to Marin Mersenne...
Figure 7. Maquette of the piece
thesised sounds “general midi”8 (symbolising technological expertise and today’s more trivial taste) may be considered furthermore as a rhetorical subject. In accordance with Charles Koechlin 9 (Koechlin,1954), I think that it is important to write for the lute as its repertoire is still somewhat limited. This can be explained by the lack of knowledge regarding this instrument or the importance of its tradition; it is high time that its repertoire grew in the same way as the harpsichord, another neglected 19th century instrument. The pre-recorded part (eight tones were selected, on eight channels) was directly taken from the OM model. For each channel, the chorus, panoramic and reverberation were determined. The instrumental score, written using FINALE 2003, includes a sketch of the pre-recorded part in solfegic notation (see figure 8).
5
Conclusions
This piece is a homage to“Minime Sarthois”’ fascination with the problems of consonance, acoustics or organology, that are of particular interest to us today. OM was crucial in writing this Tombeau de Mersenne . In particular, OM was used to calculate, from Mersenne numbers, the spectral analysis of instrumental samples, the defragmentation of old scores or the implementation of rules presented in Harmonie Universelle . Once the OM score realised, I separated the lute part from that of the synthesiser. If Mersenne
8
Tones : 10,15, 113, 11, 13, 5, 61, 62. ”One constructs modern lutes on old models; and I would wish, as I so greatly wish for the harpsichord, that this instrument could have a modern and original repertoire”. Instrumentation treatise. 9
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Michel Amoric
Figure 8. First page of the score using Finale
thought that aesthetic questions varied with time 10 , he knew that the question of science and music remains. Therefore this Tombeau de Mersenne treats the subject beyond the context of time, as described by Mersenne in the 17 th century, with the aesthetics and technologies of today.
10
”Since the long exercise of rendering sweet and easy what appeared before to be unpolished and disturbing, I do not doubt that the dissonant intervals, of which I have spoken in this proposition, to be known from 7 to 6, & from 8 to 7, which divide the fourth, to become agreeable, if one is accustomed to hearing and enduring them, & that one uses them as one must in recitals and concerts, in order to stir passion, and for various effects, of which ordinary music is deprived.” M. Mersenne, Harmonie universelle , vol. I Ch. Cons., p. 89.
18
Bibliography [1] Assayag G. : De la calculabilit´e `a l’impl´ementation musicale . S´eminaire EntretempsIRCAM, Math´ematiques - Musique-Philosophie, 7 October 2000. [2] Bosseur J-Y. and Bosseur D. : R´evolutions musicales, 4th edition. Minerve, Paris, 1993, 268 p. [3] Boulez P.: La vestale et le voleur de feu. in InHarmoniques, no 4, cr´eation », September 1988, pp. 8-11.
«
m´emoire et
[4] Kœchlin C. : Trait´e d’Orchestration. Eschig, Tome I, p. 205, 1954. [5] Malherbe C. :
L’enjeu spectral » Entre-temps, n 8, Paris, 1991, pp. 7-26. ◦
«
[6] Mersenne M. : Harmonie universelle. Paris, fac. sim. From the 1636 edition by F. Lesure, Ed. CNRS, 3 tomes, Paris, 1963.
Michel Amoric Michel Amoric holds a PhD in musicology, and lectures at Paris IV University, as well as a PhD in Sciences, lecturing at Paris VII University. He began by devoting himself to his career as a guitar and lute performer, both as soloist and as a member of the 2E, 2M, Intercontemporain, and ItinEraire ensembles, as well as the Radio France Philharmonic and National Orchestra, and the Orchestra of Paris. He participated in the world premieres of more than 100 works, and the rediscovery of hundreds of works from the 16th, 17th and 18th century repertoires. Michel Amoric is one of the very few lute players to devote himself to the rebirth of music for the lute and the theorbo.
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Electronics in Kaija Saariaho’s opera, L’Amour de loin - Marc Battier and Gilbert Nouno Abstract. This article describes, using OpenMusic, the different steps that are necessary when creating resonant filters based on a combination of instrumental models and chords that come from a specific piece. These filters are the foundation of the electronic part of the opera. ***
1
L’Amour de loin in Kaija Saariaho’s work
Before composing her first opera L’Amour de loin , Kaija Saariaho wrote works that prepared her to experiment with new approaches. Being always interested in discoveries, the Finnish composer, after studying at the Sibelius Academy in Helsinki, attended the Darmstadt courses, then studied with Brian Ferneyhough in Friburg. In 1982, she went through a workshop at the IRCAM and was initiated in the most advanced computer techniques at that time. She rapidly put these techniques into practice for the works she wrote in Paris, where she remained in touch with this institute. Her works with computers seem to be the natural continuation of the first works she started back in 1980 at the experimental studio of the Finnish radio in Helsinki. The resulting work, Study for Life , is also a first step towards theatralizing a musical work, since it involves lighting and gestures of the singer and dancer. One should also notice the composer’s affection for voice and the instruments she most often calls upon: flute (Noanoa , 1992) and cello (Petals , 1988; Pr`es , 1992; Amers , 1992). This preference , along with work on voice and song, is present in her work right from the early opuses in her catalogue. During her stay in Paris, the composer started developing a refined and complex style of work. The first work that shows how her conception of music is rooted in the potential of computers is Vers le Blanc (1982), composed at the IRCAM. Assisted by the voice synthesis program Chant (conceived by Xavier Rodet at the end of the 1970’s), Kaija Saariaho built her composition as being the transformation of a chord into another. Two of her major and ongoing concerns appear here. The first one is the gradual transformation of one type of material into another, most often by interpolating a program’s parameters. The second is the use of sound analysis methods in order to derive harmonic fields, achieving a transition from timbre to harmony 1 . 1
About the issue of passing from timbre to harmony see: K. Saariaho, ”Timbre et harmonie”, in Le Timbre, m´ etaphore pour la composition , directed by J.-B. Barri` ere, Paris, Ircam and Christian Bourgois, 1991, p. 412-453.
21
Marc Battier and Gilbert Nouno
The composer had approached melodic writing in Chateau de l’Ame , a work composed for the Salzburg Festival. Opera definitely enhances the width of melodic curves and adds to it various modes of declamation, such as scansion. However, Kaija Saariaho remains faithful to her post-spectral legacy: it can be clearly noticed in many instrumental parts and appears in the hybrid writing that oscillates between melody and the search for links between sound sources and harmony. The opera is composed on a libretto 2 written by Amin Maalouf, writer and winner of the 1993 Goncourt prize with his novel Le rocher de Tanios . There are three characters on stage: Jaufr´ e Rudel, troubadour and prince of Blaye (baryton), Cl´ emence, Countess of Tripoli (soprano) and The Pilgrim (mezzo-soprano). The historical figure of Jaufr´e Rudel, the troubadour, lives in the 12 th century. The songs he composed for his amor de lonh have been preserved. Rudel wrote several songs about the love at distance he had for the Countess of Tripoli. Kaija Saariaho used one of these songs, Lanqan li jorn son long en mai , in her work for soprano and electronics, Lonh (1996), written as if it was a prologue to the opera to come, then used it again in the opera itself. This poem is central to the troubadour’s work, and therefore in the vida , the biographic account that was written about him in the 13 th century. This anonymous vida established the legend of the poet in love with a distant lady, his journey and his death in a country far from home. Finally, a choir handles several parts: the troubadour’s companions (acts I, IV and V), and the Tripolitans’ Choir (acts III and V). The libretto is written in modern French, except the lyrical parts where Cl´emence sings 3 excerpts of Jaufr´e’s poem Lanqan li jorn son long en mai in old French : ”Ja mais d’amor no-m gauzirai” (chant V), end of act II, ”Ben tenc lo Seignor per verai” (chant II) and ”Ver ditz qui m’appela lechai” (chant VII), act I II scene 2. The voice of Dawn Upshaw, who also created the opera at Salzburg, is heard in the electronic part.
2
The electronic tools
The electronic sounds were made by Kaija Saariaho and Gilbert Nouno in the studios of the IRCAM with two types of tool: OM, a language of symbolic manipulation (like scores), and MAX/MSP, a program based on free binding of signal processing and realtime sound synthesis. Creating electronic sounds is a process that goes through several steps during which the electronic tools are articulated. These steps are most often in the following order:
• sampling voices and natural sound sources (water, wind, birds), • analysis of several instrumental samples by resonance models, • creating resonance filters based on harmonic structures (with OM), • filtering voices and natural sound sources with the above-mentionned filters (interpolating filters in the MAX/MSP environment), • spacializing the various sound layers. 2
The libretto is available online at Shrimer’s site http://www.schirmer.com/amour/indexf.html.
22
Electronics in Kaija Saariaho’s opera, L’Amour de loin
With OM, the electronic part is first written in a form close to a score and in relation to the orchestral and vocal score, in an abstract space of sounds whose sonorities are only imagined at this stage. MAX/MSP is then used to make the sound synthesis from the data defined in OM.
3
The sound materials
The original sound material includes samples of voices and instruments. The voices are mainly speaking voices, declaiming text from the libretto.
3.1
Resonance models
Resonance models allow the analysis of an acoustic instrument’s timbre and its translation into parameters. Resonance is used to collect these parameters, its classical definition being the response of an instrument’s body to an excitation from a natural or an instrumental sound. The analysis consists in making successive temporal estimations of a signal’s spectral envelope. A program refines this analysis, by keeping only the most significant regions of the spectrum’s components. These are the resonances , characterized by three parameters: frequency, amplitude and bandwidth. One of the goals of resonance models is to constitute a platform between natural and synthetic sounds. The distinction between excitation and resonance creates a rich and fruitful experimental space for transforming analysed sounds. One of the ways of obtaining sounds by the cross-synthesis method is therefore to replace the usual excitation (impulse, white noise) by a sound sample: if a voice is used, the crossing will be between this voice and the resonance given by the instrument’s model. This process of filtering a sound source by a filter to which the parameters of a resonance model are attributed is called source/filter synthesis . The analysis by resonance models was made with the ResAN program, a component of the Diphone software developed by the Analysis/Synthesis team at the IRCAM. The following instruments were used to synthesise most of the opera’s sounds: bow-cymbal, crash-cymbal, bell-tree, arco double-bass, pizz double-bass, glockenspiel, tam gong, harp, marktree, piano, piano clusters, timpani of various sizes and tubular bells. We will see further how these models were modified according to the score in order to act as extensions of the orchestra.
3.2
Chords associated to characters
The electronic sounds are based on harmonic structures that are specific to each character. The sounds diffused during Jaufr´ e’s presence are built on chords that characterize him. The same goes for Cl´emence and the Pilgrim when he joins Jaufr´ e or Cl´ emence. The figures below show the chords used to elaborate the electronic sounds for the three characters of the opera (in OM’s usual notation system two staves, sol and fa keys, have been added, see figures 1 to 3). 23
Marc Battier and Gilbert Nouno
Figure 1. Jaufr´ e: J-chord-a, J-chord-b, J-chord-c, J-chord-d, J-chord-e
Figure 2. Le P` elerin: P-chord-1j, P-chord-2j, P-chord-3j, P-chord-1c, P-chord-2c, P-chord-3c
Figure 3. Cl´ emence: C-chord-a, C-chord-b, C-chord-c, C-chord-d, C-chord-e, C-chord-f
3.3
Creating resonant filters by using chords and instrumental models
The filters used for sound synthesis, created with OM, are designed to create a cross between the desired harmonic structure (one of the chords shown above) and an instrumental timbre resulting from the analysis by resonance model. The first step consists in analysing an instrumental sample with the Resan program. The example (figure 4) shows a Bosendorfer piano sample, note fa0. The analysis provides for each resonance its fre24
Electronics in Kaija Saariaho’s opera, L’Amour de loin
quency, amplitude and bandwidth. It is worthy of note that the weaker the bandwidth, the longer the resonance. The OM patch illustrates the resonance model’s extraction.
Figure 4. Analysis of a Bosendorfer piano sample, note fa 0
In this example, Jaufr´e’s chord J-chord-a is used. After the spectral interpolation has been calculated, the amplitude and bandwidth corresponding to the instrumental model are associated to each frequency of the chord’s notes. It should be mentioned that the filter can be enriched with partials (of n order, with n an integer) added to every note of the chord. Depending on the degree to which it is enriched, there is an oscillation between a filter containing only the chord’s frequencies and a filter that draws near the spectral envelopes of the original instrumental sample. The OM patch, figure 5, illustrates how a filter is generated. The action of the synthesis filter can be described in several ways: filtering a chord with an instrumental resonant filter, cribling or grid-screening of a resonant filter by selecting some frequencies, or applying the spectral envelope of the analysed instrument to a chord. 25
Marc Battier and Gilbert Nouno
Figure 5. Patch of filter generation
3.4
Filtering sound samples and interpolating filters
For each chord associated with the characters, many filters were created by crossing them with instruments. About three hundred filters were generated for the entire work. Sound synthesis was then made with the MAX/MSP program (figure 6). Samples of whispering voices, sounds of birds, wind or elements of nature were used as sources and filtered by a group of three filters that were mixed in realtime by the composer. By moving within a triangle of which the corners represent the three filters, one can acheive a mix in which each filter is balanced by the distance separating it from the point where one stands. By looking at the number of chords and analysed instrumental samples by using the three filters, it is easy to see how numerous are the possible combinations.
4
Mixing and spatializing models
In this opera, space is an important element for sound synthesis. The sounds created previously were mixed in realtime with the spatializer developped at the IRCAM. The specific version of tridimensional spatialization that was used allows virtual manipulation via track-balls, to place sounds in the tridimensional space defined by the network of loudspeakers. The network initially included eighteen loud-speakers to diffuse sounds. They were brought down to eight to make technical settings easier. The diffusion device is a 26
Electronics in Kaija Saariaho’s opera, L’Amour de loin
Figure 6. The spatialization patch in MAX/msp including the three track-balls and spatilazers
Figure 7. Diagram of movements in the acoustic space
27
Marc Battier and Gilbert Nouno
parallellepiped in which the audience is immersed. The diagram drawn by the composer (figure 7) shows the properties assigned to the sixteen sound files of the first act, including movements in the acoustic space. Listeners are immersed in a malleable acoustic space in which the sources filtered by the resonance models move gently. Surrounded by loud-speakers, the audience is, in a way, ”inside” the electronic sounds (which themselves come from natural sound sources) and at the same time ”outside” as listeners. This perceptual ambivalence in Kaija Saariaho’s writing is like the characters’ emotions, their minds turned outwards to the ultra-mar , but inwards as well, peering deep into their most intimate feelings.
28
Marc Battier Electroacoustic music composer. Musicology professor at the university Sorbonne-Paris IV. Head of the MINT research group. Co-founder of Electroacoustic Music Studies Network.
www.omf.paris4.sorbonne.fr/MINT
Gilbert Nouno Born in 1970, he studied guitar and double bass while pursuing an engineering degree. He then became engaged in the performance of classical music, jazz and improvisation. From this time, too, begins his interest in the cross-relationships of music, science, and technology, which led to an association with Ircam. He is currently a musical Assistant with Ircam, collaborating with composers in realizing works involving the use of computer and other recent technologies. Among these composers are Michael Obst, Kaija Saariaho, Jose-Luis Campana, Philippe Schoeller, Michael Jarrell, Sandeep Bhagwati, Brian Ferneyhough, Jonathan Harvey and the saxophonist Steve Coleman.
29
Vuza Canons into the Museum - Georges Bloch Abstract. A remarkable feature of OpenMusic is, of course, the ability to experiment with musical structures that, otherwise, would be impossible to construct by hand. An example is “canons of maximal categories”, that is, non commonplace rhythmical figures that, when played in canon, form a continuum without any voice playing simultaneously with another. A mathematical theory of these canons has been developed by the Rumanian mathematician Dan T. Vuza and expanded by Moreno Andreatta at Ircam. This is a intuitively evident structure that has interested numerous composers, among them Messiaen. But the construction of such a canon was beyond the means of composers working without computers, and research on the characteristics of such objects requires a musical representation tool such as OpenMusic. Another possibility provided by OM stems from the fact it is an extension of Lisp. This allows the use of specific research (in this case, the research on constraint programming carried out by Charlotte Truchet) to be applied to musical structures. ***
1
Introduction
1.1
The Beyeler Project
In July 2001, a piece of mine was performed, in the framework of the “composers of the week”series of the Europ¨aischer Musikmonat. Entitled Fondation Beyeler: une empreinte sonore, this project basically consisted of a musical visit of the collections of the Fondation Beyeler. The music for this project made extensive use of the so-called “Vuza canons”. Fondation Beyeler is a museum designed by architect Renzo Piano to house the private collection of the art dealer Ernst Beyeler. It is located in Riehen, a small town east of Basel (Switzerland). Containing mainly pictures and sculptures from the 20th century, it is one of the most impressive private collections in the world. There are also special exhibitions, for the most part these come from well-known relatively provocative periods of modern art. The performance took place at the same time as a special exhibition entitled Ornament and Abstraction . Organized by Markus Bruederlin, the Fondation Beyeler curator, its main idea was that ornament was the “stowaway” of abstract art 1 . This special exhibition was divided into ten sections. In a Prologue, 18th Century Moroccan windows were presented side by side with Rothko and Taafe paintings. Entitled “In the Beginning was Ornament”, the first chapter displayed the long history of the line (especially in the form of Arab Calligraphy) before it was used by abstract artists such 1
See the catalog for the exhibition: Ornament and Abstraction , Dumont / Fondation Beyeler, 2001, which has been published in German and in English.
31
Georges Bloch
as Paul Klee. The next two chapters show how, in Munich and Vienna at the turn of the 20th Century, Art Nouveau and Secession artists had already achieved a transition from folk ornament or architectural shapes to Abstraction. The fifth chapter shows how Abstraction eventually spread to the mural form, as in Matisse’s “Papiers coll´es” or, more recently, through fractal murals like those by Sol LeWitt. The next sections were devoted to the relationship between ornament and signs. The two last sections showed the ornamentalisation of modernism and the birth of digital mass-ornament (including video installations by Peter Kogler and Shirin Neshat). It is important to emphasize that Ornament and Abstraction made wide use of the Beyeler collection paintings, to which were added paintings b orrowed from other museums as well as creations (from various artists such as Kara Walker, Paul Buren or Sol LeWitt) created especially for this exhibition.
1.2
The musical setup
The musical project consisted of five musical visits, each one being led by a musician (violin, clarinet, tenor saxophone, double bass and percussion). There was no question of “setting the pictures to music”, since there is absolutely no need to add music to a Picasso or Sam Francis picture. In this respect, it was really a visit in the teaching sense of the term, since the music primarily demonstrated existing relationships between pictures and space or between the works of art themselves. One visit was special in that, contrary to the other musicians, the clarinettist was accompanied by a (speaking) guide. Both followed the “Tour Fixe”, an extensive visit of the foundation (including Ornament and Abstraction ). This tour, which looked like any regular tour, was the “easy-access” visit and was followed by a large number of the German-speaking audience (at least at the beginning of the performance, since many people moved from one visit to another). Two tours (saxophone and double bass) were devoted to the special exhibition Ornament and Abstraction . The last two visits were thematic. One was about “Picasso and the human Face” (violin). Another was entitled “Imaginary Landscapes” (percussion). The first explored the fabulous Picasso collection belonging to Ernst Beyeler, as well as a large number of African and Melanesian masks, and representations of the human figure. The second one focused mainly on abstract landscape representations (Claude Monet, Frank Stella, Sam Francis, Francis Bacon. . . ), actually passing through the Stella part of Ornament and Abstraction . They were several reason for this idea of simultaneous visits. First, a museum, even a relatively small one, is a place in which it is impossible to see everything. Therefore, the presence of music in another room demonstrated the impossibility of hearing the whole “concert” and, consequently, the impossibility of grasping all the pictures that were being seen, had been or were to be seen. They were pictures that would never be seen. Also, when two guided tours meet in a room, the listener’s attention was immediately drawn — in a somewhat rebellious fashion —to the guide of the other group, especially if that person was talking about a work already explained by the listener’s own guide. Sometimes guides collaborated. A number of similar techniques were explored. The musical work was performed by four large ensembles: a trio, two duets and a finale, with all five players present (there were other smaller ensembles, with lesser structural impact). The entire event lasted approximately 70 minutes. 32
Vuza Canons into the Museum
1.3
Some reasons for using Vuza canons
Outside of my personal interest, the Vuza canons were relevant to one important idea developed in Ornament and Abstraction : the disappearance of the ground, or at least an ambiguity existing between ground and figure. In Matisse’s Acanthes or Oc´eanie , for example, the figures (leaves) become part of the huge wallpaper that is the picture. This applied also to the huge Sol LeWitt mural that marked the beginning (and the end) of the visits. Let us remember that these canons are non-trivial solutions to a basic rhythmical problem: having identical rhythmical voices which, when they are all present, fill up a rhythmical grid without overlapping. We say non-trivial, since there are obvious but trivial solutions: when the grid step is a sixteenth note, for example, a single voice playing each quarter note could be followed by a similar one a sixteenth later, a second one an eighth note later, and finally a third one three sixteenths later. This would be a valid solution since the grid is full, with no voice overlaps. An interesting aspect of these canons is that they provide a relevant metaphor to the premises of Ornament and Abstraction . The end result (when all voices are present) is a rhythmical drone, like an ostinato: the dialectic between form and content is immediately audible, since the end-result of such a contrapuntal display is a single continuous line. The canons were used in many ways: for instance, the clarinet player gave a signal every five minutes. This signal was itself the development of a canon. As with a tiling canon, these calls ended up sounding like a continuum, but each call was also a more complete version of the preceding one. The canon characteristic of these pieces became less important than their tiling aspect. The ensembles, as we mentioned, structured the performance. Three of those (corresponding roughly to the first third, the second third and the end of the visit) are Vuza canons, entitled Canon 1, Canon 2 and Canon Final . Canon 1 is scored for clarinet, saxophone and double bass. Canon 2 for violin and berimbao (a Brazilian percussion instrument which is a kind of musical bow). The last Canon starts with a repeat of Canon 1, a different version of Canon 2 for violin, double bass and vibraphone and ends after a bridge with a third canon with everybody playing. Some other versions of Canon 2 appear at various moments. One of them, for solo percussion, is of particular interest: it is scored for solo percussion and cetases to be perceived as a canon, although when Canon 2 performed later on, it becomes obvious that it is the same music. Each instance of the Canon 2 corresponded to a frame of the Matisse pictures entitled Oc´eanie.
1.4
Three practical problems
Although we will come back to the aesthetic reasons for using the canons in this project, they are not the subject of this paper. When using the Vuza canons, several questions arise, linked to aesthetic choices, but which end up being very practical problems indeed. -The number of voices. The simplest solution given for Vuza canons is a six-voice canon on a period of 72 units. What are the practical solutions when there are five players (or less) playing a six (or more) voice counterpoint with a relatively perceptible result? More especially, is the canon character (the rhythmical unity of the voices) lost? 33
Georges Bloch
-The relationship between canons. Is it possible to generate a large scale form from several canons? More precisely, how to make them relate, especially if they have neither the same period nor the same number of voices? -Continuum or texture? When the voices are played by different instruments, with diverse attack times and resonance characteristics, even a very precise execution will fail to create the impression of a continuous line, except at very slow tempi. It is perhaps more useful to think in terms of a texture of equal weight and equal distribution. Working out the harmonic evolution in such dense textures cqan be difficult, especially with notes changing at every division of the beat. That is why a global texture evaluation can be helpful.
2
Basic strategies for choosing canonic values
The choice for the Vuza values was obviously aesthetic. However, the selection process is interesting, since it is based on an examination of the existing values.
2.1
Examining the rhythmical characteristics of the values
Let’s take the period N = 144 as an example. This is a twelve voice canon, each composed of twelve note-events in one period. Below are the values given by the Vuza reconstruction algorithm. R is the time interval between the individual note-event of one voice, and S the time interval between the entrances of the voices. They are interchangeable.
R (1 5 3 21 19 8 15 6 19 5 3 39) (1 5 24 11 8 23 6 11 8 5 35 7) (1 6 1 40 1 7 17 6 17 8 17 23) (1 6 33 8 1 24 6 9 8 25 15 8) (1 7 5 12 23 8 17 12 11 1 7 40) (1 7 5 35 8 5 12 12 11 8 29 11) (1 7 17 23 8 11 6 23 1 7 35 5) (1 8 33 7 8 9 6 25 8 9 24 6) (1 12 12 15 8 25 12 3 8 1 39 8) (1 12 27 8 13 12 12 3 8 37 3 8) (1 24 15 8 19 6 15 8 1 39 3 5) (3 3 5 37 3 8 13 6 21 8 13 24) (3 3 37 5 3 21 6 13 8 21 19 5) (3 6 24 7 8 27 6 7 8 9 31 8) (3 8 13 27 8 7 6 24 3 8 31 6) (3 9 12 19 8 21 12 7 5 3 40 5) (3 9 31 8 9 12 12 7 8 33 7 5) (5 6 29 8 5 24 6 5 8 29 11 8)
S (2 2 14 2 2 14 2 16 58 16 2 14) (2 14 2 16 4 16 16 22 16 16 4 16) (2 16 2 16 2 16 10 18 18 18 10 16) (2 16 10 10 16 10 18 10 16 10 10 16) (4 10 4 14 4 14 18 26 18 14 4 14) (4 10 18 4 22 10 22 4 18 10 4 18)
Again these values can be freely permutated. Clearly, in this case, most R values display multiples of 3 (or even 9), and S values favor multiples of 2 (or even 4). This 34
Vuza Canons into the Museum
would imply a ternary rhythm for the subject of the canon, and a binary one for the voice entrance points (or the opposite, if we take R as entrance points and S as subjects). This result is not at all surprising, since 144 = 2 4 × 32 . This is not a general result: in the case of N = 108 (2 2 × 33 ), we can no longer assert that values for R are “ternary”, and that S values are rather ternary than binary.
2.2
The value of finding redundant rhythms
One of the interesting features of the canons is the way the music, starting out as a recognizable rhythmical shape (at first emphasized by the canon entries), gets transformed into a continuum. Thus, finding redundant rhythms inside the individual voices can be of value. By implementing a short OpenMusic program that analyses R time-point values, we can find those that are most divisible by 9. Of course, we take the time-points into account, because they give rhythmical values relative to a given beat: this means that (1 5 3 21 19 8 15 6 19 5 3 39), for example, will be transformed, into (0 1 6 9 30 49 57 72 78 97 102 105 [144]). Taking the permutations into account is important: indeed, if we consider a list of values such as (1 8 9 9 9 9 9 9. . . ), it would provide points perfectly on the beat of a time-division by 9; but this is not true of (8 9 9 9 9 9 9. . . 1), where all points other than the first will fall off-beat. In the case of N = 144, the program computes a sum of the reminders by 9 of the time-points of all R elements (as well as all their permutations). For the Canon 1 (played in front of Matisse’s Acanthes the solution (3 6 24 7 8 27 6 7 8 9 31 8) the third best solution was chosen. There are several (mostly subjective) musical explanations for this choice: in order to have a clear rhythm, we wanted to avoid a “scotch snap” (short value followed by a long one, like 1 8) at the onset, and this rhythm was present in the other solutions. The third note, long, accented and clearly on the first beat makes for a clear beginning. In addition, all values with the accent on every 12th unit were eliminated so as to avoid a binary feel. One has to keep in mind that all this rhythm clarity rapidly disappears as each voice enters. That is the reason for choosing an almost “clich´ e” pattern. We actually selected a ternary rhythm for the voice patterns of all canons. The reason for this was that we desired to create a link between all the canons. This is the topic of our “second problem”, namely the construction of a relationship between canons of different periods.
2.3
Ordering the voices
In order to make the redundancy more obvious, and therefore to delay the appearance of the continuum-like texture, we had the voices which start “on the beat” appear first. If we take 9 as the measure division, a good result for nine yields also a good one for 3, therefore implying a ternary division of the beat (for example, a measure in 9/16, where the sixteenth note is the rhythmical unit of the canon). So the voices starting on 0, 3, 6 will also reinforce the sensation of triple time. 35
Georges Bloch
3
Reducing the number of voices
The Vuza theory yields in many-voices structures. The smallest one (not used in the Une Empreinte sonore ) has a period of 72 rhythmical units and is divided into six voices. Six is the smallest possible number of voices. This can become a problem when one is dealing with a small number of instruments or, more simply, with a more limited number of streams in the polyphony. The problem becomes particularly obvious when we reflect that the end result of the process is a continuum, implying a monophonic texture (whether this is unfounded or not).
3.1
The basic solution: compound voices
In some respects, the problem of the number of voices is a false one: there are countless works in the history of western music written for a monophonic instrument (for example Bach’s flute pieces, etc.). The classical solution is to compound the voices, that is, to merge two lines into one by playing the notes when they are supposed to appear and stop them when another one appears, whether or not it is the same voice. This is common procedure in baroque music. Naturally, the same technique is perfectly applicable to Vuza-canons. In our project, the clarinet made a “call” every five minutes. These were Canons, with one voice being added every ten minutes.
3.2
Sub-canons
In the case of a compound solution with several instruments, another problem obscures the canon characteristics: a given value of S sets the distance between the entrances of the voices. There is very little chance that the distance between the voices of each compound will be the same. As an example, let´ıs imagine a period of 144 with S =(2 2 14 2 2 14 2 16 58 16 2 14). We can use permutation and put 58 in the end, which gives (16 2 14 2 2 14 2 2 14 2 16 58). If we try to generate four voices from these twelve, the starting points will be as follows: V 1 = (0, 0+16, 0+16+2), V 2 = (32, 32+2, 32+2+2), V 3 = (50, 50+2, 50+2+2), V 4 = (68, 68+2, 68+2+16). Only voices two and three display similar compound values (start, start+2, start+4). The other voices are different. This gives us an interesting lead in selecting the subcanon voices: if we can find a case where all values are the same, we will have similar sub-canons. 36
Vuza Canons into the Museum
Getting a smaller number of voices In our search for a smaller number of voices, we will therefore mix (compound) some voices together. The result will be called a metavoice. Using the “on the beat — offbeat” strategy For example, with a ternary triple time (that is three beats divided into three subdivisions) we can easily distinguish when the voices start. We have already emphasized how we can make the basic voice rhythm (here ternary) more obvious by mixing the voices starting on the beat. Here is an example: with a period of 144 and S = (18 10 16 10 10 16 2 16 10 10 16 10), the attack time points are (0 18 28 44 54 64 80 82 98 108 118 134). A simple modulo 9 operation shows that 0, 18, 54 and 108 start “on the beat”. 28, 64, 82 and 118 start one unit later. And that 44, 80, 98 and 134 start just before the beat. We would therefore build our metavoices with these three rhythmic groups. One starting on the beat M 1 =(0 18 54 108), one one sixteenth later M 2 =(28 64 82 118) and one one sixteenth before M 3 =(44 80 98 134). However these metavoices are not themselves similar. This is because the distance between the first and the second subvoices is 18 in the first metavoice and 36 in the second and third metavoices: they cannot yield the same global result. We cannot speak of canons between metavoices, since the compound rhythmical patterns are different. Looking for real self-similarities But the subvoices of M 1 are, as we have seen, start on 0, 18, 54 and 108. Therefore, the distances separating the respective subvoices are 18, 36 and 54. For M 2 , the subvoices start on 28, 64, 82 and 110. We find 18 between 64 and 82, 36 between 82 and 118, and. . . 54 between 118 and 28 on the next period (the period is 144, 144+28 = 172, that is 118+54). We find the same result for the third voice, if we take 80, 98, 134 and 44 (see figure 1). The basic time unit is the sixteenth note, and R = (3 6 24 7 8 27 6 7 8 9 31 8). The pitches displayed here carry no value whatsoever, they simply allow a further distinction to be made between the various voices. The first four voices (first metavoice) start on the beat. The next four voices start a sixteenth just after the beat, and the last four just before the beat. The reordering shows how the voices could be self-similar by folding some of them to the next p eriod. In other words, by delaying the entrance of voices 7 and 12 until the next period. Examining the first voices, we notice that the distance between voices is two bars (=18 units), then four bars, then six. But this is also the case for the next four lines and the last four lines. For voices 4 to 8, the distance between voices is two bars, then four, then by folding to the beginning, six. We can generate a completely similar voice if we delay these last voices by one period. We can therefore change the S to emphasize the self-similar aspect, pushing the start of metavoices 2 and 3 to their proper place. Instead of (0 18 28 44 54 64 80 82 98 108 118 134) as starting points, we get (0 18 54 64 80 82 98 108 118 134 144+28 144+44). Let us use different typographical characters to distinguish our metavoices: (0 18 54 64 80 82 98 108 118 134 144+28 144+44), which gives a transformed S , (18 36 10 16 2 10 10 16 38 16 -44). There is actually another way of constructing metavoices: we can generate four metavoices by using voices of the same rank (0 18 54 64 80 82 98 108 118 134 144+28 144+44) 37
Georges Bloch
Figure 1. The first period of a canon of period 144, with the voices reordered in order to
display rhythmical similarities
Conclusion: a slower start and the loss of the maximal category At this point we have transformed a twelve-voice canon in a three-voice canon, each voice of which is made of a four-voice canon. This is an impressive self-similar structure, a canon made of canonic voices. However, as we know from theory, it is an illusion that there are three-voice tiling canons in a 144 period. And here theory is borne out by practice. A careful examination of the metavoices shows that they actually have, as the theory would predict, limited transposition characteristics. For example, the metavoices in Canon 1 repeat three times the same rhythmical pattern (see figure 2). However, it can be taken as a virtue, because the period (48, that is a third of 144) still is relatively long, and the repetition can be taken as a characteristic of the theme. 38
Vuza Canons into the Museum
Figure 2. The same “Canon 1”, in its third period, as all voices have entered. The “maximal
category” characteristic is completed, and we note that there is a continuum every sixteenth note with no voices sounding simultaneously. We note (relatively easily in the clarinet part) that, as the theory predicts, the metavoices are actually repetitive patterns. The rhythm of the clarinet on the first five bars get repeated, starting on the second beat (E dotted eight) of the sixth bar, and again on the third beat of the eleventh bar of the excerpt (sung A). The change of beat at the end of the example prepares the transition to “Canon 2”
4
Relationship between different canons
The question of the relationship between canons is even more important, if one wishes to create Vuza canons with a form that is larger than or different from the simple repetition of the periodic pattern. We noticed a similarity between the subcanons of different periods, which led to the idea of canonic modulation . This is like any rhythmic modulation. As we know, there are two types of these: either the unit stays the same, or the whole group stays the same. We explored the latter case, by constructing canonic modulations that maintain the same duration for one period, but that has canons of different periods.
4.1
Canonic modulations
The idea of canonic modulation arose when we noticed similarities between the subcanons. We have seen that we had: 39
Georges Bloch
Canon 1 Canon 2
12 voices 6 voices
Period 144 Period 108
divided into divided intp
3 subcanons 3 subcanons
0 0
64 48
80 60
This creates a simple but remarkable numerical relationship: a- 144 = 108 × (4/3) b- 64 = 48 × (4/3) c- 80 = 60 × (4/3) to which we can add d- 0 = 0 × (4/3) We can chose to have the same span of time for the periods of both canons (that is, the canon of 144 elements goes 4/3 faster than the canon of 108) and, more remarkably, each corresponding metavoice will start at the same moment in the canon. A convenient notation is Canon 1 in 9/16 (the unit being the sixteenth note), and Canon 2 in 3/4 (the unit being the eighth triplet). 144 sixteenth notes are equivalent to 36 quarter notes, as are 108 eighth triplets. In this case, not only do the whole canons have the same duration, but the three metavoices start at the same time in the canon. M 1 starts after 64 sixteenth notes = 48 triplets = 16 quarter notes, and M 2 starts after 80 sixteenth = 60 triplets = 20 quarter notes. The same logic is used in the last part of the final canon. The period 216 (= 108 × 2) is divided into sextuplets. This gives us a canonic modulation from canon 1 to canon 2. The entrances of the voices are tiled.
4.2
Analysis of an example
The figure 3 shows the passage between “Canon 1” and “Canon 2” in the Canon Final . This page exactly follows the music shown in the preceding figure. This example is worth careful analysis, as it demonstrates most of the processes examined in this paper. Let us first examine “Canon 1”. As we said, it is a Canon of period 144 sixteenth notes, with R= (3 6 24 7 8 27 6 7 8 9 31 8) and the voices starting on (0 18 54 64 80 82 98 108 118 134 144+28 144+44). The clarinet was the first to start, and is the first to end. The saxophone was the last to start and is the last to end. The cycle lasted for 16 bars in 9/16 time, but the beat has changed to 3/4 (at the same speed for the sixteenth note). So the cycle now only lasts twelve measures. It is significant that the last note of the saxophone comes more than 144 sixteenths after the beginning of the last cycle, since the exposition of the voices lasted more than one cycle. Because the last voice of each subvoice is relatively isolated, the last notes are heard with their full values (8 9 31 8). This is clearly seen in the four final notes of the clarinet (first system) or the saxophone (second system). Twelve bars is also the length of Canon 2. The rhythmical modulation is calculated so that the period of Canon 1 is equal to the period of Canon 2. Since the Canon 2 has only 108 notes in its period, it is somewhat slower, the unit value being the triplet. The R value for canon 2 is (9 5 1 1 5 25 4 1 1 5 2 9 14 5 1 5 11), and we recognize the values and even the notes of the clarinet “appel”. The time points for the entrances of the voices are (0 48 60 81 129 141). The violin enters with the first voice, then the vibraphone, then the contrabass in pizzicato on the last beat of the seventh bar of 40
Vuza Canons into the Museum
Figure 3. The modulation between “Canon 1” and “Canon 2” in Canon Final. This page just
follows the preceding example. We are in 3/4 time, but the clarinet and the saxophone round off the “Canon 1” in 9/8 (although they are notated in 3/4 for practicality). The violin enters with the first metavoice of “Canon 2”, then the vibraphone, then the contrabass in pizz. The latter instrument goes directly from Canon1 (in sixteenths, arco) to Canon 2 (in triplets, pizzicato). The first cycle is completed four bars before the end of the example (we see the violin starting again on high C)
the excerpt. The second voice of the violin happens only 81 triplets later, i.e. at the beginning of the second system (it is mostly played in harmonics). The contrabass alternates between arco and pizzicato until its part in Canon 1 is completed. As for “Canon 1”, one cycle is insufficient for the entire the voice, and therefore we have to wait for the last bar of the example to hear a measure in which all triplets are played.
5
Texture and constraints
The last passage is very interesting Canon Final . This is a 216-period structure and, with the process of modulation, the events happened twice as fast. The duration of a whole cycle being the same, the unit was now the sixteenth note sextuplet. The quantity of notes and the fact that they (supposedly) did not occur at the same time helped to create a very dense texture. In this case, the ambiguity was not between line and contrapuntal construction, but between counterpoint and texture. 41
Georges Bloch
Even with a very precise performance, it was impossible to hear it as a continuum, since the tempo was not slow and the instruments had very different types of attack and response time (a vibraphone, a double-bass and a clarinet are clearly very different). What was perceptible, however, was the relatively equal distribution of events, enforced by the principle of maximal category canons: it was perceptible that the vibraphone, the only instrument playing two voices at a time, contained a denser passage. However, it was difficult to devise a means of controlling the harmonic structure while keeping something like a canonic melodic relationship between the voices. That is where constraint programming was useful. Charlotte Truchet developed, at Ircam, a constraint programming environment using OpenMusic. This made it possible to test several melodic solutions subject to constraints: the first constraint was that the voices should be melodically in canon, within certain limits. The second constraint was to to tend towards a harmonic reference texture. Because the program operates by random selection, it was even possible to give the melodic constraint less and less importance, while giving the harmonic one more and more. Thus the final canon converged towards a unified texture, as the original melody progressively disappeared.
6
Conclusion
Only OpenMusic allows research of this scope. We encountered two types of problems: one, the maximal category canons, presents an obvious long known musical problem. The solution, however, depends on the computer tools used for musical representation. The devices found while using them stem from the very concept of the canons: using voice mixing for example, to find sub-voices that have self-similar characteristics. Rhythmic modulation between a canon and another is another very interesting possibility. The best solutions can easily be computed automatically with OpenMusic. A more general consequence is that many canonic structures with varying periods can be grouped. The second problem is solved in a more empirical way. It turned out that constraint research could be used as a development process. We would like to express our thanks to Carlos Agon, Moreno Andreatta and Charlotte Truchet, who make all this look simple!
Strasbourg, July 2004
42
Bibliography [1] Andreatta, Moreno : M´ ethodes alg´ ebriques dans la musique et la musicologie di XXe si`ecle : aspects th´eoriques, analytiques et compositionnels . Th`ese de doctorat EHESS, Paris, 2003. [2] Truchet, Charlotte : Contraintes dans OpenMusic. Conception et d´eveloppement de programmation par contrainte adapt´ees `a la composition et l’analyse musicale. Th`ese de doctorat Universit´e Paris 7, Paris 2003. [3] Bruederlin, Markus : Ornament and Abstraction, Exhibition catalog . Dumont / Fondation Beyeler, 2001.
Georges Bloch
Georges Bloch began studying composition relatively late, at UC San Diego, after graduating in Engineering at the Ecole Centrale de Lille. He also performs as a singer. Born in Paris, he lives now in Strasbourg, where he teachs at the University. Georges Bloch´ıs music is based on three different but nevertheless perfectly compatible centers of interest: - Music and space: Palmip`edes d’agr´ ement was the first piece using the Ircam spatialiser; Palmip` edes salins takes advantage of the particular acoustics of the Salt factory conceived by Nicolas Ledoux in the 18th century; Fondation Beyeler: une empreinte sonore offers five simultaneous musical visits to the Foundation Beyeler in Riehen, Switzerland. - Interaction, mainly based on the paradox of composed improvisation (Jimmy Durante Boulevard, Palm Sax); more generally, computer assisted composition, in real time or otherwise. He is presently associated with the Omax project (computer assisted improvisation). - Collaboration with other artists – mostly sculptors or painters (Souvenirs et moments is based on pictures by Jean-Michel Alb´erola, inserted into the score). A piece such as Palmip`edes corbus´eens palm´es combines the three characteristics: a mezzo-soprano wanders into the strange acoustic space of a water tower built by Le Corbusier, and the building itself is made to resonate by an interactive sound sculpture. 43
TimeSculpt in OpenMusic - Karim Haddad Abstract. In the last decade, as regards musical composition, my work has been essentially focused on musical time. I have used mostly computer aided composition and most particularly, OpenMusic. This article deals with compositional strategies and musical duration, and skips considerations regarding pitch in order to better focus on our subject except when pitch is related to our main disscussion 1 . ***
1
How ”time passes in OpenMusic ...”
In OpenMusic time is represented (expressed) in many ways. Time could be:
• a number (milliseconds for instance), • a rhythm tree (an OpenMusic representation of musical rhythm notation [1]), • a conventional graphical symbol (a quarter note) in OpenMusic Voice editor, • an ”unconventional” graphical object (an OpenMusic temporal object). Another important issue is how musical time is conceived internally (i.e implemented as a structural entity) [2]. Most computer environments and numerical formats (MIDI for instance), represent the musical flow of time broken down into two expressions:
• the date of the event (often called onsets), • the duration of the event (called duration). We notice already that this conception diverges from our own traditional musical notation system which represents a compact, readable time event + duration2 . The only reason for this is that generally the computer representation of time is made not with symbols but with digits 3 . That, I believe, is why today’s composers should make themselves familiar with a ”listing” representation of musical events. 1
One can argue that these fields are indissociable and most particularly rhythm and duration. We will consider in this article that duration is from a different order than rhythm (think about Pierre Boulez temps strie and temps lisse in Penser la musique aujourd’hui [3] which is a well accepted view nowadays). 2 Through this conception tempo is meaningless. 3 Time is sequentially expressed and not iconically symbolized (as a whole entity like a measure containing rhythm figures, having a tempo assignement and a rhythm signature).
45
Karim Haddad
Since the MIDI standard is integrated in OpenMusic, this representation type is common to most musical objects (i.e. Chord-seq ), and since there are OpenMusic libraries that generate CSOUND instruments that use this ”time syntax”, one needs to learn this particular representation in order to deal with these objects accurately, especially when applying them to controlled synthesis.
1.1
dx->x
and x->dx
dx->x and x->dx are easy to use and are very practical when it comes to duration and
rhythm.
• dx->x computes a list of points from a list of intervals and a point, • x->dx computes a list of intervals from a list of points. Starting from a list of duration values in milliseconds and a starting point, dx->x will output a list of intervals (duration values) according to these parameters. Vice-versa, x->dx will output a sequence of time-dates starting from a list of duration values. To illustrate this mechanism, we start with a marker file created with SND. This file represents a list of time events automatically or manually generated. In figure 1, the soundfile was marked manually.
Figure 1. Markers in SND
Once the analysis file is imported into OpenMusic, we quantify it using omquantify , as shown in figure 2. Careful examination of the rhythmical result may reveal a wide range of duration values (in the present case they could be considered as a series of durations). We might also treat it as a sequence of accelerando/decelerando profiles (modal time durations). In 46
TimeSculpt in OpenMusic
Figure 2. Quantification of markers
either case, it is a potential rich rhythmical material. It can be used to notate symbolically and/or integrate a sound file into a score 4 . We can of course extend this ”symbolic”information and consider it as a compositional material for example, applying to it contrapuntal transformations such as recursion, diminition or extension, simply by multiplication, recursion, permutating etc...
1.2
Combinatorial processes of rhythmical structures
Another aspect of rhythm manipulation that I use is exactly opposite to the preceding example. Instead of extracting rhythm from a physical source (i.e such as a soundfile) I apply directly combinatorial processes of rhythmical structures using the internal definition of rhythm in OpenMusic called Rhythm Trees [1]. This is a wonderful technique for creating any imaginable rhythm, simple or complex, and since the RT standard is both syntactically and semantically coherent with musical structure, it makes rhythm manipulation and transformation efficient. It is for this reason I came to write the Omtree library, which was basically a personal collection of functions, for OpenMusic. The functions allow 1) basic rhythm manipulations 2) practical modifications and 3) some special transformations such as proportional rotations, filtering, substitution, etc...
4
It is also very practical for coordination between musicians and tape.
47
Karim Haddad
The whole stucture of ”...und wozu Dichter in d urftiger Zeit, ...” for twelve instru¨ ments and electronics is written starting from the generic measure in figure 3.
Figure 3. Generic measure of ”...und wozu Dichter in d urftiger Zeit, ...” ¨
which corresponds to the following rhythm tree: (?
(((60 4) ((21 (8 5 -3 2 1)) (5 ( -3 2 1)) (34 ( -8 5 3 -2 1))))))
Rotations are calculated on the main proportions based on the Fibonacci series (rotations of D elements – durations, and rotations on the S elements also – subdivisions). The first rotation is shown in figure 4.
Figure 4. First rotation
The corresponding rhythm tree is as follows: (?
(((60 4) ((5 ( 2 1 -3)) (34 ( 5 3 -2 1 -8)) (21 (5 -3 2 1 8 ))))))
This is generated by the patch in figure 5. The result is a six-voice polyphony. The pitches are also organized in ordered rotation and heterophonically distributed among the six voices (figure 6). The excerpt in figure 7 shows the same result but after quantification.
2 2.1
Topology of sound in the symbolic domain Form
We can consider sound analysis as an open field for investigation in the time domain, where interesting and unprecedented time form and gestures can be found and used as basic (raw) material for a musical composition. This new approach is made possible thanks to fast computers. But sound analysis being a vast field of research (in which one can find multiple kinds of analysis and visual or raw data formats), one must take care not to forget the nature of this analysis and its original purpose. Sound analysis could therefore be a rich source from which symbolic data can be retrieved and freely remodelled according to the composer’s needs. Sound analysis data can also be considered as potential correlated vectors. These, depending on the analysis type, can be streams of independent linear data, or more 48
TimeSculpt in OpenMusic
Figure 5. Rotation patch
Figure 6. Six-voice polyphony
interestingly still, data arrays. The types of data found most often are directly related to the nature of sound. On an abstract level, this can be regarded as a pseudo random flow or considered as coherent interrelated orders of data, again depending on the analysis type chosen. 49
Karim Haddad
Figure 7. ”...und wozu Dichter in d urftiger Zeit?...” for twelve instruments and electronics ¨
When using sound analysis as a basis for music material production and most particularly in the time domain, it is important to note that the following approach is not a ”spectral” one in the traditional sense 5 , but on the contrary should be considered as a spectral-time approach. Frequency domain will be translated into time domain and vice-versa following the compositional context, as will be shown later in the present article6 . This ”translation”is possible with the wide variety of analysis types (additive, modRes resonance modes, etc), not forgetting the many data formats available, whether in visual or numerical form. The way the material is used depends on the musical project. Different orders of ”translation” in the symbolic field can be applied. Form can be literally extracted from the analysis data or taken from symbolic material. The mixed sources (symbolic and analytical) are then fused together in the compositional process, and that is where the tools are very important. OpenMusic is like a black box, in which the analytical and the symbolic come together in a kind of fusion in the field of musical time.
2.2
No one to speak their names (now that they are gone)
The structure of No One To Speak Their Names (Now That They Are Gone) for two bass clarinets, string trio and electronics, is based on an aiff stereo sound file of 2.3 seconds duration.
5 6
Meaning that form and strategies are primarly based on pitch. This was the initial approach in Stockhausen’s well known article “...wie die Zeit vergeht...” [7]
50
TimeSculpt in OpenMusic
Figure 8. Segmentations
Considering the complex nature of this sound file (friction mode on TamTam), it has been segmented into 7 parts (figure 8). The segmentation is based on the dynamic profile of the sound file.
Figure 9. Array of n dimensions
We may consider a sound as an array of n dimensions (as shown in figure 9) with potential information that can be translated into time information. It seems natural to construct this array using the additive analysis model (time, frequency, amplitude and phase). This is rather a straightforward description that could be used to process the sound directly into the time domain or for eventual resynthesis. Other sound analysisdescription is available such as the spectral analysis, lpc analysis, the modRes analysis and so on. Here, the modRes analysis was chosen. All the examples described above are discrete windowing analyses, from which the time domain is absent. Most of them have time addressing, but the last one (modRes analysis) is an array of dimension 3 (Frequency, amplitude and bandwidth/Pi) computed by the patch in figure 10. 51
Karim Haddad
Figure 10. Frequency, amplitude and bandwidth data
A sound analysis/description and an array of n dimensions can be translated into the time domain from array to array, array, i.e. the analysis analysis data could be read in any plane, vertically, vertically, diagonally, etc... or any combination of arrays. This ”translation” ”translation” is of course arbitrary and is meant to be a translation in the symbolic domain, the score being another kind of array array. Although Although the operation operation may seem arbitrary arbitrary,, (which (which indeed indeed it is), in my opinion there are two pertinent points to be considered. Firstly, (as we will see later) the sound array is processed in a completely interdependent way, taking into account all the proportionate weight relations contained within it. The coherency of the sound resonance will be so to speak ”reflected” in the symbolic domain through specific analogical modes (dynamics, durations and pitch), which are not supposed supposed to be literally literally associated associated one by one (i.e. exact corresponden correspondence ce of parametric parametrical al fields is not necessary). In this piece they are permutated. The second important point is that this translational strategy establishes a strong relationship between the electronic and the acoustical components of the piece creating strong formal fusion. Moreover, if we visualize the given data in a 3 dimensional graph (see figure 9) we will see many many folds (”plis” (”plis” [5]) of different different densities. densities. These are directly related related to the polyphonic gesture representing the point-counterpoint technique used in the score. As we can see in the figure 11, there are two parallel musical processes: the electronic part (tape), which is also entirely constructed with the initial material (the Tam-Tam 52
TimeSculpt in OpenMusic
Figure 11. Two parallel musical processes
sound sound file), file), and the score score part. part. The seman semantic tic bridge bridge is shown shown as a dashed dashed arrow arrow.. It 7 is through analysis that both domains communicate with each other . In the the cas casee of resynthesis, another bridge could be established in the other direction (from symbolic to sound domain) but this is not the case in our present composition. In In No One To Speak Their Names (Now That They Are Gone), Gone) , using the modRes analysis, the bandwidth array has been chosen to order each pitch set in each fragment according to bandwidth. For each parsed pitch segment we will again establish a proportional tional relation: relation: all pitches/hi pitches/highest ghest pitch. pitch. These proportions proportions will be used as snapshots snapshots of seven sonic states in a plane of a three-dimensional array (x, y, z), each state being the sum of all energy weight weightss within one window. window. We will use them to determine determine our durations durations throughout throughout the composition. composition. The durations durations are of two two orders orders types: types:
• Macro durations that represent metric time and determine a subliminal pulse illustrated trated by dynamics. Measures Measures are calculate calculated d following following the proportions proportions computed from the last segment. • Local durations consisting of effective duration values from the four instruments. These are distributed according to proportions on either side of the measure bars, creating asymmetrical crescendo-decrescendo pairs. The main concept of the whole work dealing with pitch/bandwith/dynamic weights is that of symmetry. As we have seen in the example above, we can use it as a compositional element. Starting from one mode of resonance which was assigned to durations following our proportional translation (see figure 12) we will apply to it a new axis of symmetry where all durations will start from and then continue in asymmetric mirroring, as shown in figure 13. This was calculated by the reson-chord box patch (see figure 14) and then quantified (figure 15). 7
Analysis could be thought of as another potential aspect of a sound file, or in other terms, it is an alternative reading/representation of sound.
53
Karim Haddad
Figure 12. Resonance mode durations
Figure 13. -35 degrees symetrical axe
Figure 14. -35 degrees symetrical axe patch
54
TimeSculpt in OpenMusic
Figure 15. Quantification
Durations are not the only elements calculated from analysis. Starting from measure 59 (figure 16, pitches are extracted from analysis and distributed over all four instruments following following an order order based on bandwidth bandwidth over amplitude generating generating weight weight criteria, criteria, in descending order of values).
vl.
∑
‰ . ˜ Rœ œ F P
59
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® ˜ œj . . F
Ó.
59
&c
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&c & c Ó.
w
34 n˙.
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24
34
59
∑
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24 24
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Figure 16. Excerpt from No One To Speak Their Names (Now That They Are Gone) .
55
7
Karim Haddad
3 3.1
Hyperco Hypercompl mplex ex minima minimalis lism m Sound analyis analyis for controlli controlling ng instrume instrumenta ntall gestures gestures
In contra contrast st to the examples examples we have have already already seen, seen, where where data data took the form form of 3D information arrays, and which were therefore complex, here we see concrete use of a simpler 2D sound data array. Ptps analysis is a pitch estimation analysis (pitch and time arrays). When applied to a noise source or inharmonic sound the analyis output tends to yield interesting profiles (figure 17).
Figure 17. PTPS analysis
This data will be used after being broken down into n fragments as a means of controlling musical gesture (figure 18).
Figure 18. Fragmented analyis in OpenMusic
The fragments will be considered as potential data for the dynamic control of instrumental gestures (figure 19). 56
TimeSculpt in OpenMusic
Figure 19. Bow pressure, placement and speed control of the doublebass part in ”In lieblicher Blaue...” for amplified bass saxophone, amplified doublebass and electronics.
These ”potential”fields will be subsequently filtered and assigned according to musical context context.. As we mentioned mentioned above (section 2), the relevance relevance of this technique technique arises from the fact that all sound sources used for analysis or in the tape part of the piece are taken from samples pre-recorded by the musicians, using special playing modes (multiphonics, breathing, etc) (see figure 20).
Figure 20. Excerpt from ”In lieblicher Blaue...” for amplified bass saxophone, saxophone, amplified amplified doublebass and electronics
One however must also take into consideration the fact that musical events are a balance between complex gestures in the process of sound production and minimal activity in note and rhythm production, i.e we might distinguish two layers of activity: ”traditional” score notation, and control notation.
57
Karim Haddad
3.2 Adagio for String quartet Again in this work, a soundfile served as starting point for the whole piece. However, the technique is completely different. Instead of using an external analysis program, all the work was carried out in OpenMusic. Using OpenMusic’s handling of soundfiles, which is limited to playing and representing them in the SoundFile object under a time/amplitude curve, typical of all sound editors, it was my intention to use limited and reduced data in order to create a closer affinity with the symbolic mode, keeping in mind the instrumental nature of the string quartet. I therefore used the BPC object and downsampled the amplitude curve in order to have a globally satisfying overview of the amplitude profile (figure 21).
Figure 21. Generating durations from an amplitude enveloppe
58
TimeSculpt in OpenMusic
The amplitude having two phases and due to downsampling a more accentuated difference was therefore created between the positive and negative phase creating a somehow double choir polyphony (figure 22).
Figure 22. Amplitude curve transformed into double choir polyphony
I determined four axes intersecting the curves. Duration values were then quantified starting from these segments (see figure 23).
Figure 23. Quantified durations
In order to verify the result, the two polyphonies were synthesised using Csound and the result was put in OpenMusic’s maquette object (figure 24).
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Karim Haddad
Figure 24. Result displayed in a maquette
Figure 25 shows the beginning of the Adagio for String quartet which was written using the strategy describe above.
Figure 25. Beginning of the Adagio for String quartet
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TimeSculpt in OpenMusic
4
Conclusion
In the compositional processes presented here, we can distinguish between two fundamental procuderes: data and algorithms. Data in itself can be regarded as a conceptual idea. It represents the deterministic drive of ”what must be” in a given lapse of time decided by the composer’s Deus ex machina. The algorithms may be seen as the executive part of the composer’s idea, also deterministic when the data proposal is added, with dynamic decisional potential that models the propositional data to its own creative role. These two procedures or techniques are elements of a broad dynamic program, the computational part (analysis and processing) having been carried out with different computer programs such as OpenMusic, Diphone, etc, and can be considered part of a unique program: the composition itself. It is legitimate nowadays to consider a work of art from the performance and aesthetic viewpoints, but also from a deconstructural angle. I personally adhere to Hegel’s [6] thesis 8 , siding with his view that art has fulfilled its purpose, and that modern art cannot be understood in the same way as the art that preceded it (from Descartes to Kant). Neither the post-modernist attitude nor techno-classicism will allow the destiny of modern art to be accomplished. A meticulous study of the state of art and of its own medium is necessary, something like the Renaissance. The French composer and philosopher Hughes Dufourt states ”La musique en changeant d’´echelle, a chang´e de langage. 9 ” [4]. Techniques in composition and sound exploration must be integrated totally not only in the praxis of composition but in it’s understanding, and better, as a wholly part of composition itself.
8
”In allen diesen Beziehungen ist und bleibt die Kunst nach der Seite ihrer h ¨ ochsten Bestimmung f u ¨r uns ein Vergangenes.” ( X, 1, p.16) ”In all its relations its supreme destination, Art is and stays to us something that has been.” (X, 1, p.16). 9 In changing its scale, Music has also changed its language.
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Bibliography [1] Agon C., Haddad K. Assayag G. : Representation and Rendering of Rhythmic Structures. WedelMusic Darmstadt, IEEE Computer Press. 2002. [2] Agon C. : OpenMusic : Un langage visuel pour la composition musicale assist´ ee par ordinateur. Th`ese de doctorat de l’Universit´e Paris 6, 1998. [3] Boulez P. Penser la musique aujourd’hui. Paris Gallimard, 1987. ´ [4] Dufourt D. : L’oeuvre et l’histoire. Christian Bourgeois Editeur, 1991. [5] Delleuze G. : Le Pli - Leibniz et le baroque. Les ´editions de Minuit, 1988. [6] Hegel F. : Ph anomenologie des Geistes. Hg. von 0. Weiss. Leipzig, 1907. ¨ [7] Stockhausen K. ”...wie die Zeit vergeht...” Die Reihe, n 3, 1957. ◦
Karim Haddad Born in 1962 (Beirut Lebanon). First musical studies at the National Conser vatory of Beirut. Studies in Philosophy and literature at the American University of Beirut. In 1982, settles in Paris (France). B.A in musicology at the Sorbonne University. Follows at the Conser vatoire National Superieur de Musique de Paris studies in Harmony, couter point, fugue, orchestration, analysis and composition with Edith Lejet (Harmony, Fugue), Bernard de Crepy (Counter point), Paul Mefano (Orchestration), Jacques Casterede and Alain Louvier (Analysis), and Alain Bancquart (Composition) where he obtains six rewards and the Diplome Superieur in Composition. Workshops in composition with Klaus Huber and Emanuel Nunes. Between 1992 and 1994 he par ticipates in the Ferienkursen fur Musik of Darmstadt where he works with Brian Ferneyhough, and obtains the Stipendienpries 94 in composition. In 1995, he follows the computer music courses at the IRCAM , and becomes member of the IRCAM. Forum where he contributes in 1999, by writting the Om2Csound librar y for controlling synthesis through OpenMusic environment. He will then write OpenMusic’s reference and tutorial. Actually works at IRCAM as a technical advisor for the Ircam Forum. His works are performed by various ensembles and artists such as the Berlin StaatsOper, l’Itineraire, 2e2m, Orchestre Philarmonique de Radio-France, Diotima quartet, etc...
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The Genesis of Mauro Lanza’s Aschenblume and the Role of Computer Aided Composition Software in the Formalisation of Musical Process - Juan Camilo Hern´ andez S´ a nchez Abstract. The present article will attempt to illustrate the compositional process of Mauro Lanza’s work Aschemblume for nine instruments ensemble (Fl. Cl. Perc. Pno. Vl. Vla. Vc. Cb.). The piece was a commission from the French Culture Ministry and the ensemble Court-Circuit. In the first part, an introduction to the musical parameters that unify the piece will be presented, as well as a description of the role of OpenMusic in the pre-compositional processes; in the second part the musical material will be analysed with a discussion of their construction in OpenMusic, and finally the fundamental structure of the piece will be described to show how the sections are assembled. The writing of this article was made possible thanks to a close collaboration with the composer. ***
1
Introduction
Mauro Lanza’s work is characterized by the mental conception of musical ideas followed by a computer aid. The pre-compositional formalisation is a compulsory phase permitting the composer to discern the material that could be quickly produced by the machine. The term musical material will be used to name each minor section possessing autonomous musical characteristics. The composer’s intervention in the CAC process takes place with the programming of computerised tools that respond to the needs of his musical language. Aschenblume is a German word meaning ashes settling down taking the shape of a flower. The word is taken from a poem by Paul Celan. The literal translation could be ”Ash flower” and its literary context strengthens the semantic connotation of each component, (the flowering through the vanishing of ashes). The process applied to the initial material of the piece could be seen as a musical analogy of the word: the piece begins in a rhythmic ostinato that undergoes harmonic and rhythmic disintegration and gradually becomes a sustained chord. Then the material is reiterated several times, but bearing a new musical element at each repetition. The evolution of these new elements leads them to be progressively dissimilar from the initial material; the treatment given to their common musical principles builds up the coherence between them. 65
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The musical path allows all kinds of interaction between the different bodies of musical material; the handling of their interpolation and their contrast becomes the principal axis of tension. The development of all the bearing materials is a disintegration process. An important feature of this process is the gradual reduction of duration of each section until the end of the piece where they are perceived as small fragments, keeping the essential musical elements that characterised them. A brutal and regular pulsation finishes the piece in the form of a collision between the contracted elements.
2
Pre-compositional process
The formalisation of the compositional process implies a resolution of the principles that link the musical materials used in the piece. The main aspects are as follows:
• the development of a rhythmic hierarchical language by the polyphonic assembling of rhythmic patterns, • the creation of the harmonic field homogenising the sonority of the piece, • the descending melodic shape. Each main body of material is governed by the idea of a melodic descent, • each section of the piece is reduced in duration. The harmonic and rhythmic aspects are created almost entirely using OpenMusic; the comprehension of this process is essential to the understanding of the musical material’s construction and its development throughout the piece. Therefore, an explanation of the rhythmic and harmonic formalisation by CAC will be presented in the introduction to the analysis of the piece.
2.1
The rhythmic hierarchical language by polyphonic assembling of rhythmic patterns
Rhythmic hierarchy and periodic patterns are the main rhythmic aspects developed by Mauro Lanza. The hierarchy can be achieved when some specific points are emphasized in a rhythmic sequence, creating varying levels of importance. The accented points constitute an original rhythmic pattern that arithmetically generates all of the minor rhythmic structures. In Aschenblume , as in other Lanza works, there is a polyphonic treatment of the rhythmic hierarchies, the original rhythmic pattern is highlighted in the points where all voices are assembled; each voice has its own duration and is repeated throughout the whole length of the original pattern. The rhythmic sub patterns of each voice are obtained from a modulo division of the original pattern, that allows sub patterns to be generated, and that coincide with the original pattern onsets. The onsets of the original pattern are expressed in ratios, which are note values measured in relation to the beginning of the pattern that is the point zero. The divisor indicates the division unity and the numerator the position of each onset. For example, in a 21 sixteenths note pattern that has onset the 5 th , 13th , 15th and 2st sixteenth note will be represented as follows: 0
5/16
13/16 66
15/16
21/16
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The possible duration of the derived pattern is expressed also as a ratio and it is said to be a modulo. The numerators of the original pattern onsets are divided by the numerator of the modulo; The remainders of each division are the onsets’ values that determine the derived pattern, if there are repeated remainders this value has to be taken just once. With a pattern that lasts 8 sixteenth notes the operation will as follows: Original pattern onsets Remainders Sub pattern onsets
0 0 0
5 5 5
13 5 7
15 7
21/8 5
Sub pattern duration
Figure 1. Rhythmic pattern with two sub-patterns periodicities
The composer creates an initial CAC tool in order to accelerate this process. The tool is an OM function called Subpatterns that generates the sub patterns with any modulo and any division unity. The rhythmic density depends on the number of notes in the modulo of a sub pattern, and can also be controlled with another function created by the composer. The function creates some restrictive constraints so as to choose the less dense patterns. In order to solve the constraints the search-engine Pmc-engine (from Mikael Laurson’s PWConstraints library) is used. This search-engine yields solutions found in a search domain giving preference to the solutions that respond to the constraints. The constraints are rules and heuristic rules; the rules take the sub pattern solutions responding to a simple true or false question, the heuristic rules select the sub patterns according to the desired density value. Then the composer can find patterns determining the minimum value allowed in a voice and control the number of notes of each sub pattern depending of its density. In some sections of the piece the pitch is also formalised in order to create melodic patterns corresponding with the periodicity of the sub patterns, while the pitch reinforces the original pattern creating a heterophony. Each note of the chosen melody is allocated to each onset of the original pattern, the same notes are then allocated to the reminders of the division. When there are equal values as reminders of different divisions and the allocated note is different, this value appears in the sub pattern taking only one note from the allocated notes at each repetition. 67
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Original pattern onsets Remainders Notes
0 0 C
Sub-pattern modulo Onsets Note
5 5 D
13 5 E
15 7 F
0 C
8 5 DEG
21/8 5 G
7 F
Sub pattern duration
0 CG
7 1 5 F D
6 E
Figure 2. Heterophony over the rhythmic pattern appeared in the figure 1
3
Creation of a harmonic field
The Aschenblume’s harmony is obtained completely from two ”bell-like” spectra created by physical modelling synthesis1 . The two instruments employed are a free and a clamped circular plate; their spectra are inharmonic with a huge quantity of non-temperate partials. In order to be used, the partials are approximated into quartertones and the clarinet is tuned a quartertone lower. Tempered instruments such as the piano and some pitched percussion instruments mostly play tempered notes; in the sections where more notes are needed the harmonies are approximated into semitones.
Figure 3. Free circular plate spectra
1
This kind of synthesis permits the creation of ”virtual” instruments starting from their dimensions and the physical properties of their material. The procedure is made possible by the Modalys software, realized at the IRCAM. The composer Mauro Lanza created an interface to control the synthesis from inside OpenMusic.
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Figure 4. Clamped circular plate spectra
The harmonic field obtained is not intended as a musical representation of an acoustic model in the spectral music manner, but to give a homogeneous sonority to the whole piece. Therefore, the spectra becomes the ensemble of notes used in the piece and its coherence of form is due to the organisation of sub-ensembles of partials. Some partials have higher amplitudes depending on which part of the instrument’s register is sampled. In order to create the partial sub-ensembles, a constraint tool is used to search the instruments’ points at which there are fewer simultaneously sounding partials. Each one of the points becomes the harmony of a section, and they are played either as chords with their corresponding amplitudes or melodically as a scale for each instrument. The points with common partials are used as the harmony of the related sections of the piece, which gives them harmonic homogeneity.
Figure 5. Enumeration of chords obtained from the partials of different points of the instru-
ments
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4 Aschenblume musical materials As we explained in the introduction, new material appears constantly throughout the piece. A description of each section is necessary if the reader is to understand their formal structure.
4.1
Material A
The piano presents a homo-rhythm in sixteenth notes accentuating points that shape a melodic descent. The homo-rhythm accelerates while the accents decelerate, because the periods between them are enlarged. This process creates a temporal paradox that will be resolved as a sustained chord. All the other instruments underline the piano accents in triplet subdivision, generating a small gap between each. However, the percussion follows the same pattern as the piano accents. The melodic descent movement is applied to the other instruments in different periodicities from that of the piano. To create this material the composer developed a CAC tool, a patch that applies the following process: the harmonic field is approximated into semitones and filtered by an intervallic structure transposing in chromatic downward steps. Each transposition is arpeggiated downwards avoiding the notes from of the harmonic field, thus creating an irregular descent. There are two note chords accentuating points of a melodic descent. The filtering process is carried out in the OM patch as well as upon the acceleration of the homo-rhythm. Placing of accents is done manually by the composer. The following step is the extraction of the onsets of the accentuated notes, in order to generate the rhythm for the other instruments. A patch takes these onsets and approximates them into a triplet subdivision, the resulting rhythm being allocated to the flute, clarinet, violin and alto. The percussion accentuates in the same subdivision as the piano, approximately following its melodic descent shape with bongos and congas.
Figure 6. Material A (Meas. 1)
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The melodic descent for the other instruments is chosen by the composer from the harmonic field assigning different registers to each instrument and allowing them to have common notes. The number of notes of this descent is progressively reduced until each instrument only has one sustained note, and this procedure leads to the incoming chord. The melodic descent is orchestrated in such a way as to have three periodicity levels. The violin and flute are always have a similarly patterned descent, and notes reduction. The alto and clarinet play the descent in a periodicity that is different from the violin and flute. Finally, the heterophony principle is used to allocate some pianissimo descending notes in different periodicities for the flute and clarinet.
Figure 7. Melodic descents periodicities for Flute, Clarinet, Violin and Viola (meas. 1)
Throughout the piece the piano harmony evolves, changing the intervallic structure that is transposed, while the other instruments remain harmonically similar to their first appearance. The sustained arriving chord undergoes a harmonic enhancing metamorphosis; its dynamics and orchestration also evolve, using the amplitudes of the chords extracted from the spectra as a model.
4.2
Material B
It is a rhythmic pattern built up with the original pattern and four sub-patterns, each one in a different subdivision unity. The double bass and the vibraphone play the original pattern in a regular pulse of 9 sixteenth notes. The piano has a second sub-pattern that uses the same periodicity with an internal division, it doubles the vibraphone at each assembling with the original pattern. The viola and the violin use a triplet sub-division having a periodicity of 10 triplet eighth notes. The clarinet plays a sub-pattern lasting 3 quarter notes and its sub-division unity is the triplet. The flute and the violoncello have a quintuplet sub-division and their periodicity is equal to one half note. The harmony of this section is an orchestration of the 8 th chord from the nodes obtained in the spectra. The original rhythmic pattern is characterised by having the fundamental (C), the 3rd , and the 7th partials (Pno., Vbr.). The rest of the partials are distributed among the other instruments, the voices, rhythmically assembled, use the same notes. Therefore we may conclude that the original pattern is harmonically stable while the sub-patterns are changing, a process that generates an internal evolution of the material very important to its interpolation with the other bodies of material. 71
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Figure 8. Material B (meas. 51)
4.3
Material C
It often appears as a transition element, characterised by the rhythmic assembling of all the voices, and the p olarisation over the medium and high registers. It has a sextuplet melodic ascending figure built up in a scale whose intervallic structure is identical throughout all octaves. As a result, it is the only section constructed using a harmony out of the spectra. All the voices begin in a different sixteenth note of the sextuplet, in order to create polyphony, in which each sixteenth note should have the maximum possible number of simultaneous notes from the scale. The appearance of this material articulates the formal structure of the piece because of how it it differs from the other bodies of material, especially with regard to its homorhythmic polyphony and its ascending character.
4.4
Material D
Perceptually, this section is a reminder of the material A, the piano plays a similar homorhythm accentuating the descending notes. The main differences lie in the polyphonic and rhythmic treatment given to the other voices: polyphonically the differences lie in the instruments playing in canon with the piano; rhythmically they arise from a common sixteenth note unit division throughout all the voices. 72
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Figure 9. Material C (meas. 125)
The computer tools initially apply the filter to the harmonic field polarising around the two highest notes of the chord 2. The composer manually chooses the accents that in this case accelerate until they become constant eighth notes, whereas the homo-rhythm remains in sixteenth notes throughout the section. The appearance of the instruments follows an asymmetrical four voice canon played simultaneously by the violin and the viola, twelve quarter notes after by the flute and the glockenspiel, the violoncello joins twenty-three quarter notes after the piano entry. The rhythm is obtained from the piano accents that are taken as onsets and augmented in different proportions for each instrument. The used proportions are irregular and are approximated into sixteenth notes, which are applied as subdivision unit. The melodic descent is also used in instruments that are perceived as an irregular echo of the piano accents. In order to polarise the harmony completing Chord 2, it is formed by the gradual reduction of the descending melody until each voice has just two notes.
Figure 10. Rhythmic structure of Material D canon
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Juan Camilo Hern´andez S´anchez
The final part is the most developed element of this section; in the rest of the piece it evolves becoming a constant sixteenth note pattern where the two highest notes are alternated. Each note is harmonised with the chord notes played by each instrument with its respective register in such a way that the highest notes of each voice are simultaneous. The same is applied to the lowest notes. This fast alternation of high and low register mostly emerges at the end of the piece, sometimes transposed or harmonically enriched. In the formal scheme it is named D’.
Figure 11. Polarisation over Chord 2 in the Material D (Meas. 91)
4.5
Material E
Constructed with the rhythmic pattern tool, this section appears usually as a transition between two sections. Using the chord 27 as its harmony, its principal characteristic is the flute and the double bass sustaining the outer notes while the rest of the ensemble plays the rhythmic pattern and sub-patterns. The original pattern appears in the cowbells over the fundamental of the chord, it has a regular periodicity of 7 sixteenth notes. The sub patterns are individual for each instrument, which means that they are not doubled. The violin and the viola are sub-divided in half note quintuplets, with a 9 and 8 quintuplet eighth note periodicity respectively. The violoncello and the clarinet are subdivided in triplets and their periodicities are 11 and 12 triplet eighth notes. The piano does not have a regular periodicity; its role is to 74
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provide a link to the previous section.
Figure 12. Material E (Meas. 137)
4.6
Material F
A contrasting element appears with this material, which consists of a rhythmic unification of the entire ensemble undergoing a deceleration. This is a very short section that introduces a new element, by way of dynamical and orchestration contrast. Therefore, it has great importance in the formal articulation. The tool develops this material by expanding a spectrum that is contracted in the lower part of all registers; the computer contracts the given chord in the lower register, subsequently, the chord is gradually transposed towards its original register. The rhythmic deceleration is a simple interpolation between two rhythmic values, always begining with sixteenth notes, and the final value depending on the following section. The resulting rhythm has a regular pulsation gradually transformed into syncopations, creating a special tension and introducing a new element.
4.7
Material G
It is similar to Material C in many aspects: it has a homo-rhythmic quintuplet subdivision unit for all the playing instruments; each instrument begins at a different note of the quintuplet, creating the same polyphonic effect that appeared in Material C. 75
Juan Camilo Hern´andez S´anchez
Figure 13. Material F (Meas. 163 )
The main difference is harmony. In this case the ascending movement occurs over a B arpeggio, the clarinet part distorts the harmony with microtonal neighbour notes that are gradually eliminated to reach a sustained B unison in all instruments. It is also a reminder of the disintegration that occurred in Material A.
Figure 14. Material G (Measure 167)
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The treatment of timbre is unique to this material because of the absence of piano and pitched percussion, as well as the use of string harmonics amalgamated with woodwinds in the high register.
4.8
Material H
This section is characterized by a rhythmic pattern. The double bass rasps out the lowest note of the spectra and the flute plays the highest note in this section, accentuating the original pattern, which has a periodicity of 8 quintuplet eighth notes. The violoncello plays a sub-pattern with the same periodicity as the original, whereas the melodic treatment generates an internal subdivision. The viola also accentuates the original pattern in sixteenth notes creating a little gap. The triplet subdivision is applied to the violin, clarinet and piano, the latter being doubled by a glockenspiel. Each instrument has a different periodicity: 5 eighth triplet notes for the violin, 21 eighth triplet notes for the piano, clarinet and glockenspiel. Chord 30, obtained from the clamped circular plate, is used in this section with a strong emphasise on E. The highest notes are placed just after the original pattern accent. As a consequence, iambic polyphony is created with the short note in the low register and the long one in the high register. This idea is used as a principle to engender and develop new materials such as D’ and J.
Figure 15. Material H (182)
Two minor materials appear as a variation of Material H. The first one (H’) presents an acceleration the original pattern of Material H and a change of its subdivision unity into sixteenth notes, the main similarity being the continuous gathering of the double 77
Juan Camilo Hern´andez S´anchez
bass and the flute, even if the raspy E note played by the double bass subtly becomes a harmonic two octaves higher, recalling Material B. The second one (H”) seems to form a hybrid with Material E, because of the appearance of an accentuated C sharp note in cowbells, double bass and piano. However, the harmonic in the double bass and iambic character link it with Material H.
4.9
Material I
In this material the heterophony is much more flagrant, played over a descending melody. Not all the instruments play it in unison but in microtonal approximations, yielding a richer sonority. Only the double bass and the cowbells play the structural melody over the original pattern, the periodicity of each instrument is independent and is constantly changed at each appearance of the material.
Figure 16. Heterophony in Material I (272)
4.10
Material J
Using a lot of notes from the free circular plate spectra, the lower partials are grouped as a sort of cluster strongly attacked by the piano and lower strings with a Bart´ ok pizzicato. Immediately after this, a longer high chord ensues and develops the iambic idea set forth 78
The Genesis of Mauro Lanza’s Aschenblume ...
in Material H. The high notes will gradually be extended in a melodic descent or in overblown descending notes. Normally attributed to the flute, here they are played as a strings glissando. This procedure is often applied to create interpolation with other material.
Figure 17. Material J (291)
4.11
Interpolation
Interpolation is a transition between two musical situations. In this piece it becomes a very important bridge between bodies of material. Elements from the incoming section are mixed in with elements from the outgoing section. This gathering process is gradual and leads to the complete transformation of the outgoing section into the incoming one. A different kind of interpolation occurs, depending on the characteristics of the sections. Some specific examples are presented below to explain how the material is assembled. In Measure 121, interpolation occurs between Material A and Material C. The procedure starts when the accentuated notes of Material A are followed by sextuplet ascending notes. It begins by adding the first sextuplet note to Material A, then grows note by note into a complete ascending scale of Material C in each instrument. Another striking example appears in Measure 286, in an interpolation between Material C and J. One note is subtracted from the ascending scale of Material C to only keep two notes, one lower than the other. The orchestration is reduced to three instruments: 79
Juan Camilo Hern´andez S´anchez
Figure 18. Interpolation between Material A and Material C (121)
a violin, clarinet and viola. Each begins at a different beat of the sextuplet, the rhythm decelerates and the lower notes gradually assemble at the same point of beat and the higher ones at the subsequent point of beat. Simultaneously, the interval between the two notes grows in a contrary motion, while the rest of the ensemble appears and reinforces the process rhythmically and melodically up to the arrival of material J. Yet another interpolation type is to be found in Measure 232 between Materials J and D. In this case, after the attack over the high notes of Material J, the descending intervallic structure of the piano in Material D gradually lengthens, as do the flute and string canons.
5
General structure of the piece
The original project of the piece is to gradually reduce the length of the materials. This process is not always regular because the composer has the subjective time perception of each sub-section in mind. The length of each sub-section depends on the quantity of material played in them, as well as how they are connected. The structure of the piece possesses a special unity. It also has a formal hierarchy built in three different levels of segmentation. Firstly, the form of the piece is segmented into three, each segment being characterised by specific material and processes. Secondly, there are sub-sections that bring together elements of material that do not contrast with each other, either because there of a succession of similar material, or because there is interpolation among the elements. Finally, a local level is marked out by the incoming material, previously described in Aschenblume Musical Materials . The formal schemas presented below show the three levels of segmentation. The main section is divided in sub-sections. The measures at which they occur and their duration 80
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Figure 19. Interpolation between Material C and Material J (286)
Figure 20. Interpolation between Mat´ eriel J and Mat´eriel D (232)
in ratios are specified underneath. The third level shows the materials of each sub-section with arrows between those that are interpolated. Here is an example of their schematic representation. 81
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Section Measures Sub-sections Measures Duration in ratios Materials Table 1. Formal scheme of the piece
1 1-19 74/4 A →→→
A’
1st SECTION 1-162 2 3 20-41 42-67 83/4 + 1/8 102/4 A →→→ A’ A → B → A’
6 94-110 67/4 + 1/8 D →→ A →→
A’
4 68-77 40/4 A → C
1st SECTION 1-162 7 8 111-119 120-129 36/4 40/4 A →→→ B A →→→ C
5 78-93 763/4 + 1/8 D
9 130-137 32/4 D →→→ B
1st SECTION 1-162 10 11 138-153 154-162 64/4 35/4 E →→→ A’ A →→→ E Table 2. Formal scheme of the first section
5.1
1st Section (1-181)
It shows the first disintegration process undergone by Material A, which is repeated once without any modifications. At its third appearance the materials B, C, D and E are gradually introduced by interpolation inside the process. This first section is divided in 11 sub-sections, each of them having interpolation between two or three bodies of material. The initial disintegration process of A can be time stretched, from the 3 rd sub-section where B is introduced, then the process occurs from the 4 th to the 6th sub-sections and finally from the 7th to the 10th . The time reduction of sub-sections is irregular, due to the introduction of new materials within. Nevertheless, there is more material in less time, which means that they are gradually undergoing a time reduction.
5.2
2nd Section
The presentation of Material F articulates the piece. After it appears, the process changes and the material made up by rhythmic patterns such as B, E, I, H occur frequently. They 82
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12 163-169 F → → → G
2st SECTION 163-314 13 14 15 170-181 182-184 185-191 D → → → C H B → C
17 203-207 A →→→ I
2st SECTION 163-314 18 19 208-212 213-238 B →→→ C F → C → J-D
21 259-263 H’ E
2st SECTION 163-314 22 23 24 264-271 271-275 275-281 K → → I B →→→ I B I D
26 293-300 F →→ A
2st SECTION 163-314 27 301-314 J F H H’ K →→
F
16 191-192 H H’ → A’
20 239-258 D → C →
25 282-292 F → C →
J →→
J
J
J’
Table 3. Formal scheme of the second section
are generally bridged by short appearances of the material elements developed in the first section. The sub-sections become gradually shorter and the quantity of materials interpolated inside them increases. This means that the materials undergo a noticeable reduction in length. The main process after Material F is the assembling of materials that possess special tension, released over louder materials such as H or J at the end. Between subsections 12 and 15, it finally achieves a total release over material A’. Its duration is reduced gradually throughout its appearance inside the sub-sections 19, 20, 25, 26 and 27. Between sub-sections 21 to 24, the materials with rhythmic patterns quickly succeed each other, and finally arrive at material I, which generates a sort of rhythmic and melodic unification of the ensemble by its hetereophonic character. This unification is perceived as a point of release for the entire piece.
5.3
3rd Section
The length of the material is reduced so as to complete contract the material and bring it together in a single entity that possesses characteristics from all. The piece finishes with a strong and regular pulsing beat, the result of the total contraction of all elements. The sub-sections are no longer than 31 quarter notes, which are quickly reduced to an average of 4. When this happens, there is only one body of material left in each subsection, strongly contrasted with the others. Consequently this section is divided into several smaller sub-sections that are juxtaposed until maximum reduction is achieved. Finally in measure 417 a new body of material arises out of this contraction process. It 83
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possesses a rhythmic pattern, and all the instruments have the same subdivision unit. The constant pulsation is progressively announced by piano clusters and a Bart´ ok pizzicato, both recalling Material J. It finally arrives in measure 427 and creates a tension that is suddenly stopped.
6
Conclusions
As mentioned in the introduction, the purpose of this article is not the detailed description of technical procedures used when programming OpenMusic tools. Rather, this article emphasizes the remarkable advances in algorithmic procedures, in obtaining expressive and artistic results. Composers generally employ constraints as a tool for composition, however in Lanza’s piece the use of the computer accelerates the compositional process. The generation of hierarchical rhythmic structures is a new development in the subject of Computer-Assisted Composition. The composer has managed to open a new avenue of exploration through the control of a rhythmic generator using melodic constraints, and has achieved significant results. The value of this piece may also lay in the fact that the formalisation principles are perceived as homogeneous and musical, in turn shedding light upon the global formal structure. The present article has described these principles and the ways in which they are applied with each body of material. The purpose is to point out CAC the forethought that was applied when developing a model for programming tools. The model then became part of the musical language that the composer has used for more recent pieces. It is fair to say that CAC procedures are developed as an extension of the composer’s musical language.
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Juan Camilo Hern´ andez S´ anchez Born in Bogota, Colombia in 1982. He began by playing traditional Colombian music, moving to jazz, rock and classical music. He studied composition for two years at Javeriana University with Harold Vasquez C. and Marco Suarez. He won the Colombian Cultural Ministry National Competition which allowed him to come to France to continue his studies. In France he has studied with Jean Luc Herv´ e at Nanterre Conservatoire and Evry University where he was awarded a ”Maitrise” for his paper Formalization In The Compositional Process. In 2003 he studied at the CCMIX (Ianis Xenakis Music Creation Centre) with Gerard Pape, Bruno Bossis, Jean-Claude Risset, Curtis Roads, Agostino di Scipio among others (composers as well as software developers). He has also studied with Brien Ferneyhough, Luca Francesconi and Philippe Leroux at Royaumont Foundation where the piece An´eantir was premiered. Since 2004 he has studied composition with Philippe Leroux at Blancmesnil National School. His pieces have been played mostly in the Forum De La Jeune Creation organized by the New Music International Society, 2002 Sin Aliento, 2003 Vestiges du rˆ eve, 2004 Eblouir, as well as at the CCMIX in the Rencontres D´ıAutomne Transmutaci´on cinem´ atica.
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Generating Melodic, Harmonic and Rhythmic processes in ”K...”, an Opera by Philippe Manoury - Serge Lemouton Abstract. In order to provide some elements for musical analysis, we shall describe here how and why Philippe Manoury makes use of Computer Assisted Composition in writing ”K...”, one of the first operas of the 20 th century. ***
1
Introduction
Philippe Manoury is mostly known in the musical computing field for his research and innovation in real time computer music. In the eighties, he collaborated closely with Miller Puckette to develop realtime music software systems. The collaboration resulted in the first Macintosh version of Max in 1988. This research has never ceased, and lead to the Sonus ex Machina cycle (Jupiter 1987, Pluton 1988, Neptune 1991, La Partition du Ciel et de l’Enfer 1989) and En Echo 1993. In his first opera Soixanti`eme Parall`ele (premiered at the Theatre du Chˆ atelet in 1997) he also used realtime electroacoustic music elements. ”K...”, his second opera (after ”the Trial” by Franz Kafka), was commissionned by the Opera de Paris . It was premiered at Opera-Bastille in March 2001, and played again in April 2003. The electronic part of this opera is much more developped than that in Soixanti` eme Paral l`ele . Manoury’s style uses post-serial writing techniques. These constraints or rules of composition can be easily automated. While composing ”K...”, Philippe Manoury asked me to implement his melodic, harmonic and rythmic generation systems into Computer Assisted Composition software. OpenMusic speeds up the automatic generation of this material on computer, a daunting operation usually done ”by hand”. The very simple OpenMusic patches shown in this article have therefore been used to create musical material that was printed in several bound copy-books, containing reservoirs of melodies, chords and rythms from which the composer drew while writing the score.
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2
Generating rhythmic material
A major rythmic character in ”K...” is made up of the following proportional durations series: 2153813214 if the sixteenth note is taken as the basic unit, this numerical series generates a rythmic sequence. OpenMusic allows us to represent this rythm in musical notation (figure 1).
Figure 1. Rhythmic material
Figure 2. Rhythmic material generation patch
The OM patch (figure 2) operates permutations of groups of 2 or 3 duration values, using the following groupings of the numerical series: (2 1 5) (3 8) (1 3) (2 1 4) The result of all the permutations is a set of 24 different rythms (figure 3).
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Generating Melodic, Harmonic and Rhythmic processes in ”K...”
Figure 3. Rhythmic permutations
These rythms are then displayed using the 9 following different base duration values (tempo 60 MM).
sixteenth note triplet eighth note quintuplet quarter note quintuplet sixteenth note quintuplet eighth note eighth note sextuplet sixteenth note triplet quarter note quarter note
250 ms 333 ms 800 ms 200 ms 400 ms 500 ms 167 ms 666 ms 1000 ms
An actual application of these OpenMusic generated rhythms can be found in the opera’s prologue, in the string section, from bar 11 to 51 (see fig 4). Here, the same rythmic processes are presented simultaneously on different time scales (Contrabasses : quarter notes, alti : triplet eigth notes, violin II : sixteenth notes). This section is followed (from bar 52 to 80) by another polyrythmic presentation (Contrabasses : triplet eigth notes, cellos: triplet eigth notes, alti : sixteenth notes, violins : triplet quarter notes, see figure 5). 89
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Figure 4. Excerpt from the orchestra score of ”K...”’s prologue (bar 21-25)
Figure 5. Excerpt from the reduction for piano of ”K...”’s prologue
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Generati Generating ng Melodic, Melodic, Harmonic Harmonic and Rhythmic Rhythmic processes processes in ”K...” K...”
3
Melod Melodic ic gene genera rati tion on an and d serial inlayings
The pitch organization of the whole opera is based upon four main series of 7, 8,6 and 7 notes respectively. respectively. (see figure 6).
Figure 6. Series a,b,c and d
Figure 7. Patch generating the different forms of a serie
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What Manoury calls a process of inlaying (incrustations (incrustations ) is applied to this series. This process consists in searching, within the 48 canonic forms of each series (The transposed, retrograde and inversed forms are generated in OM by the 4 ser-op functions in the patch figure 7) all the occurences of all the intervals present in the original series. All the forms containing this interval are then selected. The intervals between all the notes of the series of taken into consideration (and not just consecutive pitches) : 7 notes yield 21 intervals (formula (formula : N * (n-1)/2). (n-1)/2). In the printed printed book of material material generated generated by OpenMusic, OpenMusic, the selected series are vertically aligned to so as to clearly display the interval in question (see figure 9). The same process is applied to the 3 other matrix-se matrix-series, ries, (resp. (resp. 28, 15 and 21 incrustations).
Figure 8. Serie c, inlaying on mi/sol
Figure 8 shows another page of the printed notebook in which P. Manoury was able to choose a form of series b containing the interval E-G. This process allowed the composer to find classes of transposition with intervals in common, and to create an atonal equivalent of tonal modulations. modulations. In the first scene of the opera (when the inspector tells the unfortunate K. that he is under arrest), arrest), the vocal parts are based on the E/A inlay inlay. This pivot-int pivot-interv erval al is first presente presented d by the inspector when he shouts: shouts: ”Josef K. ?” (see figure 10). Then from bar 240 to bar 252, the vocal lines follow the series presented on page mi/La of the notebook (refer (refer to line line 1 to 11 of figure 9). This This allow allowss the composer composer to mo move ve through through vario various us series while maintaining focus on the emblematic fourth interval. Note that the accompaniment of the vocal part is built on the duration value series (2 1 5 3 8 1 3 2 1 4) shown above. In the trumpet calls, symbolising the judicial tribunal (scene 4 of the opera, see figure 11) is to be found another example of the serial inlaying process, in which the same series is polarized around another emblematic interval, the fifth E-B (present in the original form of series b). 92
Generati Generating ng Melodic, Melodic, Harmonic Harmonic and Rhythmic Rhythmic processes processes in ”K...” K...”
Figure 9. Serie a, inlaying on mi/la
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Figure 10. Excerpt from scene 1 of ”K...” (piano (piano reduction reduction by the author) author)
Figure 11. Beginning of ”K...”’s scene 4 (manuscript)
4
Orna Orname men ntati tation on
The OpenMusic patch shown in figure 12 generates very long melodic lines starting from a 27-note series constructed by the concatenation of the four above-mentioned series (see figure 6). ser-op is a function from the Combine library, Combine library, written by M. Malt for B. Ferneyhough. hough. This function function generates generates the inversion inversion of the matrix-serie matrix-series, s, with sol2 (midi55) as a pivot-not pivot-note. e. The pma-mul abstraction abstraction calculates calculates classified classified chord chord multiplic multiplication ations. s. The transpositions of this series from its inversion (diagonal pivot-note) are joined end to end 94
Generati Generating ng Melodic, Melodic, Harmonic Harmonic and Rhythmic Rhythmic processes processes in ”K...” K...”
Figure 12. Patch generating the diagonal transpositions of a series
Figure 13. Excerpt from the orchestra score of ”K...”’s prologue (bar 21 to 25)
in order to form harmonic harmonic compounds. compounds. The linking of these transpositio transpositions ns is grouped using the 2 looped density series:
(4 1 14 9 5 12 1 16 8 9 12 9 16 16 5 12 1 14 7 5 8 13 1 14 15 21 18 25) (4 1 2 9 5 1 4 8 9 1 9 4 5 1 2 7 5 8 1 2 9 6 1)
The same process is applied using E, G sol and E flat as pivot-notes, then on the reverse reverse version version of the matrix-serie matrix-series. s. This process is used, for instance, instance, in the wood-wind wood-wind ornementations (gro (groupe upe-f -fus us´ ´ees ee s )) that can be heard throughout the opera’s prologue (see figure 13). The number of notes of each group follows the density list shown above. 95
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5
Conc Conclu lusi sion on
Philippe Philippe Manoury Manoury used Computer Computer Assisted Assisted Composition Composition in a very very pragmatic pragmatic way way. His goall was goa was the automati automaticc genera generatio tion n of music musical al materi material. al. Analys Analysing ing this process process may provide avenues of approach and clues to anybody interested in the study of Philippe Manoury’s methods of composition.
Figure 14. The courtroom scene. Director: Andr´ e Engel. Scenography: Nicki Rieti
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Serge Lemouton Serge Lemouton was born in 1967. After studies in violin, musicology, harmony and counterpoint as well as composition, he specialised in various computer musique domains at the Sonus Department of the Conservatoire National Sup´ erieur de Musique de Lyon. Since 1992, he has been music assistant at the Ircam. This has enabled him to collaborate with Ircam researchers in developing computer musique tools, and he has taken part in the musical projects of numerous composers, among them Michael Levinas, Magnus Lindberg, Tristan Murail and Marco Stroppa. He has been in charge of realtime creation and performance in the operas of Philippe Manoury, ”K”, and ”La Front`ere”. He is also teaching assistant at the Paris VIII University.
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Composing the Qualitative, on Encore ’s Composition1 - Jean-Luc Herv´e and Fr´ ed´eric Voisin Abstract. In this paper, we will present the use of CAC in the writing of the electroacoustic parts of Encore, for ensemble, two Disklaviers and live electronics. Jean-Luc Herv´e, the composer, and Fr´ed´eric Voisin, the musical assistant, have experimented with new features of OpenMusic software using LISP language. The concept of musical gesture has been developed a ”top-down” perspective to generate soloing. *** Encore is written for 18 musicians, electronics and two Disklaviers, one of which is tuned one quarter of a tone lower than the other. The Disklaviers were chosen in the instrumentation for two reasons. First, a Disklavier, being a mechanical instrument, has a presence of its own, quite different from a musician’s and from sound diffused through loud-speakers as well. This oddness itself creates a slight change in the usual concert scenography that enhances the sharpness of the listener’s perception, and provokes more careful listening. The second reason is the Disklavier’s peculiar quality of being at the same time an orchestra instrument and able to receive MIDI data in order to diffuse directly a musical material composed with the help of computers. Therefore, writing the Disklaviers’ scores is closer to an electroacoustic work, than writing for an instrument, and the fact that the limits of an interpreter are not to be taken into consideration increases that closeness. It was possible to think of the Disklaviers’ scores as a direct work on sound and not as plain instrumental scores. In Encore , the Disklaviers make it possible to cross the two usual modes of emitting sound: acoustic instruments and loud-speakers. Here, an acoustic instrument diffuses computer-made sounds and musical materials. It was this ability of being at the same time an instrument and an electroacoustic tool - the possibility of adding to the two usual modes of emitting sound a third one, a hybrid of both - that interested us. We composed the Disklaviers’ MIDI scores with OpenMusic. When we were working on the creation of Encore in the studios of the IRCAM, the kernel of OM was still being developped. We experimented with the early versions and were interested in particular by the possibilities of meta-programming they offered. A LISP program was conceived to create MIDI sequences with the possibility of organizing sound ideas - compositionnal gestes - without having to elaborate them from the ”physical” musical material (pitches, intensities...). The program had to create the details of the sequences from macro-structural data. However, although developing a 1
Encore was created at the Centre Georges Pompidou, Paris, on June 10, 2001.
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material of pitches and durations, starting from a lower structural level (ascending by succession of embeddings) is natural with OM , the reverse operation, descending, is much less developped. The idea was to be able, in the first place, to construct ”prototypes” of compositionnal gestures - musical situations foreseen in a global way that would be then upgraded with the program, in terms of pitches, durations and intensities. The Disklaviers scores in Encore , the ”gestural” musical sequences (textures), were thus built upon three basic gestures: an ascending stroke, a descending stroke, and a repeated note. We first started this approach by experimenting with a ”natural language”interpreter. Constructing a syntax interpreter and a dictionnary that associated words with LISP functions allowed us to generate digital musical sequences based on propositions that were expressed in a human language. The LISP language was perfectly suited for this experience. For example, the following statement: ”repeat a descending line, by tones, from fa3 to do3, decrescendo” was translated into a corresponding MIDI notes sequence, according to an arbitrary grammar (recursive syntax rules) and a dictionnary, calling LISP methods, that could possibly be redefined (see figure 1).
Figure 1. Generating a musical sequence by means of statements expressed in ”natural” lan-
guage
These basic gestures are meant to be articulated with each other. But unlike a plain combinative or juxtaposition, the change of a gesture within a sequence might have an incidence on the other gestures’ upgrades, upstream and downstream as well. For instance, an ascending-descending movement is different from an ascending movement followed by a decending one, since there is a common point (a pivot). It was appropriate to be able to apply the following principle: two juxtaposed gestures put side by side can be linked by a relation- established in a linguistical proposition - that modifies the instantiation of its own components. Therefore, in this same example, the pivot-note though belonging to both the ascending and descending stroke, should be produced only once, as long as the two strokes are juxtaposed and explicitly linked (see figure 2). In OM, it was appropriate to adapt the linguistic steps to a graphical musical description of music, comparable to the composer’s. For this, we developped a function (strait) that calls, if needed, either a human language interpreter or arbitrary LISP functions (”lambda” functions, possibly) that interpret graphic objects, notes, chords, temporal objects, lists and links, in complement to other linguistic indications.
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Figure 2. Generation
Figure 3. ”Strait”, the LISP function that enables to create the basic gestures
In Encore , a gesture could be defined by the ambitus, harmonic color, rythmic material, dynamic profile and the duration. The ambitus is made of two notes, a starting note and an ending note, represented in a ”chord” object that determines also the gesture’s type. If the ending note is higher than the starting one, the gesture is an ascending stroke, in the reverse case it is a descending thread, and if the notes are the same, the gesture is a repeated note. The harmonic color is given by a harmonic field, a list made of notes that will be played in a preferential way. If no harmony is indicated, like in figure 3, notes will be calculated without harmonic constraints. In the whole Disklavier’s score, the rythmic values are very quick and constitute the gesture’s ”grain”. If speed is very high, the impression will be of a gesture with a slight and very rapid ondulation. If it is slower, the gesture will have a more abrupt aspect. If speed is not regular but repeats a rythm with rapid values, this rythm will give the 101
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”grain” a special characteristic. The dynamic profile is given by the shades of every note in the stroke. Last, the duration of the stroke is determined by the object’s length when it is put in a maquette and becomes a temporal object. This is where the program creates the notes that correspond to the graphic or linguistic descriptions, and effects a ”gesture” according to its contextual and therefore temporal charecteristics. Figure 4 shows a gesture resulting from the datas of figure 3.
Figure 4. The ”Strait” function put into a maquette
Time in seconds is shown on the x-axis, and the y-axis has no significance. Here, the gesture lasts a little more than 2 seconds (figure 5). Each voice (channel) commands a Disklavier: channel 1 commands Disklavier1 (tuned normally) and channel 2 Disklavier2 (tuned one quarter of a tone lower).
Figure 5. The resulting transcription
If one of the datas used to construct this gesture is modified, the program will recalculate the stroke. This allows to vary a gesture upon one of its own charecteristics while maintaining all of the others. Figure 6 shows the ascending stroke in figure 4 if the speed of its notes is changed. Duration is the same (2 seconds/ 2 temps ` a 60 ), but the number of notes is doubled.
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Figure 6. Gesture of figure 4 with higher speed
If a harmonic field is specified (see figure 7), the notes in the stroke will be in part different.
Figure 7. Example of figure 4 with a harmonic color (here, an A spectrum)
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The program will write the notes between the ambitus’ two limits so as to fill the interval of time that is determined by the length of the temporal object and in accordance with the given speed. It will divide the interval between the first note and the last one in equal parts and the resulting notes will be approximated to a quarter of a tone. The harmonic field will modify this approximation in order to obtain as many notes that belong to the harmonic field as possible. The stroke has the same duration and number of notes as in figure 4 but the notes were approximated in a different way: the stroke goes this time through les harmonics 9, 12, 13, and 14 of a harmonic spectrum of fondamental Do (33Hz). If duration is lengthened by stretching the object in the maquette , the program adds automatically notes to the stroke in order to maintain the grain given by the notes’ speed (see figure 8).
Figure 8. Example of figure 4 stretched
The gesture has the same characteristics as figure 5 but has been streched graphically (click and drag) in the maquette to 1 additional second (see figure 9).
Figure 9. The resulting transcription
These last 3 examples are 3 different realizations of the same gesture. This way, a large variation of the 3 basic gestures (ascending, descending, repeated) could be reached, and once combined, juxtaposed and/or bound, these gestures could generate a lage variety of musical sequences. The combination could be done by superposing, juxtaposing or sequencing gestures. With superposition, the resulting gestures are simple but with a more complex harmonic and rythmic substance. 104
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In a maquette , sequencing gestures is different from simply juxtaposing them, because of the link between two ”Strait” temporal objects.
Figure 10. Multiple gesture (made by sequencing)
In sequencing (figure 10), as we have already seen, the properties of a gesture must be ”echoed” and taken into consideration while interpreting the following gesture, in order to achieve real binding, unify the resulting gesture and thus adapt every initial part of it. We also realized that it was necessary at times, depending on the nature of the bond, to ”reverberate” properties of upstream gestures in downstream ones. In other words, not only did we have to adjust the preceeding gesture in accordance with the following one, but we had to go backwards in the LISP chain of evaluation (we probably reached at that moment a certain limit in OM where in a maquette , the chain of evaluation depends on time-axis, from left to right)
Figure 11. Multiple gesture (made by juxtaposition)
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In order to make the modifications of a multiple gesture easier, the data is put together in a ”material distributor” (top most box in the maquette , figure 11) created graphically in OM , that determines - depending on the bounds - the starting and ending notes, harmony, rythm, and speed of every gesture, and their shades. Other boxes represent an individual gesture made with as many ”Strait” temporal objects. In the special case of identical starting and ending chords, the result is a texture of repeated notes within the same harmony. In the reverse case, when they are different, chords are interpreted by the ”Strait” function depending on graphic and/or linguistic descriptions, located in the ”patches” (temporal objects, represented here, figure 12, by the generated sequences).
Figure 12. Texture of repeated notes
In figure 13, the word motif is interpreted by the ”strait” function as a succession of notes that will form a pattern. This pattern is to be repeated as long as the temporal object , in the maquette , will be defined by hand and/or by the resulting interpretation (calculation). If several patterns with different speeds are superposed upon the same harmony, the texture will be different from the ones made with repeated notes. 106
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Figure 13. A texture composed by superposing different patterns, running through all the
notes of the chord at different speeds
By sequencing in succession the superposition of gestures, we were able to build bigger musical sequences. At the end of Encore , there is a long Disklavier cadence, made of maquettes nested into each other on several levels.
Figure 14. Maquette of the whole sequence
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The maquette of the whole cadence shows a succession of 10 objects corresponding to the 10 phrases of the cadence (see figure 14).
Figure 15. Maquette of phrase 1
Each phrase-object itself is a maquette that contains the sequencing of all of the phrase’s gestures. Each object-gesture in the maquette of a phrase is also itself a maquette that contains the stacking of the basic gestures (see figure 15). These basic gestures are temporal objects containing a strait module.
Figure 16. score trancription of phrase 1
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Thanks to the possibility of encasing maquettes into other maquettes on several levels given by OM, we were able to build complex musical sequences and thus compose all the Disklaviers’ cadence. The follow-up to this studio-work of creation, was to expand the ”Strait” tool, regardless of the properties Encore required. It was to develop a more general composition tool that would not only realize MIDI scores, but also musical sequences based on sound synthesis (CSound, Max-MSP...). This problem is wholly different in nature: the need is no longer to create a discreet approach such as MIDI encoding, but to integrate continuous data. In order to have a wider range and to be of interest to both instrumental music and electroacoustics, we have considered gestures as the basic elements of musical construction, because a note is nothing more than an amorphous and static point, whereas a gesture is already animated by movement. We therefore imagined a generalisation of the class note in OM, based on the notion of gesture. A class gesture has been defined, as a curve describing a course between an initial and a final state, like a change of state and a way to go through this change of state. For example, regarding the pitches field, it would be a sliding of pitch (upwards or downwards)and the curve (linear, exponential or any curve that can be described) to carry out this sliding. A new class ”gesture” has been defined in OM : it is not an augmented ”chord-seq” as with ”Strait”, but a special BPF (breakpoint function) with which several behaviour types are associated. The class note is thus expanded and includes the notion of gesture. A gesture object (a BPF describing each dimension) is assigned to each parameter of a note (pitch, intensity etc). When a gesture is defined by a horizonal line, it means this is a ”traditional” note. Access to the continuous domain enables us to expand this note, its articulations and developments by means of synthesis programs (such as CSoundor Max-MSP) and their related protocoles (SDIF or TCP-IP).
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Jean-Luc Herv´e Jean-Luc Herv´e was born in 1960. He studied composition at the Conservatoire de Paris with G´erard Grisey. He was composer in research at Ircam and has obtained several residences (Villa Kujoyama - Kyoto, Daad - Berlin). His orchestral piece, Ciels , was the winner of the Goffredo Petrassi prize in 1997.
Fr´ed´ eric Voisin Frederic Voisin was born in 1966. In 1980 he discovered the ancestor of the sea siren (Alitherium Schinizi) in an exhibit at the Natural History Museum of Venice. Before becoming a researcher in ethno-musicology at the LACITO-CNRS from 1989 to 1995, Voisin studied musicology at the University of Paris IV and Inuit linguistics at the Insitute National des Langues et Civilizations Orientals. He carried out research in central Africa with Simha Arom on the Aka Pygmies and then on Java, Indonesia. There he produced the first in situ musicological experiments using sound synthesis using a DX7 and computers he had brought along. Voisin has been a musical assistant at Ircam in Paris since 1995 in addition to taking part in artistic activities at CIRM and ArtZoyd. Frederic Voisin has worked on the computer production of several pieces in collaboration with the composers Daniel d’Adamo, Jean-Louis Agobet, Jean-Baptiste Barri` ere, Heiner Goebbels, Jean-Luc Herv´e, Horatiu Radulescu, Philippe Leroux, Martin Matalon, Emmanuel Nunes, Fran¸cois Paris, Roger Reynolds, Fausto Romitelli, Atau Tanaka, Kasper Tœplitz, Giovanni Verrando, and Iannis Xenakis. He has also collaborated with the choreographers Myriam Gourfink, Rachid Ouramdane as well as the producers Maurice Benayoun and Peter Greenaway. Since 2003, Frederic Voisin has been the head of research at CIRM in Nice where he is working on musical research and artificial intelligence (Neuromuse Project). 111
Navigation of Structured Material in ”second horizon ” for Piano and Orchestra (2002) - Johannes Kretz Abstract. Several aspects of computer aided composition (CAC) were combined in the realisation of ”second horizon” for piano and orchestra 1 : modelling of physical movements was used to generate organic, physically plausible gestures. ”Constraint programming” made it possible to shape these organic - but vague - gestures into precisely structured, consistent musical material with strong inner logic. The ”spectral approach” helped to define rules for obtaining ”well sounding” solutions from the given material and provided tools for composing microtonal pitches. Finally constraint programming again was used to implement some (basic) tools of computer aided orchestration. This article describes the promising potential of the interaction of all these techniques in the frame of the OpenMusic environment. The techniques presented highlight the fact that CAC is moving far beyond being ”algorithmic” or ”mechanical”. The approach of ”composition through interactive models”, as developed in the international composer’s group PRISMA 2 Helps to create structures that can carry ... emotions! ***
1
Challenges
One of the particular challenges of composing is (and always was) finding the balance between simplicity and complexity, or, what is even more difficult, the creation of a piece of art that can be perceived at various levels of attention, for example in such a way, that the most obvious level (the surface) can be understood and enjoyed easily without special knowledge (even intuitively), but other, deeper, less obvious layers of the work provide more subtle contents satisfying the more sophisticated tastes of connoisseurs. On the other hand, it turns out to be particularly difficult to formalize such a process of creation, where various structural layers of material from the surface to the inner structures have to interact permanently, and where various parameters (pitch, time) in various layers of complexity (melodies, chords, rhythmic cells, formal parts etc) influence each other. Finally the use of both, simple functional programming techniques as well 1
”second horizon ” was commissioned by the Swiss foundation ”Christoph Delz” as part of an international competition for orchestral works. 2 ”Pedagogia e Ricerca Internazionale sui Sistemi Musicali Assistiti” with Jacopo Baboni Schilingi, Hans Tutschku, Paolo Aralla, Nicola Evangelisti, Giacomo Platini, Michele Tadini, A. Sandred, Frederic Voisin, Kilian Sprotte, the author and many others. For further information see Baboni et al (2003).
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as the development of a complex rule-based interactive system of creation turned out to be useful.
2
Starting point
The basis of the whole piece is the dodecaphonic row shown in figure 1. It was composed with particular attention to its potential of being segmented into chords of a certain aesthetical quality. All the melodic and harmonic material of the piece is unfolded from this row, even the rhythmical domain is - although more indirectly - influenced.
Figure 1. Dodecaphonic row
3
Simple unfolding of material
In order to obtain an organic extension of the row, in order to let it ”grow naturally”in the domain of pitch (but in a way which avoids the triviality of simple copying/transposing as well as a periodicity of groups of 12 notes), the following simple (but nevertheless efficient) technique was used: For each ”repetition” of the row the list of intervals forming the row was rotated in such a way, that the first interval of the precedent version became the last interval in the current one (see figures 2 and 3). The continuous moving of the first interval of the row to the last place for each subsequent instance produces a permanent shifting between the ”true” beginning of the series of intervals (marked by ”i1”, ”i2”, ”i3” etc. in figure 4) and the apparent beginning of the series of notes (marked by ”r?” in figure 4). Therefore after hearing the row in its original form it seems to have disappeared, (because its ”head” - the most noticeable part, moved to the end), and then it reappears growing each time by one note (but always shifted in position), until the complete series appears again at the end (although transposed).
Figure 2. Beginning of the unfolding the row by rotation of intervals
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Figure 3. Patch for rotation of intervals
Figure 4. Complete unfolding of the row by rotation of intervals
4
Generating chords from melodies
Another ”simple” technique already used in many of the author’s compositions is the ”scrolling” through a melody (the dodecaphonic row in this case) for obtaining a ”family” of chords with strong similarities. A certain number of subsequent notes from the row (in this example 5) is always grouped into a chord. (In order to keep the number of notes in constant for each chord, the row is looped.) Adjacent chords always have many notes in common (in this example always 4 notes), which gives a strong coherence to the series of chords and lets the listener perceive the original row ”through” the chords. 115
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Figure 5. Patch (inside the omloop-Object) for obtaining chords by ”scrolling” through a series
of pitches
Figure 6. Result of the patch of figure 5 applied to the row (figure 1)
5
Simulation of physical movements to shape structured musical material
To obtain interesting gestures, which have plausibility as movements of physical bodies, a modelling of jumping rubber balls in a closed room, subject to gravity, wind, air friction, reflection etc. was used. By defining a vector of position (x and y coordinates) and speed (vx and v y ) for each ball and by updating this vectors in regular time intervals according to the influences, which position, gravity, speed, wind etc. have on each other, a simple but efficient model was developed. This was programmed in the Max3 environment in order to have interactive real time access to these movements. Finally the position data were recorded into text files for transfer into OpenMusic (see figures 7, 8 and 20). It is evident that a simple translation of the position parameters of these shapes into the domain of chromatic pitch would produce flat, rather unsatisfying musical results. While they showed to be useful to shape (or influence) the surface of music, other tools were needed to shape the inner, structural side of music in interaction with these curve (Kretz, 3
Originally developed at IRCAM, now www.cycling74.com
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2003).
Figure 7. Simulated movement of a rubber ball
Figure 8. Simulated movement of two rubber balls being attracted by each other
The pmc-engine , an OpenMusic library4 providing an environment for constraint programming proved to be the ideal tool for this task. First a search space of allowed chords had to be defined. In this case it was obtained by scrolling through the dodecaphonic row as described above (figure 6). The search space was composed by all inversions, octave permutations and transpositions of those chords. Additional constraints were applied as rules: The range of the piano should not be exceeded. Two adjacent chords should have not more the three common notes, but at least one. The shape of the rubber ball movement was implemented as heuristic rule . This means, that from all possibilities passing the (strict) rules the engine always chose a solution as close as possible to the ”ideal” shape of the jumping rubber ball (figure 7). Figure 9 gives an overview on the flow of information, figure 10 shows a possible result. It can be clearly seen, that the shape is not represented perfectly, and that some of the inner - structural - necessities results in compromises of the shape, especially the rule enforcing common notes between to adjacent chords. But exactly this interaction between outer and inner conditions of creation gives interesting, organic results.
4
¨ Based on PWConstraints by Mikael Laurson (1995) ported to OpenMusic by Orjan Sandred (1999)
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Figures 12 and 13 show the use of this ”jumping rubber ball arppegio” in the final ¨ score. The rhythm of the piano was generated again by the pmc-engine using Orjan Sandred’s wrapper for rhythmical constraint programming OMRC (Sandred, 2003). The pitches of figure 11 are grouped in various rhythmic cells of possible subdivisions of a quaver: 1 rest + 3 notes, 2 rests + 2 notes, 0 rests + 4 notes, 1 rest + 4 notes, 1 rest + 5 notes, 0 rests + 5 notes, 0 rests + 6 notes, 1 rest + 4 notes. Additional rules defined the favouring of subdivision changes from cell to cell and limited the complexity of the result.
Figure 9. Overview
Figure 10. Arpeggiated chords in a shape close to the ball’s movement (beginning)
6
Harmony and counterpoint
The following example is from the first tutti section of ”second horizon ”. Two layers of six voices each were generated. The search space for the lower layer was obtained from the first six notes of the dodecaphonic row (figure 14) by transposition, inversion, and 118
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Figure 11. Arpeggiated chords in a shape close to the ball’s movement
octave changes. Already in the process of generation of the search space (done with the help of another instance of the pmc-engine ) a certain amount of attention was paid to the sounding quality of the chords: only those octave transpositions of the mother chord were allowed, thus excluding undesired intervals (tritones or semitones in this example) between adjacent pitches (see figure 15). This chord material was then put together in a sort of choral by applying the following rules: The lowest note of each chord should always come from the melody of figure 4 (the expansion of the dodecaphonic row by rotation of its intervals), but transposed and constrained in a very low register (figure 16). Heuristic rules were used to express the following ”wishes” or tendencies. Preference was given to adjacent chords with 2 common notes, followed by chords with 1 common note and (with much less weight) with 3 common notes. Also, when deciding which chord to choose, the one with the biggest value for its smallest frequency difference between adjacent pitches was preferred. For each ”candidate” the frequency differences were calculated by using x->dx-object, and the minimum of this differences was used to decide, which chord would ”sound best” (least dissonant). This rule is certainly inspired by spectral thinking, that is interpreting pitches similar to the overtones of a spectrum. If the frequency difference between two notes is too little, it is hard to perceive an interval. Usually this happens when playing a small interval in the low register, which is perceived by most listeners as an unpleasant or dirty sound. The result can be seen in figure 17. Also the rhythmic design of this choral was done with the help of the smallest frequency difference as criterion: more dissonant chords were given a shorter duration, less dissonant ones a longer (figure 18). Finally a ”counter”-choral for the high register was created by combining those pitches not used in the hexachords of the low choral in order to get a dodecaphonic balance. This was done again with the help of the pmc-engine in such a way that certain intervals and chords between adjacent chords (tritones, minor seconds but also major/minor triads) were avoided and again the minimum of the frequency differences was as big as possible (figure 19). 119
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Figure 12. From the score of ”second horizon ”: application of figures 10 and 11
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Figure 13. From the score of ”second horizon ” (continuation): application of figures 10 and 11
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Figure 14. Chord being the first hexachord of the row
Figure 15. Beginning of search space of chords derived from the chord in figure 14
Figure 16. Bass melody (compare figure 4 after the first 11 notes)
Figure 17. Chord series on given bass (figure 16) using a family of chords (from figures 14 and
15)
7
Composing by interactive models
The following example (figures 20-22) starts quite similarly to the previous ones. A series of chords is ”guided” by the movement obtained from a physical modelling of a decaying pendulum, but a set of numerous strict rules ensure that the chords are connected by a certain inner logic: parallel chords are prohibited, the same chord can only be used after at least three different ones, the frequency difference between adjacent pitches as to be greater than 40 Hz. Heuristic rules include the preference of opposite or oblique movement of voices to voices moving in the same direction and again verify the number of common notes between adjacent chords. Finally another (strict) rule was added for prohibiting repeated notes, repeated melodic 122
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Figure 18. Rhythmical realisation of figure 17 in six voices
Figure 19. Dodecaphonic complement of figure 18
patterns or sequences in the highest voice. The ”appearance” of the latter rule is characteristic in ”composing through interactive models”. In contrast to the other rules, the necessity for this one was not foreseen or planned by the composer. But listening to the results generated (”suggested”) by the pmc-engine it was obvious that such a rule was essential. This shows the interactivity of the creative process: The composer formalizes his ideas into rules and wishes. The machine generates one or more solutions. Being confronted with these, the composer becomes aware of aesthetic problems and refines the rule system. The musical result is optimised through repeating this loop of interaction between man and machine. 123
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Figure 20. Simulation of the movement of a decaying pendulum
Figure 21. Series of chords following the shape of figure 20 (beginning)
Figure 22. Chords of figure 21 with dodecaphonic complement in between
8
Computer aided orchestration
Figure 23 shows the result of an experimental system for computer aided orchestration. In this example all the notes played by the piano (explained in the previous section, compare figure 22) should be spread in a pointillistic manner among all the woodwind and brass instruments (while the strings are playing a calmer layer of the four voice chords without the dodecaphonic complement). Here the search space for the pcm-engine consisted not of pitches or rhythms but of symbols representing the possible instruments. The search space was set up in this way that for each note only those instruments were considered, whose range made it possible to realize the corresponding note. The range for each instrument was defined in table 1. The following simple rules controlled the process of orchestration: a) Woodwind and brass instruments should not be used simultaneously in a chord. This was achieved by defining allowed sets of instruments and prohibiting a mix of elements of several sets (see table 2). 124
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Figure 23. Computer Aided Orchestration: section from the score of ”second horizon ”
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((d 5 n) (c 8 n)) (((c 4 n) (c 7 n)) (((c 4 n) (c 7 n)) (((b 3 n) (f 6 n)) (((b 3 n) (f 6 n)) (((e 3 n) (a 5 n)) (((d 3 n) (b 6 -)) (((b 2 -) (c 6 n)) (((b 2 -) (c 6 n)) (((b 2 -) (e 5 -)) (((b 2 -) (e 5 -)) (((c 1 n) (g 4 n)) (((b 2 -) (f 5 n)) (((b 2 -) (f 5 n)) (((h 1 n) (c 4 n)) (((h 1 n) (f 4 n)) (((a 3 n) (d 6 n)) (((e 3 n) (a 5 n)) (((e 3 n) (a 5 n)) (((f 2 n) (c 5 n)) (((e 2 n) (a 4 n)) (((d 1 n) (a 4 n)) (((a 1 n) (c 4 n))
picc fl1 fl2 ob1 ob2 englh clarB bclar1 bclar2 fag1 fag2 cfag hr1 hr2 hr3 hr4 tr1 tr2 flgh pos1 pos2 bpos tba
Table 1. Ranges of instruments
(setf
allowed-sets ’((picc fl1 fl2 ob1 ob2 clarb englh bclar1 bclar2 fag1 fag2 cfag) (tr1 tr2 flgh hr1 hr2 hr3 hr4 pos1 pos2 bpos tba))) Table 2. Sets of instruments for computer aided orchestration
b) Within such a set the order of instruments has to correspond to the order of pitches. This means for example that if flute, oboe and bassoon are playing a chord together, the highest pitch has to be played by the flute, the middle one by the oboe and the lowest by the bassoon, (which is not so far from the rules of traditional orchestration). In future this system could be expanded by additional, more sophisticated rules, preferring favoured instrument combinations, making decisions on the basis of information about the instruments formants or registers.
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9
Using constraint programming to improve musical material
While the previous examples showed complex interaction of rules for filtering solutions from a big search space, it sometimes turned out to be more efficient to compose by stepwise material optimisation. The following example was inspired by the famous ”endless glissando” by Roger Shepard, (an acoustical illusion created through overtones going down in parallel octaves with smooth fading). By repeating the ”scrolling through the dodecaphonic row” and transposing each of the resulting chords one semitone lower than its precedent, the strong coherence of the chords (originally sharing 4 of 5 pitches) allows the listener to clearly perceive the continuos chromatic decline. It is obvious that this processus cannot be continued for a long time without reaching a register, where the pitches of the chords cannot be perceived clearly any more. Therefore all chords with neighbouring pitches closer than 40 Hz were subjected to a recursive modification process, iteratively transposing low pitches up an octave until the final result passed this criterion (see figures 24-26).
Figure 24. Series of chords obtained by scrolling through the dodecaphonic row and transposing
the resulting chords each one semitone lower than the precedent
Figure 25. Improvement of the previous example (figure 24)
Figure 26. Improvement of the previous example (figure 25)
10
”Spectral prediction” technique
The last section of ”second horizon ”develops - to the author’s knowledge - completely new approach of linking harmony and melody, presence and future, spectral and structural thinking. The classical spectral school usually creates harmony by using the harmonic 127
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series (or parts of it) of a present fundamental pitch (figure 27 shows a melody with the harmonics 3, 4 and 5 added to each fundamental). Differently or additionally to this approach particularly interesting results were obtained by adding multiples of the coming, future fundamental to the current bass note (see figure 28). In this way the actual chord already carries some ”hidden” information about the coming fundamental, which can be ”felt” by the listener. In this way the current and the following chord are always syntactically linked allowing the listener to develop intuitive expectations about the future of the series of chords, and so making him perceive the music as logical. In particular, the simultaneous use of the classical spectral harmony and this ”spectral prediction”-technique (i.e. playing the pitches in figures 28 and 29 together), gave very satisfying results.
Figure 27. Melody with added harmonics 3, 4 and 5
Figure 28. Same melody like figure 27, but with ”spectral prediction” harmonies
Figure 29. Details of the ”spectral prediction” technique
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11
Conclusions
With the exception of two sections, the beginning (m. 1-10) and a sensitive, calm moment in the centre of the work (m. 231-273), almost the whole piece was ”generated” with the help of the OpenMusic environment and exported directly into score editing software. At no stage of the creative process were paper and pencil needed. Certainly the material from OpenMusic was complemented by the composer through additional - supplementary and contrasting - musical elements and voices. But it is most especially the interactive use of the ”constraints engine” that shows that musical material produced by software can go well beyond mechanical sounding results. One of the difficulties, which became evident during the work on this piece, was the need for a more structured representation of musical data. Handling the parameters independently, (like lists of midicent values for pitch, which are ignoring the existence of rests, lists of fractions for durations, where rests are represented as negative numbers etc.) made it rather difficult for parameters to interact. In future a rich, hierarchically organized data structure for notes (a bundle of information containing many parameters like pitch, duration, loudness, voice number, position in bar, expression marks, harmonic context, etc.) should help to create even more ”intelligent” rules.
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Bibliography [1] Baboni Schilingi, J. and al. : PRISMA 01. Euresis Edizioni, Milano, 2003. [2] Kretz, J. : Continuous Gestures of Structured Material. published in Baboni et al. (2003), p.185ff. ¨ [3] Sandred, O.: Searching for a Rhythmical Language. published in Baboni et al. (2003), p.185ff.
Johannes Kretz born 1968 in Vienna, - studies of composition at the Vienna Music Academy with F.BURT and M.JARRELL, studies of pedagogy and mathematics at the University Vienna, - 1992/93: studies at IRCAM, Paris, development of a software-environement (”KLANGPILOT”) for sound synthesis - 1994: co-founder of the NewTonEnsemble specialised on electronic and instrumental music, - 1994-2003: teacher of computer music at the International Bartok Seminar in Szombathely (Hungary), - numerous lectures on computer music in Austria and Germany, presentations at international conferences, various workshops at the Music Academies in Stuttgart and Hamburg and at the National University for Arts in Seoul (Korea), . - 1996-2001: teacher of music theory and composition at the Vienna Conservatory, - since 1997: teacher of computer music at the Academy in Vienna, since 2001 also music theory, since 2004 assistant in the composition class of M. JARRELL, ¨ - since 2001: board member of several Austrian composers unions (ISCM, OKB and ¨ OGZM), - member of the international composers group ”PRISMA” (centro tempo reale, Florence/Italy) on computer music and musical research - numerous performances in Austria, Germany, France, Poland, Hungary, Argentinia, Turkey and Korea, - numerous broadcasts in Austrian and German radio, - commissions of works from Konzerthaus Wien, Klangforum Wien, Ensemble On Line, Vienna Flautists, quartett22, Internationale Lemgoer Orgeltage, Haller Bachtage, Triton Trombone Quartett, Wiener Kammerchor, - numerous grants, - prize at the competition for orchestral composition ”Stiftung Christoph Delz” (CH, 2002), K¨orner prize Austria 2004, composition prize for an orchestra work from the Austrian government 2004.
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When the Computer Enables Freedom from the Machine (On an Outline of the Work H´ er´ edo-Ribotes)1 - Fabien L´ evy Abstract. In some cases, when the musical process is sufficiently verbalised and formalized, the computer allows the composer to concentrate on the music and to spend less time on the calculation. I will present a very simple example of a technique used in my orchestral work H´er´edo-Ribotes for viola solo and fifty-one orchestra musicians, and illustrate the aesthetic ideas underlying this piece. I will also show different cases in which the computer was a good musical aid in creating this esthetical meaning, and other cases in which the work, on the contrary, was better done by hand. *** As far as I’m concerned, it is extremely difficult for a composer to limit a musical intention to formalised and verbalised procedures: aesthetic effect is more valuable than technical skill. Apart from the fact that an intention cannot always be rendered explicit, a technique’s effect is interesting only if one reaches beyond, so to speak, the kitchen utensils in order to engage with the chef’s aesthetic, and even with his political obsessions. With this in mind, I will present my personal use of the OpenMusic software, guided by two considerations. The first is epistemological, and I will show that rather than restraining the composer to making purely technical considerations, the use of computers in musical composition enables him/her to free him-/herself from such limitations. The second consideration is aesthetic, and I will attempt to describe succinctly the artistic reflections that motivate my computer-based procedures presented here.
1
A generation of paradox
The composers who, like me, were born around 1968 are neither members of the generation who were in their twenties at the end of the Second World War (Boulez, Ligeti, Stockhausen, Xenakis, et al) nor of the generation for whom the events of 1968 were defining moments of their adolescence (Ferneyhough, Grisey, et al). This accounts for one of the traits of my generation: that we are generally detached from the attitudes of refusal of the past that marked the former generation or of systems that distinguished the latter. Many of us, however, have inherited from our ”musical grandparents” the 1
Thanks to Christian Pinawin for the help in the translation into English.
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desire to construct new grammars and share with our ”parents” the dream of developing new concepts that go beyond the sign and beyond analytic thought2 . But in this socalled ”postmodern” era, some of us are wary of notions of stylistic progress, preferring instead notions of sincerity and originality, just as we are wary of the idea of universal perception, favouring instead the idea of cultural listening conventions being interrogated and deconstructed. Personally, I prefer paradox to forms and processes that are overly demonstrative. In fact, on the level of technique alone, I was exposed to computers at an early age3 . However, perhaps because I became familiar with computers at an early age, I vigorously strive to demystify the contribution of technology to the creative act, composing everything by hand, and mentally.
2
Transparametric techniques
One of the recurring questions in my work deals with the closure of analytic thinking and perception4 . From 1996 onwards, I began to think hard about the notion of transparametric musical inflexion – research into the smallest musical tensions, where the action would be detected by the senses but not be intelligible or analysable, and in particular, not reducible to a transformation according to any of the traditional parameters of Western music – duration, pitch and intensity. The challenge was to musically construct moments of presque rien and je ne sais quoi , to use Jankelevich’s expressions. I borrowed, for my instrumental music, an acoustic principle which was associated with analogue samplers, bringing together in the same relation the frequency of transposition and the pulsational speed of a sound. This technique was already used by Karlheinz Stockhausen (Kontakte 1960; see also his article Wie die Zeit vergeht , 1957), but with a different objective – so that the serial differentiation of pitches reflects that of rhythms. In my work, this principle allows, on the contrary, the concealment of the parametric origin of a phenomenon: an infinitesimal variation in pitch, for example the transposition of a quarter-tone of a musical element, would be systematically accompanied by a change of the same order to the other parameters, particularly to the speed of rhythmic repetition of this element (figure 1). The accumulation of these tiny inflexions applied to all parameters in similar ratios would create a tension without one being able to perceive its objective cause. It should be made clear that in order to develop this technique 5 and to assess its 2
Analytic thought is characterised in Western music in particular by a separation of musical parameters in rhythm, pitch, and duration, by a reduction of complex, continuous phenomena to finite, discontinuous alphabets, by functional thought, and consequently by considering the sign in a combinatorial way. 3 When I was eleven, I was playing on a elementary ZX80 Sinclair computer; a few years later I performed my first experiments in computer music with the Yamaha CX5M musical computer and in programming (BASIC, and then PASCAL). I pursued advanced coursework in the sciences at the same time as my studies in music. 4 Perception and writing are closely linked, and to work on the closure of one has implications for the deconstruction of the other. We think according to how we perceive and represent the world; likewise, we perceive according to how we think, for example by focusing in the West on the fundamental – or tone – of a complex sound, by separating the parameters of listening, by instinctively hearing tonal functions, etc. 5 The technique itself remains somewhat naive; but seen from a strictly algorithmic point of view, so too do the techniques of derivation of dodecaphonic series, the production of spectra or the canon.
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Figure 1. Technique of transparametric musical inflexion: extract from Les deux ampoules d’un
sablier peu ` a peu se comprennent (1996), for amplified solo harp (Billaudot publisher)
aesthetic consequences, it was initially necessary to work on it manually, determining what it put at stake as well as its musical consequences due to the painstaking slowness of transcribing first onto graph paper and then to music manuscript paper. It was only when this technique was properly verbalised and formalised, when its aesthetic stakes were defined, and when my research began to shift focus to other techniques, making it necessary that no more time should be spent on calculations of transparametric pulsations that I decided to program the technique in OpenMusic.
Figure 2. Formalisation of the technique of transparametric musical inflexion: patch pro-
grammed on OpenMusic software (at left) and example of a result (at right, sketch from H´er´edoRibotes , for solo viola and 51 orchestral musicians, mes. 210 )
3
Passage to the machine
The formalization of such a technique on OpenMusic raises numerous interesting issues. In the pieces that followed Les deux ampoules d’un sablier peu `a peu se comprennent , I focused more upon the ”styling” of the cloud of points obtained by the technique of transparametric inflexions. The task was to give form and colour to each of the tiles of the mosaic, so that one’s perception would be lost between totality and detail. This reflection on confusion is a prior step in the deconstruction of analytic thought in music. So I needed a simple, effective tool that allowed me to create the cloud of points and their different inflexions and to hear them immediately, like a composer searching for and selecting chords at the piano. OpenMusic, with its musical interface, its capacity to hear 135
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immediately in quarter-tones, its double representation of music – metric (in the form of voice ) and proportional (in the form of chordseq ) was the ideal tool. The other noteworthy property of OpenMusic is its structure in patches of patches, in abstraction of abstractions, very close to a composer’s thought modes: once a technique is established, the composer reuses it often in slightly modified configurations or integrates these configurations into more extensive techniques. The capacity to transform a patch into a functional abstraction, that is, to transform certain data into variables in OpenMusic, and the possibility to insert a patch into another encourages this compositional practice.
Figure 3. Combination and abstraction of Patches in OpenMusic: sketches for H´ er´edo-Ribotes ,
for solo viola and 51 orchestra musicians (mes. 169 `a 219)
4
On the utility of manual labour
Once the cloud of points has been calculated by the computer, one must evidently render it musical – in particular, one must style it, orchestrate it, give it rhythm, and – should the occasion arise – make local modifications. At this stage, Kant , an OpenMusic’s library that permits the quantification of a chord sequence (such as the one illustrated in Figure 2) in rhythmic notation and traditional metric, would have proved effective. However, I prefer to perform this transcription/quantification by hand, despite the slowness of the work, printing the chord sequence onto graph paper and then copying it again slowly. In fact, it is this manual operation that permits me to understand, to control – in 136
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short, to listen to this primary material with my inner ear, in order to render it musical subsequently. This technical presentation of a use of OpenMusic will appear naive to some. The applications of this software can be more complex, in my personal use (calculation by OpenMusic of ”first spectra”, calculation of ”iterated harmonic transpositions”, representation by ”vectors of Tanner ”, software Pareto)6 . The issue here, however, is to outline the stages that proceed from the elaboration of a technique that arose from aesthetic preoccupations up to the point of its formalisation and ”normal” - almost normative application. An additional concern here is to show that in a simple case, even when the formalisation of the patch is easy and makes the work less arduous, it is more important to make use of the slower pace of pen and ink, and manual calculation. OpenMusic is an extraordinary tool for symbolic calculation of the musical thanks to its interface as well as the unmatched freedom it affords the composer from certain constraints imposed by calculations, allowing him to concentrate better on musical quality. By way of conclusion however, let it be clear that OpenMusic remains a tool for calculation of classical musical categories (pitch, duration, dynamic, parameters midi) that arise from categories of western musical writing established by Boethius, Hucbald de Saint-Amand, Guido d’Arezzo and Franco of Cologne between the sixth and thirteenth centuries. With the appearance of recording technologies at the beginning of the twentieth century and of its deployment as archi-writing , to use Derrida’s expression, from the ¨ and of electro-acoustic music, complex sound 50’s on by composers of musique concr Ete has become an essential category of recent music. Today, numerical means of increasing capability open the way to a symbolic approach to thinking about complex sounds, which still lack means of clear and ergonomic semiotic representation for composition (L´evy, 2002). One can hope, nevertheless, that in the near future a tool for ”the composition of complex sound” will appear that brings together the possibilities of sound transformation software such as Protools , Max , or Logic Audio and the capacities for high-level symbolic calculation such as OpenMusic.
6
Pareto – [Patch d’Analyse et de Resynth`ese des Echelles dans les musiques de Tradition Orale] (Patch of Analysis and Resynthesis of Scales in Oral Tradition Music) is software programmed on OpenMusic that aids in the determination of pitch scales in the musical repertoires of oral traditions. Once the chart of virtual fundamentals from a sound file has been extracted by software such as Diphone, Audiosculpt, etc. and imported into OpenMusic in the form of a text file, Pareto evaluates the average scale of the motif with statistical tools of averaging and time smoothing. Then, in order to confirm that the average scale thus determined makes sense to the musicians, it is possible in Pareto to transform the initial sound file by microtransposition via SVP according to precise hypotheses about the scales (hypotheses of different scales, a hypothesis calculated to confirm by auditory consent, ”placebo” scales, etc), in order to offer it to the musicians again. Pareto was used for the first time in July 2000 in Cameroon, in the course of an ethnomusicological mission with the Bedzan pygmies. More information on http://membres.lycos.fr/fabienlevy/Pareto.html
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Bibliography [1] L´evy, Fabien : L’´ecriture musicale ` a l’`ere du num´erique . Culture & recherche n 9192, Musique et son: les enjeux de l’`ere num´erique, Minist`ere de la Culture, mission de la recherche, July 2002. ◦
[2] L´evy, Fabien : complexit´e grammatologique et complexit´e aperceptive en musique. Etude esth´etique et scientifique du d´ecalage entre la pens´ee de l’´ecriture et la perception cognitive des processus musicaux sous l’angle des th´ eories de l’information et de la complexit´e. Ph.D in music and musicology of XXth Century, Ecole des Hautes Etudes en Sciences Sociales, Paris, February 2004. [3] Stockhausen, Karlheinz : Wie die Zeit vergeht . in die Reihe, T.III, Herbert Eimert ´ed., Vienne, 1957.
Fabien L´ evy Fabien L´evy was born in December 1968 in Paris (France). He studied composition with G´ erard Grisey at the Conservatoire National Superieur de Musique in Paris. Parallel to his compositional activities, he was awarded a Ph.D. for his work on the complexity of musical processes at EHESS and CNRS and has written numerous theoretical articles. He was resident in 2001 in Berlin for the DAAD Berliner-K¸nstlerprogram, and in 2002 in the Villa Medicis / French academy in Rome. His orchestral work H´er´edoRibotes was nominated at the International Rostrum of Composers (2002) and in 2004 he won the Foundation Ernst von Siemens F¨orderpreis for Music. His works for soloists, chamber music, ensemble, orchestra (used as a large ensemble of soloists) or computer, have been performed across Europe and the United States. His instrumental works are published by Billaudot. He is currently living in Berlin (Germany), where he teaches orchestration to composition students at the Hanns-Eisler Hochschule f ¨ ur Musik. Software PARETO downloadable on: http://membres.lycos.fr/fabienlevy/Pareto.html
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Some Applications of OpenMusic in Connection with the Program Modalys - Paola Livorsi Abstract. The basic idea behind Os for male voice and electronics (realized at Ircam in 2001-2002) is the production of resonances: partly produced by vocal soundfiles exciting Modalys objects (e.g. simulation or basic models of percussion instruments or their parts), partly by other soundfiles. The vocal soundfiles were recorded with Nicholas Isherwood and Armelle Orieux. They comprise both sung examples and readings of excerpts from Saint-John Perse’s poem Vents1 , on which the piece is based. ***
1
Introduction
OpenMusic2 has been important throughout the whole work, for preparing part of the material, taken from vocal soundfiles (from Ohnfad for female voice and electronics 3 ), and analysed with AudioSculpt; for collating and examining data, and for calculating interpolations between harmonics. Its usefulness lay mostly in amplifying and refining the possibilities of the processing afforded by Modalys 1.8.1. The piece makes use of both realtime interaction and prepared soundfiles, in both cases triggered by the performer, via a Midi device. After to a short introduction, the piece is made of various stages of voice-Modalys object interactive events, from simple ones (played by Max/MSP, through the object resonators∼) to more complex, synthezised sounds. In this case the OpenMusic library OM Modalys 1.0 plays a central role 4 . At the same time, the material used to build the objects evolve from dry (e.g. cork) to resonant ones (various kinds of metal, such as iron, bronze and silver); the object types change accordingly, starting from simple strings and moving up to rectangular and circular plates. The two types are then blended into hybrids, morphing into each other, or combining their characteristics to form a ”super” dual-material ob ject (e.g. a circular plate with a spectrum with the combined characteristics of more than one material). In this case the two objects used to build the hybrid needed to be of the same type (e.g. two strings or plates, and so on). 1
Perse, S.-J. (1960), Vents, Gallimard, Paris. Extracts: II, 3, pp.15-17; I, 6, p.22. The version referred to here is OM 4.0. 3 Realized in 2000 at CCMIX, Centre de Cr´ eation Musicale Iannis Xenakis, Paris. 4 I gratefully acknowledge the work of Mauro Lanza, who created this feature and familiarized me with it. 2
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Another progression is carried out during the concert diffusion: seven speakers are used (three speaker pairs around the room plus one on the ceiling), a front stereo pair (for the voice onstage), moving through various configurations of the seven channels; this especially concerns the realtime part, where the gestures are more obvious.
2
Real-time resonances
A Modalys object can be used in realtime interactions if reduced to a single point, that is, simplified so as to be one-dimensional; this makes it possible to preserve the physical characteristics of the material, while at the same time reducing the amount of data needed. The data is collected in a Max coll, and eventually played by resonators∼. For example, in the first part of Os , at event no. 5, an iron clamped-circular-plate is struck by the onstage voice. The Modalys script defines the material and the pitch, and then saves the object as a single point. Next step the coll is extracted, with the library OM Modalys 1.0 function for-msp-resonators (see figure 1), which makes it possible to choose the resonance source in the object: an object that contains 200 modes for example, in order to generate a reasonably ”harmonic” sound, requires a value around 100 (i.e. a centre value. As always in such cases, only experimentation and listening will yield the right settings. In the present case, a value of 45 gave an interesting result).
Figure 1. Passage from the single-point object to the coll file for Max/MSP with the library
OM Modalys 1.0
The file thus obtained has three orders of values (frequences, bandwidth and amplitudes), as well as a mass of data that can be easily filtered and converted into the right format using OpenMusic, ready to be injected into a coll. Here is an example from a Modalys script (event no.5) obtained with the save-object function:
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@ geometry info: clamped circ plate r points = 10 Modal data for Modalys object: number of modes: 200 number of points: 200 freq0 Hz: 49.00000000 abs0 1/s: 1.20216090 freq1 Hz: 101.97498122 abs1 1/s: 1.20935901 freq2 Hz: 101.97498122 abs2 1/s: 1.20935901 freq3 Hz: 167.28689844 abs3 1/s: 1.22518642 freq4 Hz: 167.28689844 abs4 1/s: 1.22518642 freq5 Hz: 190.76130153 abs5 1/s: 1.23275089 freq6 Hz: 244.76442865 abs6 1/s: 1.25391866 freq7 Hz: 244.76442865 abs7 1/s: 1.25391866 freq8 Hz: 291.76326374 abs8 1/s: 1.27661322 freq9 Hz: 291.76326374 abs9 1/s: 1.27661322
phi points = 20 @
0.14514700 0.13701389 0.12409865 0.10731958 0.08788252 0.06720917 0.04685580 0.02842945 0.01350962 0.00358314
This is an example using the same file from the Modalys library: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
49.0 101.97498122 101.97498122 167.28689844 167.28689844 190.76130153 244.76442865 244.76442865 291.76326374 291.76326374
0.06720917 -0.01291711 0.12874027 -0.13967415 -0.01401416 -0.07748765 0.01363864 -0.13593152 0.00513917 -0.05122025
1.2021609; 1.20935901; 1.20935901; 1.22518642; 1.22518642; 1.23275089; 1.25391866; 1.25391866; 1.27661322; 1.27661322;
Figure 2. Filtering data with OpenMusic
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This text may yet be filtered by OpenMusic, to reduce the number of decimals to a value below 6, to allow Max/MSP to properly process the data flow (see figure 2). Event no. 7, figure 3, makes use of string resonances in realtime, as well as no. 1 (cork string)5 , this time combining iron, silver and bronze materials, in a richer multi-channel configuration.
Figure 3. Os for male voice and electronics (2001-02), real-time events no.7-11
The two more significant realtime events are no. 7-11, figure 3 and 16-21. In both cases the text refers to ”forces” (e.g. wind, but also to more abstract energies) to ”flourishing” (prosp´erer ) and to ”spreading” (propager ), culminating at event no. 23 (toute col`ere de la pierre et toute querelle de la flamme ); in this section realtime resonances are combined with more complex soundfiles, which eventually dominate the other elements. The resonances are still rather light and simple in event no. 7 and following, but they become richer and richer until no. 21, where a dual-material object is used in realtime. In this case, after saving the two objects (as seen above) they can be imported into an OpenMusic patch, via the Modalys library, and their characteristics can be combined; the resulting object is richer and denser, in this case combining frequencies from a bronze clamped-circular-plate with bandwidths and amplitudes from an aluminium one. The last section of the piece uses realtime objects as well, this time rectangular and circular plates made out of skin, making deeper, wider resonances possible, in addition 5
Numbers in rhombus refer to real time events, in circle to reverbs, in square to soundfiles. The score is available on request at the Finnish Music Information Center (www.fimic.fi).
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to a new, warmer timbre. The text refers to ”scattering” (disperser ) and ”lacerating” (lac´erer ): this extract from Vents is essentially about opposing forces leading to final destruction; but it also tells of a release of energies, not necessarily negative ones, capable of bringing about the birth of something new, by preparing a new space. In order to obtain good results this technique requires a fair amount of processor power; the maximum number of modes, to balance out quality sound and processor cycles, is around 300, less if a large number of colls are used in rapid succession.
3
Working soundfiles with the Modalys library
The Modalys library, now has a new version 6 making it possible to efficiently connect the two programs, widening and refining Modalys’ possibilities while at the same time making it easier to use. Combining vocal soundfiles and objects is simple, the objects being the same as those used in realtime; next, a second, female voice is used in conjunction with the male one, for example two soundfiles may be used simultaneously to excite an object (event no.15, figure 4).
Figure 4. Events 15-18
Again, the simplest interaction consists of exciting an object by voice (in most cases a mono or stereo soundfile): but in this case Modalys and OM give greater control over, 6
The new library version makes this procedure much simpler
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as well as differentiation of, way the sound evolves. Typically a richer sound is obtained by combining two instrumental types, using a hybrid (not yet possible in realtime). OM enables the user to control parameters more efficiently than by hand, in Scheme 7 : e.g. the access envelopes which in Modalys are the point(s) of contact between player and instrument (simulation of a plectrum, etc), and the microphone position point(s). Other parameters that may be controlled by OM are synthesis time (e.g. duration of resonance), name and length of the soundfile, and so on. Another important advantage in controlling access with OM is the possibility of maintaining their movement throughout the sound, for example using a random envelope, which gives a richer result. These examples generally use mono soundfiles, but stereo or even multichannel soundfiles can be exploited by increasing the number of accesses and other parameters. First the Modalys file must be prepared: the object is created, then the parameters intended for processing by OM are exported with the function export 2OM; this makes it possible for OM to load the file (through the Modalys Library function get-mosparameters). In this way a new class is created, which can be dragged from the folder User (in Packages) and displayed in the OM patch with all its characteristics. It can be sent via inputs and outputs. This is the basic preparation required for any Modalys file data that is to be processed in OM. Here is the procedure extraction from the preliminary Modalys file, using the export2OM function: (export2OM ’((access-env env 2 ”access-env”) (listen-env0 env 2 ”listen-env0”) (listen-env1 env 2 ”listen-env1”) (sfname string nil ”name of sf”) (sflength number nil ”length sf”) (synth-time number nil ”time of resonance”))) Extract from the final Modalys file, with a part of the access random envelope: (define access-env (make-controller ’envelope 2 (list (list 0 0.2896651022797322 0.0908634551271315) (list 0.2915204383796462 0.31293824977942974 0.09440941172674323) (list 0.3148427421782962 0.3434790739590433 0.14632212124212246) (list 0.6271550746711997 0.3287648616816715 0.197080263919739) (list 0.7129107505286313 0.31194877272057675 0.19123511318479822) (list 1.1984812810467207 0.21228409317901742 0.16405085594348906) (list 1.432428384601005 0.28785242137253353 0.13269917529711484) (list 1.6964336544301988 0.25413045827291614 0.13143346991789379) (list 2.0600987094661196 0.32732066143890587 0.14597496441879437) In this example both the play function and the object access are controlled by a random envelope, created by the OM function brownian1 (simulation of the brownian motion, from the library OMAlea, see figure 6; the random envelope boundaries are 7
The programming language used in Modalys.
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Some Applications of OpenMusic in Connection with the Program Modalys
written so to approach values 0 and 1 without actually reaching them (which in this case Modalys would refuse). The library function synthesize-for-modalys makes it possible to control some interesting parameters, such as sample rate and number of channels. At the end of the process we have a new Modalys file (located in the modfolder, inside the main OM folder where the application is), containing both the parameters of the previous file and those controlled by OM, which can now synthesize the sound (figure 5).
Figure 5. Synthesis of a sound with accesses moving in time
Figure 6. Simulation of the brownian motion (sub-patch of figure 5)
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The same procedure has been applied to obtain soundfiles where two voices (e.g. two mono soundfiles) strike the same object (in this case a bronze clamped circular plate): this time the patch structure is doubled, each mono soundfile referring to a dimension of the object (see figure 7).
Figure 7. Two sound files hit the same object, with moving accesses
Example from the initial Modalys file, with the two sound controllers: (define sf1 (make-controller ’sound-file 1 0 (const 44100) sfname0 0 sflength0 30)) (make-connection ’force ccpl-bronzo-hit1 sf1) (define sf2 (make-controller ’sound-file 1 0 (const 44100) sfname1 0 sflength1 30)) (make-connection ’force ccpl-bronzo-hit1 sf2) (define ccpl-bronzo-out (make-access ccpl-bronzo listen-env ’normal))
The same brownian function has been used to create an envelope for the hybridization of an object, in this example morphing from an aluminium clamped circular plate into a brass string: the object is once more struck by the voice (this time the male one), the technical procedure being far less complex, but still musically effective (see figure 8). 148
Some Applications of OpenMusic in Connection with the Program Modalys
Figure 8. Synthesis of a sound with a hybridation envelope created by OM
A yet richer way of working with soundfiles and hybrids is to focalize on material that does not change with time, but that has a richer timbre: OM makes it possible to superimpose the characteristics of two objects of the same kind made out of different materials, and obtain a third object, which can be excited by soundfiles, as seen above. Here it is of interest to filter the object, enhancing the harmonics, which are an important element in the work. As can be seen in the example below, once the objects have been saved in Modalys, OM can import and display them as classes: the next step is to connect the two elements, by using the frequencies of the former with the amplitudes and bandwidth of the latter; exploiting two objects that are of the same type but made of different materials generates a stable hybrid, in which the absence of temporal evolution is compensated by richer harmonics and timbric presence. This can be increased and controlled by adding a filter, i.e. a text file with certain frequencies injected into the object (see figures 9 and 10). It is interesting that in this manner rather heavy objects (up to 300-400 modes) can be created and processed, even if with some reservations: importing them may be slow and it is better not to save the objects’ icons in the OM patch, so as avoid overloading the programme. The same procedure can be used in combination with a soundfile and access structures as seen above: the number of accesses and of channels may be increased (in the first example up to 4 accesses and 2 channels, in the second up to 8 accesses and 4 channels, see figure 11). In the following examples other soundfiles have been employed, respectively a percussion sample (bˆ aton de pluie ) and a concrete sound (the crackling of fire); 149
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Figure 9. Creation of an object made of two different materials
Figure 10. Sub-patch of figure 9
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Some Applications of OpenMusic in Connection with the Program Modalys
both choices have to do with themes and materials in the poem: fire and wood appear frequently, together with iron, and other natural elements. Perse’s world bristles with materials, sounds and odours, as well as images: for me this was a powerful incentive to realize the piece with Modalys.
Figure 11. Object made of two different materials, with moving accesses
4
Vocal techniques and object interaction
So far we have seen a few examples of interaction between soundfiles and instrumental models, the vocal soundfiles mostly consisting of spoken or sung material. These can be further divided into spoken or whispered voices, isolated phonemes and sung examples, requiring different techniques. An important reference was Nicholas Isherwood’s research on vibrato techniques8 , such as throat tremolo, which I used in some parts of the piece (regarding the electronic part, please see above, event 23, figure 12). 8
Isherwood, N. (1994) Le Vibrato dans le chant contemporain . M´ emoire de DEA Musique et musicologie du XX`eme si` ecle, Paris (with an essay by LARGE, J., An Air Flow Study of Vocal Vibrato ).
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Figure 12. Event no.23, vibrato techniques, random wide vibrato
Not much needs to be said about the first category, except that spoken (or whispered) soundfiles are easy to use and are generally effective, sometimes dissolving into the texture of the object’s resonances, sometimes remaining distinct (obviously this depends on their respective frequencies). An interesting case is that of phonemes: for this project I recorded plosive consonants (such as ‘d’, ‘p’ and ‘k’, which play an important role in Perse’s verse), in order to generate maximum resonance. The material was then processed by Modalys, using a wrought iron rectangular plate hit by the phoneme ‘k’: the result is an interesting mixture of percussive but nevertheless vocal sound, subsequently used in vertical combination, forming a kind of a chord (see event 22). Phonemes also play an important role in the realtime part: for example in the first section of the piece, where ‘s’ and ‘d’ (from os and discorde ) go directly to strike the virtual objects (a cork string in event 1 and an iron clamped circular plate in event 5). The quasi glissando technique (written in microtonal pitches in the score) is used a lot in the piece, to create a vocal style close to spoken language: this was also the point of departure from which the duration values were derived, on the basis of the number of syllables in Perse’s poem. The numerical structures were then used throughout the work. This technique was applied more directly to resonance in the final section, in combination with the skin instruments: here too the amount of energy, and the subtle frequency variations generate a rich response in the realtime objects, in this case circular and rectangular membranes. Vibrato has an important place both in the first and in the last part of Os , first appearing in the solo (see figure 13). As a vibrato that varies in amplitude and width, it becomes important in event 23, the last soundfile in the piece before the final, realtime part. 152
Some Applications of OpenMusic in Connection with the Program Modalys
Figure 13. Vibrato techniques, throat tremolo
In the first section of Os two types of vibrato are used: the tremolo, made up of a regular swaying movement, almost one tone wide (but still perceived as a single pitch) 9 ; and the throat tremolo (in French ’balancement’), where the swaying movement, generated by the glottis, is irregular and is accompanied by strong intensity variations 10 . As seen above, in event 23 male and female voices are used in combination, where the text reads elles ´epousaient toute col` ere de la pierre et toute querelle de la flamme 11 (they - e.g. the wind forces - married the anger of stone and the quarrels of fire): with the image of fire, the voice onstage executes a wide throat vibrato which is a continuation of the vocal style of the recorded voices. This vocal technique generates a great amount of fluctuating energy, provoking colourful variations in the resulting soundfiles.
5
Conclusion
As mentioned earlier, the present article is only a rapid survey of what can be achieved by connecting OM to Modalys. Os has been an important experience for me, one that I wish to develop further. Os is intended to be a part of a larger cycle of vocal works on Perse’s poem Vents , Spazi (for vocal ensemble – five voices, and electronics 2000-2005 12 ). Spazi is nevertheless a work-in-progress, where I would like to explore the many possibilities of interaction between human voice and machine. Program interaction seems to me especially worth developing, providing as it does subtler ways to widen musical expressiveness.
9
Ibid., pp.43-45. Ibid., pp. 51-53. 11 Perse, S.-J. (1952) Winds, transl. by Hugh Chrisholm, Pantheon Book, The Bollingen Series, New York. 12 Premiered in Helsinki on June 3rd 2005, Ring Ensemble, Prisma expert meeting 2005. 10
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Paola Livorsi Paola Livorsi, who is a free-lance composer, was born in Italy in 1967, and has lived in Helsinki since 2001. She studied composition in Turin, Lyon, Paris (at Ccmix in 1999 and Ircam in 2000) as well as Helsinki. She graduated in music history in Turin under Giorgio Pestelli in 1994. Livorsi’s works have been performed at several festivals, in Turin (Settembre Musica 1998), Paris (Agora 2002), Rome (ControCanto 2002), Helsinki (Musica Nova 2003), Saarbr¸cken (Musik dem 21. Jahrhundert 2003, Klangforum Wien) and Takefu (Japan, Takefu International Music Festival 2004, Arditti Quartet). Livorsi has received commissions and grants from Italian and Finnish institutions. Since 1997 Paola Livorsi has been foreign correspondent for the review Il Giornale della Musica.
155
Fractals and Writing, Six Fractal Contemplations - Mikhail Malt -
1
Introduction
This text is intended to show how the notion of fractals may be applied to construct a ”self-similar” form that ”drives” the general evolution of the composition process of a set of short solo pieces for instrument and electronics. In an initial phase, this ”guide-line” will act as a ”conductor” for the instrumental sequence, and will have also an important harmonic function by accentuating the ”poles” to which the writing will gravitate. In a second phase, the instrumental sequence will undergo contrapuntal inter-play with the ”guide-line”. As a result, the fractal form will emerge in the synthesis part of the electronics as well. The basic tool for constructing fractals will be the Iterated Function System (IFS) found in OpenMusic’s Om-Chaos 1 library.
2
Context
This strategy was used to create a group of six short pieces for solo instrument and CD, the Six fractal Contemplations , commissionned by Bagnolet Conservatory for teaching purposes. These pieces can be played either separately or as a suite.
3
”Off-Time” formalization
3.1
The basic form
Since the constraint was that the six pieces could be played as a suite, it seemed to me important that formal conditions be imposed on the sequencing. As a first step, I established the order in which the pieces were to be played. Guided by the register I was going to use for each instrument and the timbre relations between the instruments, I chose the following order: trumpet, flute, alto, guitar,voice, guitar and clarinet. This order made a possible evolution of registers (figure 1). The representation of the sequencing of registers as the evolution of two curves offered another way of considering this evolution (figure 2) and so a third representation emerged: the evolution of the ”centers” of these registers (figure 3). The latter representation is used as a basic form to create the ”conductor”. 1
OM-Chaos, Mikhail Malt, Ircam, Paris, 1998.
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Figure 1. Registers
Figure 2. Registers as curves
Figure 3. The evolution of the registers ”centers” as a curve
However, the curve in figure 3 suffered in my opinion from a lack of ”satisfactory” dynamics, whether as an isolated piece or as a whole group. It should be noted that this curve represented for me not only the writing of the notes in space, but also a kind of evolution of the density of events and the ”drama” of the sequence. Therefore I reversed the curve (figure 4) that reaches a climax towards the end of the sequence. Figures 5 and 6 show the patches used to ”reverse” the curve. It should be noted that in the OM environment the curves have been represented in a BPF (Break Point Object), an editor in which data can be represented as fuctions by segments. We notice in the patch of figure 5 that the registers are first shown as a list of associations: ((tr (57 81)) (fl (68 91)) (alt (48 84)) (vx (57 76)) (guit (40 76)) (clr (52 88))) in which every sub-list contains a first and a second element (a symbol for the instrument) (a sub-list with the ends of the register in MIDI). 158
Fractals and Writing, Six Fractal Contemplations
Figure 4. The reverse curve of the registers ”centers”
Figure 5. Patch reverting the BPF
3.2
Proliferation and self-similarity
The form in figure 4 should show the general evolution of the sequence and the evolution within each piece. This is where the idea of self-similarity comes in. Here, the evolution of each piece should be identical (”congruent” might be a better word) to the evolution of the entire six-piece sequence. For this purpose I used fractal ”proliferation” with IFS 2 (Iterated Function System), modules in order to manipulate and create recursive linear 2
The OM-CHAOS library possesses the folowing tools: ifs-lib, IFSx, make-w and app-W-trans in order to control IFS.
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Figure 6. Abstraction of the patch for reversing the BPF
systems. This kind of system makes it possible to construct fractal objects and is a way of generalizing linear transformations in the plane. Indeed, one of the most interesting modules for composers is make-w. Any musical process that can be formalized by a linear transformation, such as temporal and-or frequential dilatation and compression can be calculated using this module. make-w makes it possible to apply the following linear transformation w(x, y) to any object in the plane (figure 7).
Figure 7.
The expression of w(x, y) [GOGINS 1991] is given by the following relation: x a b x e x w(x, y) = (ax + by + e,cx + dy + f ) or = + = A × y c d y f y The matrix A can be expressed by:
A =
r cos θ 1
1
r1 sin θ1 160
−r2 cos θ2 r2 sin θ2
+t
Fractals and Writing, Six Fractal Contemplations
The expression of w(x, y) turns into :
x x
w
x rw cos yθ y
=
1
1
r1 sin θ1
= A
y −r2 cos θ2 r2 sin θ2
+ t x e ×
y
+
f
where r1 is a factor applied to the horizontal co-ordinate. If r 1 is bigger than one (1), it is a factor of expansion. If it is smaller than one (1), it is a factor of contraction. r2 is a factor applied to the vertical co-ordinate. If r2 is bigger than one (1), it is a factor of expansion. If it is smaller than one (1), it is a factor of contraction. θ1 is a rotation angle applied to the horizontal co-ordinate, θ2 is a rotation angle applied to the vertical co-ordinate. t is the matrix
e f
where:
e is a horizontal shift associated in this particular case with a temporal shifting, f is a vertical shift, associated in this particular case with a transposition. The following examples help in understanding how the transformation w(x, y) generalizes the concept of linear transformation in the plane.
Figure 8. Linear transformation in the plane
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Imagine a bidimensional musical structure, defined in a space temps × notes , time being the horizontal co-ordinate and the notes the vertical one, see figure8 a). Figures 8 b) and 8 c) show the action of parameters e and f , and figure 8 d) shows the effects of the rotation parameters θ1 and θ2 . Notice that this type of transformation allows us to formalize contractions and expansions, starting from the medieval and going all the way to the spectral chords in our century, including the serial rotations of series of the Fifties [O’CONNARD 1965]. In our particular case, we used a recursive system of ”six” transformations w(x, y) shown in the diagram below:
x 1/6 w = y 0 x 1/6 w = y 0 x 1/6 w = y 0 x 1/6 w = y 0 x 1/6 w = y 0 x 1/6 1
2
3
4
5
w6
y
=
0
x 0 + × y 38 x 1500 −31/51 + × 0 y 36 x 3000 −12/17 + × 0 y 20 x 4500 −19/51 + × 0 y 42 x 6000 −12/17 + × 0 y 12 x 7500 −12/17 −8/17 0
0
×
y
+
24
The parameters of the equations (seen below) were found empirically. However, the arguments show up the characteristics of the sequence. θ1 and θ 1 being zero (cosinus=1) and r1 (the factor of horizontal contraction) 1/6, the values r1 cos θ1 are equal to 1/6. The average sequence duration being 150 seconds, the parameter e is equal to 1500 and the transposition f depends on the intervals between registers. The construction of the IFS was made with the make-w object (figure 9), which allows us to construct the transformation function w(x, y) from the linear (r1 , r 2 , e and f ) and angular (θ1 and θ 2 ) transformation data. The main patch used is shown in figure 10.
Figure 9. Construction of the IFS
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Figure 10. Graphic definition of the six w(x, y ) functions
The calculation was made in 3 steps, with the following algorithm: 1) basic form 2) curve inversion 3) ”fractalization”, i.e. applying the six w(x, y) functions with the ”IFSX” object. 4) valuation of the curve and if needed return to ”2)”. Figure 11 shows the 3 steps of calculation, with the final curve inserted into the 2 register curves.
4
”Harmonic” correction of the curve
The curve calculated in this way could not be used immediately. Although this curve had a ”self-similar” profile, its values were not necessarily adequate for the harmonic constraints I imposed. Each piece had, from a harmonic point of view, twelve main sections. The harmonic material, a sequence of chords, originates from the chord-sequence type of analysis (made with Audiosculpt ) of an audio excerpt, the recitation of a fragment from Victor Hugo’s second poem in ”Les Contemplations”: ”...l’homme est un puits o` u le vide toujours recommence...” 163
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Figure 11. The 3 steps of calculation
A description of this process is outside the scope of the present text, so we shall say only that the material collected by analysis was processed via ”harmonic reverberation” and split into two groups. A first group containing all the frequencies, to be used for the synthesis part, and a second one containing only the frequencies that belong to the tempered chromatic twelve-tone scale, were used to determine the instrumental compositional fields. Figure 12 shows the harmonic reservoir used in the first piece (for trumpet) containing six main chords and their ”reverberations”. It is important to notice that the last chord corresponds to the first chord of the second sequence (piece for alto).
Figure 12. The harmonic reservoir of the first sequence (trumpet)
Therefore, if we wish to insert the calculated curve in a writing process, it is of fundamental importance to ”correct” it harmonically so that it fits the harmonic fields 164
Fractals and Writing, Six Fractal Contemplations
proposed for each section. Figures 13 and 14 illustrate this operation.
Figure 13. Harmonic correction of the self-similar curve
Figure 14. Detail of the omloop module from the patch in figure 13
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Figure 15 shows the superposition of the two profiles, the original one (in the foreground) and the corrected one (in the background, colored gray). The differences are obvious, but the global profile remains the same.
Figure 15. Comparison between the ”original” and ”corrected” curves
5
The relationship between the ”conductor” and writing
Figures 16 to 20 show excerpts from the trumpet sequence (first stave) written in relation to the fractal sequence (second stave).
Figure 16.
Figure 17.
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Fractals and Writing, Six Fractal Contemplations
Figure 18.
Figure 19.
Figure 20.
As I mentioned in the introduction, the writing creates a relationship that is either contrapuntal or that enhances the fractal sequence through synchrony and dephasing.
6
Valuation test for relationships between curves
In order to gain a more global vision of the evolution of both sequences (that written for instrument as well as the calculated one) we shall superimpose them so as to compare the ways in which they evolve. Figure 21 shows the patch used to make the comparison. In A, the object midifile contains a midi file with both sequences. In B , the object omloop choose-track (figure 22) splits the sound-tracks of the MIDI file. In C , the abstraction set-bpf-color , which is in lisp mode, contains the following code: (lambda (self color) (setf (bpfcolor self) color) self)
to assign a respective color to each BPF 3 .
3
This function was suggested by Carlos Augusto Agon
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Figure 21. Patch used to make the comparison
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Figure 22. omloop choose-track
Figure 23 displays both sequences. The foreground sequence is the written one, and the sequence in the background, the fractal one. Notice how the ”written”sequence either follows the fractal sequence or plays against it in contrapuntal mode.
Figure 23. Both sequences
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Even though figure 23 gives an idea of the relationship between the two sequences, the details of the written sequence obscure this relationship. In the interests of clarification, I ”smoothed out” the curves, using an ”average” filter, described by the following expression/statement: 1 xi = 2 × index + 1
i+index
xj
j =i−index
However, before applying this process, both curves must be sampled.
Figure 24. The abstraction bpf-sampleinit
Figure 25. omloop mean-filter2-rec
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In figure 21 E , the abstraction bpf-sampleinit samples both curves over 300 points (see figure 24). In H the omloop mean-filter2-rec operates a recursive filtering (see figure 25), F being the index (i.e. window size for smoothing), and G the depth level of recursive filtering.
Figure 26.
Figure 26 shows the superimposition of the two sequences (written sequence in the foreground, fractal sequence in the background), and the ”interplay” between them.
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Bibliography [1] BARNSLEY M. : Fractals Everywhere . Academic Press Inc, 1988. [2] GOGINS M.: « Iterated Functions Systems Music » Computer Music Journal, vol 15, n 1, MIT-Press, 1991. ◦
[3] MALT M.: Chaos - librairie de mod`eles chaotiques et de fractales Ircam, Paris, 1994. [4] MALT M.: « Lambda3.99 (Chaos et Composition Musicale) » Troisi`emes Journ´ees d’Informatique Musicale JIM 96, Ile de Tatihou, Normandie, France, 1996. [5] MALT M.: Les math´ematiques et la composition assist´ee par ordinateur, concepts outils et mod`eles Th`ese en musique et musicologie du XX`eme si`ecle, Ecole des Hautes Etudes en Sciences Sociales, directeur de th`ese Marc Battier, Paris, France, 2000, p. 703-767. [6] O’CONNELL W. : “Tone Spaces” Die Reihe, n 8 pp. 1965. ◦
¨ [7] PEITGENH. O., JURGENS H., SAUPE D.: Chaos and Fractals New Frontiers of Science, Springer-Verlag, New York, 1992.
Mikhail Malt Mikhail Malt, has a double formation, both scientific and musical (engineering, composition and orchestral conducting). After conducting youth orchestras for ten years, he began his musical career in Brazil as a flutist and orchestral conductor. He is the author of a PhD thesis written at the Ecole des Hautes Etudes en Sciences Sociales on the use of mathematical models in computer-assisted composition, and a researcher at MINT-OMF Sorbonne Paris IV (Musicologie, informatique et nouvelles technologies Team, a branch of the Observatoire Musical Fran¸cais ). Malt currently teaches computer-assisted composition and musical synthesis at Ircam. He is currently pursuing his composition and research activities in the fields of artificial life models, musical representation and compositional epistemology.
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Algorithmic Strategies in A Collection of Caprices - Paul Nauert Abstract. This essay describes the author’s use of OpenMusic to assist in the composition of a piece for solo piano. The composition process involved two principal stages. The first stage yielded a rhythmic sketch of the entire piece, using a controlled random process implemented with functions from the OMTimePack library. The second stage involved the selection of pitch material suited to the rhythmic sketch; a variety of functions in the OMPitchField library supported this task. ***
1
Introduction
In late 2001 I began discussions with the pianist Marilyn Nonken about a new composition for solo piano. The work that resulted, A Collection of Caprices , was completed by me in August 2002 and premiered by Nonken on October 2, 2002 in Santa Cruz, California. She subsequently gave several additional performances during a coast-to-coast tour of the United States; my work shared the program with pieces by Milton Babbitt, Jason Eckardt, Michael Finnissy, and David Rakowski (all written for Nonken). A Collection of Caprices is not a set of character pieces; the title alludes instead to the way in which this continuous, single-movement piece frequently - and capriciously - shifts character. The title is a phrase used by the American composer Mel Powell describing a group of his short compositions from the 1960s; the refinement and poise of Powell’s music represent ideals for which my own work aims, and I wrote the piece as a tribute to him. My compositional process involved many of the same strategies I have employed regularly since the mid-1990s, including software tools of my own design to assist with the organization of rhythmic and harmonic aspects of the work. What was new in the process this time was the integration of these tools into the OpenMusic visual programming environment developed at IRCAM by the Music Representations Team. This essay describes the strategies used to organize A Collection of Caprices and the role played by OpenMusic in implementing those strategies. My compositional process over the past ten or so years has involved a fundamental separation of temporal structure and pitch structure. I habitually complete a rhythmic sketch of a piece, from start to finish, before returning to measure 1 and beginning to work out pitch choices. (As pitch details fall into place, I am also concerned with all of the remaining dimensions that are important to the musical result; but these aspects of the compositional process are the least structured and I will therefore say the least about them.) This essay begins with a section devoted to rhythmic strategies and continues with another devoted to harmonic strategies. 175
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2
Organizing time
My approach to constructing a rhythmic sketch is generally top-down, working from the large to the small, and I decided initially that A Collection of Caprices would consist of 11 sections, alternating between longer principle sections and shorter interludes. I chose section durations from the geometric series 12 × (49/40)n = {..., 12.0, 14.7, 18.0, ... }. Figure 1 illustrates the sectional plan.
Figure 1. Overview of rhythmic sketch, showing section durations (top), plan for stochastically
generated rhythmic streams (layers I and II at bottom) and additional derived material (layer III at bottom)
Figure 1 also shows the design according to which rhythmic details for the piece were generated. The OMTimePack library in OpenMusic provides tools for generating streams of durations with specific statistical profiles. When designed appropriately, these profiles determine characteristic ”rhythmic behaviors”; in this case, I worked with four contrasting profiles, corresponding to behaviors I named fragmented motions , continuity , whisps , and supple . The design is organized into three layers, which correspond partially to layers in the texture of the finished composition. Reading across the row for layer I, the plan begins with a stream of continuity , maintaining this profile throughout sections 1 through 3. A gradual interpolation from the continuity profile to the fragmented motions profile takes place across section 4, with a corresponding gradual shift in the behavior of the rhythmic stream. Once the new fragmented motions profile is fully established at the beginning of section 5, it is maintained throughout that section. Layer I becomes inactive at the beginning of section 6. The rest of the overview can be read in the same fashion. (Layer III is derived from transformations of parts of layer II, according to procedures described further on.) Figures 2 and 3 show excerpts of the detailed rhythmic sketch that I generated according to the plan discussed above. Figure 2 is from the beginning of the sketch, illustrating the continuity behavior in layer I and the fragmented motions behavior in layer II. The contrast between these behaviors is somewhat hard to judge in such a short excerpt. The continuity behavior involves a great deal of motion at a rate of two to three attacks per beat, with frequent excursions into more rapid zones of activity. In contrast, the fragmented motions behavior moves more often at a rate of one or two attacks per beat, and its excursions into rapid terrain are briefer and occur less often. Both behaviors reach occasional points of repose on longer durations. 176
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Figure 2. Rhythmic sketch, mm. 1-13
Figure 3 shows the entirety of section 4, plus the immediately surrounding material (layer I only). A gradual shift in behavior from continuity to fragmented motions occurs across this section, although the compressed scale of the section, and the presence of a couple of very long durations within it, make this shift a little more difficult to follow. Despite this difficulty, the passage does what I needed musically, ushering in material that moves with a greater sense of momentum. In order to illustrate what becomes of this rhythmic material, Figure 4 provides the opening of the completed score, which corresponds to the sketch given in Figure 2. In this case, the multiple layers of the sketch become quite tangled in the completed score, although repeated pitch cells can be seen emerging in one layer or the other at various points (this is perhaps most clear in m. 10, where contrasting cells are seen in each layer). To generate the rhythmic streams on which A Collection of Caprices is based, I made extensive use of OpenMusic’s OMTimePack library, a specialized collection of tools for creating and manipulating rhythms. The generative engine at the core of this library is the function marktime, which creates a rhythm by repeatedly selecting a duration event at random from a pool of possible events and appending it to the end of the resulting rhythm until a specified total duration is reached. As its name suggests, this function involves a Markov process: each new selection is made with the possible events weighted according to the last few selections already made. A Users Guide and function-by-function Reference for the OMTimePack library is included along with the software itself in the materials distributed by the IRCAM Soft177
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Figure 3. Rhythmic sketch, mm. 87–107
ware Forum. Here I will focus on aspects of the marktime function and the role it played in the creation of A Collection of Caprices . The marktime function can assemble rhythms using both simple duration events (each one a single duration) and compound duration events (each one a ”cell” formed by a specific string of durations). And it can operate as a zeroth, first, or second order Markov process (event probabilities at each step being static or depending on the preceding one or two selections). I exclusively used simple duration events and first order Markov processes to construct the rhythmic streams I needed. For the benefit of readers who are unfamiliar with the basic operation of a first order Markov process, this paragraph describes a simple example. More experienced readers may proceed to the next paragraph, which returns to the specifics of my composition. (Ames, 1989 provides a good general introduction to compositional applications of Markov processes; its primary emphasis is not on rhythm construction.) Figure 5 presents two events, e and h; assigns probabilities to them; and shows a rhythm built with them. The probabilities are static in this example - each selection is made with a 30% chance of choosing e and a 70% chance of choosing h - so it represents a zeroth order Markov process. Figure 6 replaces the static probabilities with probabilities that vary according to which event was most recently selected: if the previous choice was e, then the next selection is made with an 80% chance of choosing e and a 20% change of choosing h; but if the previous choice was h, then the next selection is made with an equal chance of choosing either event. A process in which probabilities are conditioned like this is called a first order Markov process. Figure 6 also shows a rhythm built according to this process. The OpenMusic marktime function requires four input parameters: event-space represents the pool of duration events for random selection; p-table controls the Markov process of random selection; tot-time specifies the desired duration of the output rhythm, and init-conds provides context for the first few random selections. To generate the 178
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Figure 4. A Collection of Caprices, mm. 1–13
Figure 5. (a) Static probabilities; (b) representative output
rhythms used in A Collection of Caprices , I constructed the following pool of simple duration events1 : 0.09, 0.12, 0.37, 0.75, 1.2, 1.88, 2.88, 4.67, 8.25. These values provide the possibility of two contrasting rates of very rapid motion (based on strings of 0.09 or 0.12), two additional durations that are still qualitatively short (0.37 and 0.75), enough choices
1
Each one a single duration expressed as a fraction of a quarter note at the tempo M.M. q = 76
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Figure 6. (a) Probability table for first-order Markov process; (b) representative output
in the medium-short through medium-long range to provide variety, and two contrasting durations that are sufficiently long to serve as points of repose (4.67 and 8.25). All of the rhythms in layers I and II of the rhythmic sketch for A Collection of Caprices were generated by random selection from this pool. Once the event space was established, I designed a two-dimensional table for each of the four rhythmic behaviors called for in my initial plan for the rhythmic sketch. Figure 7 illustrates the tables corresponding to the fragmented motions and continuity behavior patterns.
Figure 7. Probability tables : (a) fragmented motions ; (b) continuity.
Figure 8 shows an OpenMusic patch using marktime with inputs configured to reproduce layer I of the opening of the rhythmic sketch for A Collection of Caprices . The 180
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patch is almost trivially simple, because marktime is specialized to accomplish exactly the task called for in this patch. The event-space is the pool of nine durations describe earlier, and the continuity p-table is organized as in Figure 7(b). The total duration, 165.7, is the sum of the durations planned for sections 1, 2, and 3, because the rhythmic behavior of layer I is determined by the continuity profile throughout these sections. I no longer have a record of the actual value supplied to the init-conds input. This is the value that marktime uses in place of a ”previous selection” at the very beginning of the process, before any selections have actually been made. The value 2 is a good guess here, because it sets up the process in such a way that the third row of the continuity table determines the probability of each event; in this row, the event 0.37 is assigned a high probability of 58%. It can be seen in the resulting rhythmic sketch (Figure 2) that this event was the one actually selected by marktime - 0.37 after quantization appears as a triplet eighth note. (Of course, because marktime implements a random process, the output ldur won’t reproduce the rhythms in my composition but will constitute another, statistically similar rhythmic stream.)
Figure 8. OpenMusic patch used for the beginning of the rhythmic sketch (layer I).
The empty input sockets in Figure 8 are for optional parameters that allow the generative process to evolve over time in a variety of ways. At the beginning of my composition, the rhythmic behaviors remain fixed, so these optional parameters are left unused. But during section 4, the rhythmic behavior of layer I evolves gradually from continuity to fragmented motions . To create this gradual shift, (and a more protracted one in section 9), I supplied a second probability table to the evol-table input of marktime. The specifics of this patch are detailed in Figure 9. The marktime module at the left is responsible for the rhythms in sections 1–3, with static continuity behavior. The marktime module at the right is responsible for the rhythms in section 4, which evolve from continuity to fragmented motions . In this second marktime module, the continuity table is supplied to the p-table input and the fragmented motions table is supplied to the 181
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evol-table input. This causes the module to use values from the former table at the
beginning of the process, to use values from the latter table at the end of the process, and to interpolate between these beginning and end values over the course of the process. (The rightmost socket of this module is empty, so interpolation occurs with the default linear shape). Finally, the first module’s fin-conds output reports the context at the end of section 3; feeding this value to the init-conds input of the second module ensures that the transition from section 3 to section 4 in the rhythmic sketch is seamless.
Figure 9. OpenMusic patch used for the first four sections of the rhythmic sketch (layer I).
Layers I and II of the rhythmic sketch for A Collection of Caprices were generated entirely according to the techniques outlined so far. To produce layer III, I began by processing a copy of the data from layer II, sections 9–11. Using simple arithmetic modules in OpenMusic, I rescaled this data so that it spanned sections 5 through 9. The behavioral profile of this data, supple , focuses on a moderate rate of motion and makes no excursions into very rapid territory; and the scaling applied to it slowed it down further. In an early conception of the piece, I intended to use this slow material as is. But on further reflection I felt I needed greater rhythmic activity in the middle of the composition. So I worked outside the visual-programming environment of OpenMusic and cobbled together some functions directly in Common Lisp that take an existing rhythmic stream, make controlled random selections from a pool of rhythmic cells, and return a new stream formed by embedding the randomly selected cells into the durations of the original stream. This technique resembles one I am developing for the next release of OMTimePack . 182
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As I worked to craft the rhythmic sketch into a completed composition, I decided to make one drastic alteration to the original plan. The conclusion of section 5 shaped up to be a passage that develops strong forward momentum. In my plans, this buildup was followed by an interlude (section 6); but I felt that it made more dramatic sense to proceed directly to the next principal section (namely, section 7). Therefore I simply deleted all of section 6 and made minor adjustments to fix up the ”seam” between sections 5 and 7.
3
Organizing pitch
Because the entrances and exits of rhythmic layers, and the changes of rhythmic behavior within each layer, are timed according to the 11-section structure of my composition, these higher-order rhythmic events help to articulate its sectional plan. At some of the sectional boundaries, however, there are no higher-order rhythmic events (e.g. the starts of sections 2 and 3) or only subtle ones (the beginning or end of a gradual behavioral change, e.g. the start of section 4, where the beginning of a transition from continuity to fragmented motions is not immediately obvious). The strategies I have developed for pitch organization begin with my concern for contributing to the articulation of large-scale structural divisions. Specifically, I use fixed-pitch formations called ”pitch fields” in several pieces - including A Collection of Caprices - to create a sense of uniformity within each section and contrast between sections. Within each section, a structural ”middleground” emerges when subsets of the field are projected as harmonic units. So there is note-to-note activity in the foreground, chord-to-chord activity in the middleground, and field-to-field activity in the background. Figure 10 traces these different levels in a passage spanning the end of section 1 and the beginning of section 2. The boundary between sections 1 and 2 coincides with the pitch-field change indicated on the lowest pair of staves in Figure 10. In the middle level of the same Figure, the basic harmonic plan is laid out as a series of chords. The chord level is reproduced more or less as it appears in my sketches. The foreground activity in the completed score sometimes breaks these chords into smaller units, and other pitches from the field are sometimes worked into the texture as well. Despite its volatility, the harmonic middleground is essential to my conception of the entire piece. The remainder of this portion of the essay offers a closer look at the OpenMusic patches I used to organize this chord-to-chord level. The reader is assumed to have some familiarity with basic set-theoretic models of pitch as presented in (Forte, 1973), (Rahn, 1980), (Morris, 1987), and (Lewin, 1987); readers unfamiliar with this or similar work can still read on for a general idea of my strategies. Figure 11 shows a patch with the ”master configuration” that assisted my harmonic choices throughout A Collection of Caprices . During the gradual process of developing the rhythmic sketch into a completed composition, the master configuration remained constant while I made repeated changes to the data supplied within each subpatch and to some of the particular functions that were plugged in to these subpatches. The master configuration can be read in stages, which the essay will trace through twice: first to provide a general overview, and then in more detail, to show more precisely how data flows through the network. During this second pass, we will look inside the main subpatches. But we begin with the overview. The first stage of the master configuration assembles a pool of pitch class sets (pcsets) according to criteria for interval class (ic) content; 183
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Figure 10. A Collection of Caprices , mm. 31–38, with underlying chords and pitch fields
these criteria constantly shift as I work, as a result of relatively improvisational decisionmaking, informed by previous harmonic choices and details in the rhythmic sketch. The second stage filters the pcset pool according to criteria for pc content; again, the specific criteria shift according to a series of more-or-less spontaneous decisions. In a separate branch of the network, a pitch field (resembling those depicted above in Figure 10) is constructed; this field determines which pitches are available for chord-building. The two branches of the network converge as inputs to the function find-pcset-in-field , which determines, for each pcset in the filtered pool, all the corresponding pitch sets ; the results of this search constitute a pool of pitch sets. (Given a pcset X and a field F, a corresponding pitch set is a subset of F that contains exclusively one instance of each pc in X.) The final significant stage of the master configuration filters the pool of pitch sets according to criteria for pitch and interval content. The result of this stage is a short list 184
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Figure 11. Master configuration of the patch used to assist harmonic choices
of chords, focused according to multiple criteria; feeding this list to a chord-seq factory allows me to view it in conventional music notation and audition it via MIDI. I make harmonic choices from these short lists, or adjust the criteria and try again if none of the choices satisfies me. Let us take a closer look at how each stage of the master configuration behaves. Figure 12 provides details about the construction of the pcset pool. This subpatch begins with a list of pcsets, each of which represents a family of transpositionally equivalent pcsets. As readers who are familiar with the twelve-tone landscape may know, there are 66 such families of pentachords and 80 of hexachords. The next stage within the subpatch sorts these 146 families in order of decreasing similarity to a target pcset, 0, 2, 3, 5, 6, 8, and selects the first fifth of the sorted list - the 29 families with the strongest intervallic resemblance to the target. The similarity computation makes use of the ”interval angle” measure proposed in (Scott & Isaacson, 1998). The final stage of this subpatch expands the result by replacing each family’s representative with a complete list of family members, yielding a list of 336 pcsets at the output. (Without the sort-andselect procedure, the raw list of pentachord and hexachord families would have expanded into a total of 1716 pcsets.) Figure 13 illustrates the subpatch responsible for filtering our pool of 336 pcsets according to specific criteria for pc content. The specialized function filter-chordlist performs the filtering, and the criteria controlling this process are defined here by a pair of make-pc-vldg-test modules The ”vldg” in this name stands for voiceleading, and these modules can be seen as tools for testing chords according to the voiceleading connections 185
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Figure 12. Generating the pcset pool
each one has to some reference pcset. Specifically, the module on the left tests whether each pcset in the pool contains at least 2 and at most 2 pcs that form ic 0 relative to some pc in the set { 2, 9} - in other words, it tests whether each pcset contains both pcs 2 and 9. Similarly, the module on the right tests whether each pcset contains at most one pc in common with the reference set R = { 4, 6, 8, 11} and also whether each pcset contains at least 2 and at most 4 pcs that form ic 1 relative to R. The mathematical model of voiceleading underlying these computations is described at length in (Nauert, forthcoming). Of the 336 pcsets in the input pool, 11 pass through the filter: {9, 11, 0, 2, 3}, {9, 11, 0, 2, 5}, {9, 10, 0, 2, 3, 6}, {7, 9, 10, 1, 2, 4}, {0, 1, 2, 3, 6, 9}, {9, 10, 0, 2, 3}, {9, 11, 2, 3, 5}, {9, 0, 2, 3, 4}, {9, 10, 0, 1, 2, 4}, {7, 9, 10, 11, 1, 2}, and {9, 11, 0, 1, 2, 5}. (Reviewing the multiple criteria in operation so far, these 11 pcsets are pentachords and hexachords that are intervallically similar to { 0, 2, 3, 5, 6, 8} and have particular voiceleading relationships to { 2, 9} and { 4, 6, 8, 11}.) To keep the presentation streamlined, this discussion omits details about the subpatch responsible for constructing pitch fields. Readers who are interested these details can study the OpenMusic documentation for the main function at work within that subpatch, make-pfield; the structure and uses of different kinds of pitch fields are considered at length in (Nauert, 2002). For the purpose of continuing our detailed trace through the master configuration we will use the same pitch field used throughout the opening of section 2 of A Collection of Caprices . This field appears at the bottom of Figure 10. 186
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Figure 13. Filtering the pcset pool
Note for instance that the only instances of the pc G in this field are the pitches G1 and G5, so if a pcset contains G, each corresponding pitch set will contain G1 or G5. Despite the constraining effects of the pitch field, the pitch sets corresponding to our 11 pcsets multiply rapidly. One of our 11 pcsets is {9, 11, 0, 2, 3 }, and one of the pitch sets corresponding to this pcset is {A1, B2, C3, D5, E5}, as readers can verify by locating these pitches in the appropriate field in Figure 10. The find-pcset-in-field function in the master configuration finds this pitch set and 1826 others. Thus the filtered pool of 11 pcsets corresponds to a pool of 1827 pitch sets.
Figure 14. Filtering the pitch set pool
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The final stage of the master configuration filters the large pool of pitch sets as illustrated in Figure 14. This subpatch consists of two stages. First, the pitch set pool is filtered according to criteria specified in an additional subpatch named P test. Next, the results of this initial filtering stage are then sorted in descending order according to the lowest pitch of each chord, and the highest third of this sorted list is sent to the output. Figure 15 shows the P test patch that controls the first of these two stages. Filtering is based on a combination of three tests. The make-spacing-test module requires each chord to be spaced such that the interval from the lowest to the second lowest note is at least 5 and at most 21 semitones, and such that the interval from the second the third lowest note, from the third to the fourth lowest, and so on, is at least 2 and at most 11 semitones. The make-p-vldg-test module requires at least 1 and at most 2 notes in each chord to form interval 0 relative to some pitch in the set {14, 21} - in other words, it ensures that each chord contains D5, A5, or both. Finally, the make-inclusion-test requires each chord to contain at least 1 and at most 3 transpositions of the pitch set {0, 14, 21}. Only chords meeting all three requirements pass through the filter. Together, the filtering, sorting, and selecting procedures depicted in Figure 14 reduce the pitch set pool from 1827 chords to just the 8 depicted in Figure 16.
Figure 15. Combination of three tests for filtering the pool of pitch sets
Figure 16. The result: eight chords meet criteria established throughout the master configu-
ration
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Bibliography [1] Ames, C. : The Markov Process as a Compositional Model: A Survey and Tutorial. Leonardo 22.2: 175–187, 1989. [2] Forte, A. : The Structure of Atonal Music. Yale University Press, New Haven, Connecticut, 1973. [3] Lewin, D.: Generalized Musical Intervals and Transformations. Yale University Press, New Haven, Connecticut., 1987. [4] Morris, R. : Composition with Pitch Classes: A Theory of Compositional Design. Yale University Press, New Haven, Connecticut, 1987. [5] Nauert, P. : “Field Notes: A Study of Fixed-Pitch Formations”. Perspectives of New Music 41.1: 9–60, 2003. [6] Nauert, P.: The Progression Vector: Modelling Aspects of Posttonal Harmony. Journal of Music Theory (forthcoming). [7] Rahn, J. : Basic Atonal Theory. Longman, New York, 1980. [8] Scott, D., and Isaacson E.J.: “The Interval Angle: A Similarity Measure for PitchClass Sets”. Perspectives of New Music 36: 107–142, 1998.
Paul Nauert Paul Nauert holds degrees from the Eastman School of Music, where he was awarded the McCurdy prize in composition, and Columbia University, where he earned his Ph.D. in music theory in 1997 with the assistance of a Mellon Foundation Fellowship. His principal composition teachers include Joseph Schwantner, Robert Morris, and Fred Lerdahl. On the faculty of UC Santa Cruz since 1996, Dr. Nauert has recently held visiting positions at IRCAM in Paris and Columbia University in New York. As a composer, he has worked with internationally prominent soloists (including pianist Marilyn Nonken and guitarist David Tanenbaum) and ensembles (including the Peabody Trio and NOISE). His scholarly publications on aspects of pitch and rhythmic organization in contemporary music appear in Perspectives of New Music, the Journal of Music Theory, and The Musical Quarterly, and his software tools for algorithmic composition are published through the IRCAM Software Forum. The latest information about Dr. Nauert’s work as a theorist and composer can be found at http://arts.ucsc.edu/faculty/nauert/. 189
Sculpted Implosions : Some Algorithms in a Waterscape of Musique Concr` ete - Ketty Nez Abstract. Sculpted Implosions, for live French horn and 8 track tape, was written at IRCAM as a cursus project during 1998-99. This personal introduction to programming and computer music was an ongoing exploration - of electroacoustic sound treatments, algorithmic procedures, and real-time processes - using software developed at IRCAM, including OpenMusic, AudioSculpt, and Max/MSP. *** For this piece, algorithms to control pitch and rhythm were written using OpenMusic, further developing compositional techniques already present in the author’s instrumental music. The resulting MIDI information was then transferred into breakpoint filter parameters for further treatment in AudioSculpt, using Hans Tutschku’s library OM-AS 1 . The sounds which were filtered were prepared using standard concr`ete treatments. All from nature, these were various samples of water, e.g. ocean waves, fountains, and rain. As a ”clin d’oeil” to the notion of the corporality of a live performer, and in particular the French horn as a (rather watery!) brass instrument, samples of teeth-brushing and gargling were also included. These were subjected to time stretching, pitch shifting, and cross synthesis using both AudioSculpt and Max/MSP. Resulting individual sound files were spatialized in circular rotations at varying speeds and recorded out into 8 tracks, using the Max/MSP Spatialisateur software. During performance, the live French horn is similarly ”rotated” over the same 8 loudspeakers. The French horn plays an obligato which floats in and out of the watery sounds, doleful riffs of oddly remembered nineteenth-century orchestral quotes from Mahler, Strauss, and Wagner, lost on a surreal ocean voyage. The author soon realized, however, that the tape part could well represent a composition on its own, thus producing a second version of only the 8 tracks which is often performed in concerts, Sculpted Implosions II . This paper will discuss the OpenMusic algorithms used to create the tape part, giving some example patches of processes, as well as briefly touch on the AudioSculpt and Max/MSP processes used. The compositional ”journey” for this piece began with modifications to 1
First released at the November 1998 IRCAM Forum. This library is explained in Hans Tutschku,
L’application des param` etres compositionnels au traitement sonore dans la composition mixte et ´ electroacoustique , in PRISMA 01 (Florence: EuresisEdizioni, 2003), 77-116. Also, processes specifically etres compositionnels from Sculpted Implosions are discussed in his dissertation, L’application des param` au traitement sonore (Formation Doctorale Musique et Musicologie du XX e si` ecle, Universit´ e Paris-
Sorbonne (Paris IV), Ecole des Hautes Etudes en Sciences Sociales Paris, 1999).
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the simple harmonic series starting from E, the lowest note of the piece, and chosen in reference to the infamous and luxuriously orchestrated E pedal tone of Wagner’s prelude to Das Rheingold. As pedal tone, this occurs at the beginning and penultimate sections, featuring rich low sounds multiply layered, slightly detuned, slowly glissandoed, and treated by slowly-opening low-pass filters. To give pitches for various simultaneities, variants of the E series were derived from intervallic modifications to successive intervals. Thus 1, 2, 3, and 0 semitones were successively added to consecutive intervals, as well as rotations of this set and subsets of this set, [2, 3, 0, 1] and [3, 0, 1, 2] etc., or [0, 1, 2]. In figure 1, the E harmonic series has been progressively altered by rotations of semitones [0, 1, 2, 0, 1, 2, . . ], [1, 2, 0, 1, 2, 0, . . . ] and [2, 0, 1, 2, 0, 1, . . . ].
Figure 1. Morphing the E harmonic series with progressive changes of 0,1 and 2 semitones
Inspired by music for the Indonesian gamelan, where simultaneous attacks of the various metallophones delimit structural points and produce rich resonances saturated in overtones, these clusters formed a slow chaconne which progressed throughout the entire piece. They were placed at precisely spaced intervals, a colotomic division of form into sections. Each section featured one or more of several types of processes which moved slowly between the different clusters framing the edges, and the compositional choice was made to quantize to the pitches to the nearest 100 midicents as contrast to the various microtonal interpolations which were constructed to span between them.
Figure 2. Self-onlist process
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One such interpolation process carved out successively smaller subsets of a cluster, the onlist function of omloop. Onlists of pitches were sorted in ascending order to give increasingly higher and higher subgroups, suggesting the ascending notion of a harmonic series. For further textural interest, alternate tones from the same chord were selected to create a ”trill”: tones index [0,2,4,6 . . ] with index [1,3,4 . . ], both subsets onlisted as well. To form a connection with the next chord, the process were reversed resulting in a descending reverse-onlisted ”trill.” Juxtaposing two such ”trills” thus gave an arch profile, with ascending and descending contours (see figures 2 and 3).
Figure 3. (a) Self-onlist of the E harmonic series. (b) Self-onlist linking two clusters
More standard interpolations between two sonorities were used. In a specified number of steps, tones of corresponding index number between two clusters were spanned (see figures 4, 5 and 6). However, for variety, this regular interpolation process was carried out in several stages. For example, an intervening ”hybrid” chord was formed from specific tones of chord A which moved to specific tones of chord B, but not necessarily of corresponding index position. In figure 7, the tones of index [1, 2, and 3] were interpolated to tones [3, 4, 5] of chord B, the other tones of chord A remaining unchanged. Then interpolation to the following B chord was linear, i.e. with corresponding index positions (see figure 8). Instead of a hybrid chord dividing interpolation into stages, an interval could be placed between sonorities A and B. This created a wedge profile: tones of A were constrained to move to the closest tone of the intervening interval. This interval then itself fanned back out to tones of B (see figure 9). Using this same ”bipart interpolation” algorithm, but reversing the ordering of either A or B, a swivel reversed the mapping of index numbers. Now, traversing registers, each note of one cluster was interpolated to the ”other” note of the interval, i.e. that not closest, and back out again. The highest note of A was interpolated to the lowest note of B, similarly, the next-highest of A to the next-lowest of B, etc., as shown in figure 10 193
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Figure 4. Interpolation patch
Figure 5. Interpolation omloop
Figure 6. Interpolation process
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Figure 7. Hybrid interpolation patch
Figure 8. Hybrid interpolation
(NB: the interpolation patches were shown in figures 4, 5 and 6). Two adjacent clusters were occasionally directly interleaved [A B A B . . . ]. However, each cluster was constrained either to grow out of or collapse into a single note, variations of omloop’s onlist process created by various ordering of the indices of chord tones. The single ”target” tone was chosen variably to be the highest, lowest, or median tone. This produced for each cluster a wedge of differing triangular shapes, and those of two adjacent clusters were interwoven attack for attack (figure 11). In variation to interweaving, movement from iterations of cluster A to those of cluster B were shaped with controlled amounts of randomness added to repetitions of subsets of the chords (figure 12). The minimum and maximum number of tones possible for each attack were specified, for each subsection of this ”gamelan” tintinnabulation. Shown in in figure 13, given a total of x attacks to move from A to B, the omloop partial_sums found the highest number y of an arithmetic which would yield a sum of terms equal or smaller than x. This y was then divided by two to account for sampling from both the A and B collections. Subsequently, omloop two_series created two arithmetic series of [1, 2, . . . y/2] and its reverse [y/2, y/2 - 1, . . . 1]. These represented the number of times for omloop choice to chose, respectively, from the pool of A and B clusters: 1 tone from A, y/2 from B, then 2 from A, (y/2 - 2) from B, etc. (figure 14). The combined results from A and B, eg. 1 selection from A and y/2 selections from B, were randomly permuted among themselves to avoid any audible linear predictability. Associated with the various types of pitch interpolations between clusters were convex 195
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Figure 9. Bipart interpolation patch
Figure 10. (a) Swivel interpolation: chord-interval-chord. (b) Single line interpolation reversing
registers.
or concave tempi curves of attack times and durations. Growing either shorter then longer, or vice versa, these time-attack arches were calculated from sampling exponential growth and decay breakpoint functions, BPF objects in OpenMusic. Gauss sampling was used to add a controlled amount of random variation to each sample of a BPF curve, using the gauss object from the OMAlea library of chaos functions. To create a concave shape, two exponential curves were simply juxtaposed, one in reverse of the other, and inverting this arch gave the other shape (see figure 15). As shown in the patches of figure 16, the minimum and maximum possible durations of attacks for each section were specified, as well as number of subsections desired. Pairs of durations were generated for each such subsection [x, x × y], y representing the amount of ”bend” in the curve, i.e. max deviation from x, for example 1.5, or 0.5. The y bend-values themselves changed for each subsection, and were derived from sampling an arithmetic 196
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Figure 11. Interweaving two onlisted clusters
Figure 12. Moving from cluster A to cluster B
series. Using these ”bend duration pairs”, series of durations was generated spanning in value from x, to x × y, back to x. The durations of attacks for each subsection were summed, and compared to original subsection lengths, which had been derived by sampling a BPF curve of exponential growth or decay. Any extra attack durations were discarded. To differentiate between increasing or decreasing subsection lengths, the output BPFsampling of the exponential curve was simply reversed. Successive lengths of the composition were successively shortened until a climactic middle ”interruption” by a whooshing glissando, a clin d’oeil/oreille to the tradition of musique concr`ete. Then sections were lengthened until a reprise of the opening material of the very-low E pedal point and irregular glissandos. The form of the entire work thus suggested a ”wedge”, correlated with changess in frequency content of the types of sounds being filtered for each section. Starting from lower-frequency sounds, e.g. ocean waves, AudioSculpt cross-synthesis between adjecent sections of with progressively higher-frequency material continued until the middle section. Here with the highest frequency sounds were used, e.g. teeth197
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Figure 13. partial_sums omloop
Figure 14. choice omloop
brushing. Then the entire process was reversed. Thus, in terms of sonic material [A, A+B, B,..., M+N, N, N+M, ..., B, B+A, A]. The results of the above algorithmic processes, all MIDI information, were imported into Audio Sculpt using the seq-to-fbreakpt object in the OM-AS library2 . This object interprets pitch and rhythm information as textfiles of parameter vectors to be used for breakpoint filtering. Subsequently, the textfiles are designated as the parameterfiles for
2
Tutschku, the developer of the OM-AS library, has commented that this library permits one to sculpt sounds by applying formalized parameters, in reversal of the spectral approach to composition of the 1970s, which sought to apply acoustic phenomena to instrumental writing. L’application des param`etres compositionnels au traitement sonore dans la composition mixte et ´ electroacoustique ; in PRISMA 01 (Florence: EuresisEdizioni, 2003), 79.
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Figure 15. Creating the tempi curves
Figure 16. Concave and convex arches tempi curve patches
SVP commands addressing the phase vocoder engine behind AudioSculpt, whose interface is not addressed. This object’s input parameters include fft-size, filter bandwidth, scaling the maximum and minimum input MIDI velocities to output dB values, scan speed, i.e. how fast breakpoint curves are sampled, and random variation of this scan speed. For Sculpted Implosions , the bandwidth was kept very tight, around 10 hz, to produce clearly pitched articulations. In addition to filtering, the MIDI information from some of these interpolative processes were also used to play SampleCell. This sampler was filled with sounds resulting from modifications of the Cross Dog AB patch by Zack Settel and Corte Lippe. Using fft∼ and ifft∼ objects of max/MSP, amplitude and phase information was exchanged 199
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between different articulation types of the same note played on the French horn, eg. with mutes of different types, unmuted, flutter tongued. The wavering sounds were not dissimilar to viola di gamba tremoli and effectively cut through the filtered sounds, suggesting another textural layer. Starting with the second half is another process which stands out in relief by both compositional and sonic means, a slow-moving chaconne of mid-register sonorities subject to successive steps of microtone detuning. Horn samples of individual tones were analyzed in Audio Sculpt to determine the exact fundamental frequency before subject to the Max/MSP cross-synthesis described above. Based on the 7th chord CFGBD, clusters were constructed from calculating pitch transpositions maintaing each of these tones fixed as ”pedal.”Each such ”morphed”cluster was the result of successive shifts of x/4 tones as well as 1/8 tones, a kind of progressive ”stretch” upwards. By again sampling an exponential growth BPF curve, progressively lengthening attack times were chosen, coordinating with the lengthening sections of this second ”chaconne”at the second half of the piece, to give an overall impression of ”sinking” back down to the low E pedal texture. To calculate the changes of transpositions for these clusters, eg. keeping C fixed at 6000 midicents, F was shifted 1/4 tone (= 50 midicents), G 2/4 tones (= 100) and D 3/4 tones (= 150). Then each of these was detuned +1/8 and -1/8 tone (-25 and +25 midicents). Another group of chords, still keeping C as pedal, now shifted the other tones by multiples of 3/4 tone: a shift up of 3/4 tones (150) for F, 6/4 tones (300) for G, 9/4 tones (450) for B, 12/4 tones (600) for D. This process once again was repeated using multiples of 5/4 tones, i.e. 250 midicents (see figure 17 and table 1.).
Figure 17. Horn Chaconne: successive 1/8 tone steps of two series with C and with F as pedal
tones
These detuned mid-register ”chaconne” clusters reappear in the final section of the piece, chosen continually at random by an aleatoric ”music box” which added random amounts of frequency shift. The audio output of this Max/MSP patch was treated with external reverberation using an effects box to add sizzle. The Spatialisateur module of Max/MSP and its GUI interface were used to control dynamic movements. Using a feature of this software package, positions and rotations of a sonorous object, the soundfiles themselves, were controlled by mouse, and the output was recorded onto eight tracks. Using the circular GUI and hand movements of the mouse, sounds were made to approach from and recede back to large distances compared to putative speaker locations. Rotation speeds were automated with lists for the Max object line. Rotations were calculated to form Fibonacci ratios with each other, becoming increasingly faster and 200
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shifts of 1/4 (2/4 3/4 4/4), 3/4 (6/4 9/4 12/4) and 5/4 (10/4 15/4 20/4) tones and +- 1/8 tone for each CFGBD = 6000 6500 6700 7100 7400 (midicents) Keeping C fixed: +4/4 +-1/8 +12/4 +-1/8 D = 7400 +175-225= 7575-7625 +575-625 =7975-8025 +3/4 +-1/8 +9/4 +-1/8 B = 7100 +125-175=7225-7275 +425-475 =7525-7575 +2/4 +-1/8 +6/4 +-1/8 G = 6700 +75-125=6775-6825 +275-325=6975-7025 +1/4 +-1/8 +3/4 +-1/8 F = 6500 +25-75 =6525-6575 +125-175=6625-6675 C axis 6000 6000
+20/4 +-1/8 +975-1025=8375-8425 +15/4 +-1/8 +725-775=7825-7875 +10/4 +-1/8 +475-525=7175-7225 +5/4 +-1/8 +225-275=6725-6775 6000
Keeping F fixed at 6500 midicents: +3/4 +-1/8 D +125-175=7525-7575 +2/4 +-1/8 B +75-125=7175-7225 +1/4 +-1/8 G +25-75 =6725-6775 F 6500 -1/4 +-1/8 C -25- -75=5925-59756
+15/4 +-1/8 +725-775=8125-8175 +10/4 +-1/8 +475-525=7575-7625 +5/4 +-1/8 +225-275=6925-6975 6500 -5/4 +-1/8 -225-275=5725-5775
+9/4 +-1/8 +425-475=7825-7875 +6/4 +-1/8 +275-325=7375-7425 +3/4 +-1/8 +125-175=6825-6875 6500 -3/4 +-1/8 -125-175=5825-5875
Table 1. Horn Chaconne calculations: examples with C and F as pedal tones
suddenly reversed direction at maximal speeds, then slowing down. This entire process was repeated several times. Though this 3-D process cannot be recreated in a stereo mixdown, it comes across quite effectively with a diffusion of eight loudspeakers encircling the audience. The ambience of the entire piece is ”drenched”: use of water samples, a contour for the entire work which ascends slowly from a low pedal then sinks back down again, use of rapidly moving filtered-sounds which lack high-frequency content, as if played and heard ”underwater,” and spatialization which surrounds and engulfs the audience. To some listeners the final section may seem like an unexpected shift in musical material, but to the composer these sounds suggest having finally reached very deep waters - as some listeners have remarked - outer space (!).
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Ketty Nez Composer/pianist Ketty Nez completed in 2002-3 a res´ idence of several months at the Ecole Nationale de Musique in Montb´eliard, France, where she worked with faculty and students on projects of live electronics and improvisation. Her chamber opera An Opera in Devolution: Drama in 540 Seconds was premiered at the 2003 Festival A*Devantgarde in Munich. New projects include commissions for various ensembles in France and at the University of Iowa, where she currently teaches as Visiting Assistant Professor of composition and theory. This fall she joins the faculty at Boston University. In 2001 she was a visiting composer at Stanford University’s Center for Computer Research in Music and Acoustics (CCRMA), and in 1998, she participated in the computer music course at the Institute de Recherche et Coordination Acoustique/Musique (IRCAM) in Paris. Prior to her studies at IRCAM, she worked for two years with Louis Andriessen in Amsterdam, where she co-founded the international contemporary music series Concerten Tot and Met. Her music has been played at festivals in the US as well as abroad, including Bulgaria, England, Finland, France, Germany, Holland, and Japan. She spent the year 1988 in Japan, studying with Michio Mamiya and writing for traditional Japanese instruments. She has participated as fellow in the Aspen Music Festival (in 2001, 1991, and 1989), the 1998 June in Buffalo Festival, the 1997 Britten-Pears School Composition Course (Aldeburgh, England), the 1996 California State University Summer Arts Composition Workshop, the 1995 Tanglewood Music Center, and the 1990 Pacific Composers Conference (in Sapporo, Japan). Her education includes a doctorate in composition from the University of California at Berkeley, a master’s degree in composition from the Eastman School of Music, a bachelor’s degree in piano performance from the Curtis Institute of Music, and a bachelor’s degree in psychology from Bryn Mawr College.
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STRETTE - H` ector ector Parra Parra Abstract. Strette 1 is a 14 minute monodrama for soprano, live electronics, lighting and real time video, based on the poem by Paul Celan Celan Engf uhrung. u intended effect effect ¨hrung. The intended of the piece, in which the various elements of the show (sound, human voice, text, image and scenography) are processed, and relate to each other, in such a way that the dramatic nucleus is constituted by the sound flow itself, is to immerge the public in images and in psycho-ac psycho-acousti ousticc spac space. e. This may result result in a polyhe polyhedr dral al perce erception ption of the content ontent of Engf uhrung. u ¨ hrung. In the pages that follow I will attempt to explain the specific issues and problems we tackled while composing Strette composing Strette.. An important role was played by the Computer Assisted Composition Program OpenMusic in the development of the musical structures and the vocal score. ***
1
Dram Dramat atic ic and and mus music ical al iss issue uess
1.1
The inter interpla play y between between langu language age,, poetr po etry y and vocal vocal music music
Engf uhrung by uhrung by Paul Celan is a vivid and poetic example of the restoration of the Ger¨ ¨ man language language after it had been perverted perverted by the Nazis. The poem does not describe describe a reality; it is the text that constitutes the ’reality itself’. Consequently, there is no room for mimicry nor for the representa representation tion of a reality reality lying outside the language. language. This noteworthy characteristic of Celan’s poem makes it possible to establish direct links between music and text at a very basic language level. The music benefits from a greater degree of autonomy autonomy,, allowing allowing for a less destructive destructive treatment treatment of its acoustic acoustic and syntactic syntactical al identit identity y than is usual in vocal works. works. We could say that the primary goal of of Strette is the recovery of the tragic ethos through a more abstract dramatization than those customarily afforded by declamatory performances. If the experience is a moving one, it is the result of the tension between the temporal sound flow created by the music (vocal and electronic) and the simultaneous interacting flux of visual images. 1
Strette was composed during the Cours de Compositi Composition on et d’Informati d’Informatique que Musicale Musicale de l’IRCAM 2002-2003 and premiered by the soprano Val´ erie erie Philippin at the IRCAM’s Projection Space on October 15th 2003. The teaching teaching assistant assistant was Mikhail Mikhail Malt and the video assistant assistant was Emmanuel Emmanuel Jourdan. Benjamin Benjamin Thigpen, Thigpen, Jean Lochard Lochard and Mauro Lanza helped with the electronics electronics.. I would like to thank them for their confidence and for their help in creating Strette . This work was sponsored sponsored by a grant grant from the Departament Departament de Cultura of the Catalan Catalan Governmen Government. t. I would like to thank Josep Manel Parra for his wise advice and his help in creating the present text.
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The first step was to develop a style of vocal writing that, while maintaining reasonable contact with the rhythmic and declamatory characteristics of the poem, would be strictly based on organizational musical principles. The next phase, linking music and image (shape and colour) was accomplished in writing a vocal and instrumental script according to principles analogous to those of the colour theory the ory in oil painting. p ainting. Greatly inspired in spired by C´ezanne’s ezanne’s Chˆ ateau noir a noir a set of patches in OpenMusic OpenMusic was constructed, constructed, allowing allowing me to compose along strongly strongly gestural lines. Finally, with the help of the program Max/MSP-Jitter, certain image-based control procedures were carried out in realtime, enabling live interaction between the soprano’s singing face and the music. In a nutshell, a certain amount of hard work using the above mentioned computer programs resulted in a set of new questions and opened new paths in the search for more direct direct (i.e. non-metaph non-metaphoric orical) al) relationships relationships between between acoustic acoustic and visual thought, thought, and sensory experiences.
1.2
Dramat Dramatic ic role of the image image.. Commu Communica nicatio tion n between between sound sound and image
The intention was that the public would experience as absolute reality the interaction between between the text, the sound and the transforme transformed d image of the soprano. soprano. In accordance accordance with the essentially open nature of Celan’s poem, the soprano does not give a theatrical performa performance nce.. She simply simply sings. sings. The drama, drama, which which lies lies within within the sound itself itself,, is simultaneously developed and exposed in the visual domain. A veil, which together with the lighting, constitutes the only scenery, acts as a kind of resonating membrane for the action in the piece. The projection projection of the video-image video-image of the soprano transformed transformed in realtime with Max/MSP-Jitter creates technology-driven communication between the singer and the public.
Figure 1. The stage
Strette ends Strette ends much in the same way as it begins. But for the listener there is a striking difference difference - at least there there should should be! After having having watche watched d the dramatico-m dramatico-musica usicall piece he or she should have gained a more acute and distinct perception of the musical, textual and spatio-visual material, as well as a vivid awareness of having been in a unique global communication space. 206
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2 2.1 2.1
Working orking Strett Strette’s e’s vocal par partt Star Starti ting ng poin points: ts: Engf uhrung uhrung and Chˆ ateau ateau Noir ¨ ¨
The structure and articulation of the vocal discourse, comprising not only its main division into sections but also the rhythmic and interval sequences, are based on a twofold source. The first one is obviously the poem itself, with its nine sections and multiple subsections. We have tried to respect the semantic and syntactical elements of each stanza and each verse. This was necessary in order to achieve a meaningful musical development of the drama expressed by Celan. The other source was Chˆ ateau ateau Noir (1904); (1904); an oil painting painting by C´ ezanne ezanne that was owned owned by Picasso Picasso and that that now now hangs hangs in the Picasso Picasso Museum Museum in Paris Paris.. I believ believee it was the perception of a deep structural analogy between Celan’s impact on language through the poem and a ’pictorically guided’ two-dimensional visual intended to convey C´ ezanne’s ezanne’s impact upon form and colour colour that make up the basis of this work. I believe believe this is important in understanding the present essay. Thus, Strette Strette was conceived as a sequence in which the rhytmic and interval materials are subjected to driving forces and structural tensions that follow aesthetically significati significative ve colour relationship relationships. s. With this in mind, we began b egan to search search for quantifiable quantifiable relationships between spaces that would parametrize the music or sound phenomena and perception on one hand, and the spaces that parametrize colour vibrations and modulations on the other. other. These relationsh relationships, ips, which we will consider in detail, were a way way of gaining control over the rhythm and the intervals, which were intended to be a flexible representation of the poem’s rather strict syntactical and semantical character. The analysis of the poem Engf uhrung by uhrung by Peter Szondi and Werner Wogerbauer o¨gerbauer proved a useful ¨ ¨ guide, and provided valuable ideas for controlling the dramatic flow and achieving proper coordination. In Chˆ ateau Noir , after a strong initial blue-orange polarization, the light is progressively sively broken broken down down into into its spectra spectrall com compone ponent nts. s. At the same same time, time, because because of the emerging gray scale tones, and the tension generated by the diminishing colour, we begin to penetrate penetrate the variou variouss levels levels of the paintin painting. g. It is as if the modulat modulation ion allows allows us to bridge the chasm between the initial extreme blue and orange tones. However, a feeling of tension is generated by the conflict between this depth and the bi-dimensional character of the surface, a character that C´ ezanne ezanne strongly reinforces by means of abstract patches. We subjected the rhythmic and internal parameters to temporal formalisation, in accordance with the above ab ove described chromatic path taken by [the treatment of] of ] C´ezanne’s ezanne’s painting. painting. The guiding idea was that because of its specific musical musical nature, the rhythmic and interval characteristics of the vocal line could act upon the listener’s hearing in a similar way to the effect of the colour modulations of Chˆ ateau Noir Noir upon visual perception. The tool used to implement this idea was OpenMusic. We must stress that only a fraction of the colours used in the realtime modification of the soprano’s video-image actually correspond sequentially to those that have were used used in struct structuri uring ng the vocal vocal part. part. We believ believee that that this this process process,, carrie carried d out via the Jitter/MaxMSP program, Jitter/MaxMSP program, shows up the structural linkages that were created between sound and colour. 207
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Figure 2. Chˆ ateau Noir chapaeu chapae u dans d ans chateua by Paul C´ ezanne ezanne
2.2
Formalisatio ormalisation n of the the relation relationships ships colourcolour-rh rhythm ythm and colour-pitc colour-pitch. h. Implemen Implementatio tation n in OpenMusic OpenMusic
I should mention that the expressed aim to connect and develop parallel lines in colour and sound spaces does not imply any confusion of identity or actual mixing of the two spaces spaces - I am aware aware that each has its own distinct distinct charac characte terr and behaviou behaviour. r. Rather Rather the idea was to take advantage of the qualities of the colours and their effect on our perceptual and cognitive processes in order to create a set of pitch and duration values. The latter, based on clear and effective organisational principles, turned out to be able to accommodate a considerable degree of musical variation and richness. Colorimetri Colorimetric c system used as a basis for the formalizatio formalization n process. Data taken from Chˆ ateau ateau Noir The colorimetric colorimetric system system is founded upon the three perceptual perceptual colour colour parameter parameters: s: HueSaturatio Saturation-Int n-Intensit ensity y. HSI lies at the basis of my formalization formalization of rhythmic rhythmic and interv interval al thought, thought, which may be subject to a parallel parallel (and even even synchrono synchronous) us) developmen development. t. The three dimensions of HIS space are usually represented by a solid cylinder with luminosity 208
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along the vertical axis, saturation along the radial coordinate and Hue the along the angular angular one. Each Each colour colour is then represent represented ed by three three coordinates coordinates or numerica numericall values: values: the specific colour tonality (from 0 to 360), and saturation and intensity from 0 to 100 (figure 3).
Figure 3. Hue-Saturation-Intensity
It is obvious that the painting possessed many other interacting dimensions specifically related to colour and plasticity as, for instance, texture density, opacity and directionality of the brushstrok brushstrokee (fundamen (fundamental tal in C´ ezanne), ezanne), the shapes and kinds of colour colour patches, patches, etc. They are very difficult to analyze and cannot be manipulated in a simple way, even using a computer. After a number number of visits visits to the Picasso Picasso Museum Museum for detailed detailed study study of C´ ezanne’s ezanne’s masterpiece I was able to gain some ideas for my visual path through the painting, as well as an understanding of which colour patches were interacting at any given moment, and to what degree of intensit intensity y. I then carried carried out a temporal temporal articulation articulation of the chosen sequence of interacting patches, assembling them in little groups which could be made to correspond to each of the stanzas of Celan’s poem. This segmentation process was in no way a straightforward mechanical one. Each segment had to possess its own pictorial sense and, at the same time, share some semantic or syntactical characteristics with the correspondin corresponding g stanza. The central central part of the poem provides provides an illustration illustration of this. The language possesses a highly detached character and the two worlds, in opposition at the beginning, beginning, are reconciled reconciled at the end. The pictorial pictorial equivalen equivalentt can be found in the full spectral breaking down of the light after the extreme initial blue-orange polarization. Although it is subjective to draw parallels of this kind, we are convinced they are often at the very very root of creative creative artistic activity activity.. Naturally Naturally Celan’s Celan’s poem p oem has its own very special and suggestive qualities; as W¨ Wogerbauer ”Tout au long du Engf du Engf uhrung u ¨ogerbauer has noted, ”Tout ¨ hrung la cr´eation eati on po´ etique eti que est analys´ anal ys´ee ee dans une succession successi on d’´etapes etapes au sein d’une d’un e synesth´ syne sth´esie esie 2 g´en´eral ra le ” e ” .
2
W¨ ogerbauer, Analyse de Strette, 1991. ogerbauer,
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With this in mind I proceeded to choose, for each colour patch in a digitized image of the Chˆ ateaux Noir , those pixels that seemed to me as close as possible to the colour I had experienced at the museum. Then I evaluated the colorimetric mean of each zone that seemed to be of relevance during my visual path or pictorial reading of C´ezanne’s work. The network of HSI indices obtained in this manner was the expression (albeit a partial and oversimplified one) of the successive strains and stresses I experienced while looking at the painting. This data was now ready to be used as a starting point for the set of musical patches that we present below. Colour to rhythm: formalisation and implementation into OpenMusic In accordance with the overall plan of the piece, I designed a rhythmic space based on small units, each of them possessing its own temporal identity. Each has a minimum of three attacks and a maximum of seven. Each is associated with a colour, and the vertical polyphonic interaction between them had to produce a dynamic tension similar to that generated by the visual clash of colours. A way could now be found to translate Cezanne’s pictorial rhythmical structures and tensions into musical language. We outline below how this translation from the colorimetric to the musical space generated a rich basic material appropriate to the original conception of the piece. Each of the rhythmic units comprises two superimposed cells of attacks, one in progressive accelerando and the other in progressive rallentando. Each attack is triggered by a fixed discrete amount of an exponential (for the accelerando) or logarithmic (for the rallentando) curve that is characteristic of Hue and is defined as Saturation=100. The number of attacks for each rhythmic unit was kept to a minimum to maintain the character of each cell. The colours in the blue-orange axis, which constitute the pillars of C´ezanne’s painting, were assigned either seven or eight attacks while other colors were assigned six attacks. With decreasing saturation these functions tended to become linear, producing regular attacks in such a way that grays corresponded to complete regularity. The upper or first cell in time has its maximum acceleration at yellow, and maximum rallentando at magenta. The lower or second cell is opposed in character. The opposition is reduced for the flat complementary colours red and green in which one of the cells presents equally spaced attacks. These characteristics are shown in figure 4. The size ratio of the upper to lower cell is also fixed as a function of Hue for each value of saturation. It ranges from 1/10 at yellow to 5/1 at violet. Again the relative size tends towards value 1 (uniformity) with decreasing saturation, as is reflected in a non-quantified manner in figure 4. The delay between the upper and lower cell is also a characteristic function of hue that tends towards zero with decreasing saturation in a huedependent way: hot colours decay more quickly than cold ones, in accordance with colour perception theory. Flat colours (red and green) always present zero delay (simultaneity). Orange, yellow and violet, that give pictorial depth can achieve a maximum delay of a 20% of the size of the first cell. Again this fact has been qualitatively reflected in figure 4. Finally the physical extension of the time of each rhythmic unit is also a function of hue and intensity. At the maximum intensity of 100, yellow-orange colours have a maximum duration of 6 and 5 seconds, respectively. Their complementary colours violet and blue are given the minimum duration of 1 second. With decreasing intensity this 210
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Figure 4. Rhythmic units
distribution of duration values becomes almost inverted, in accordance with the visual rhythmic tension in C´ ezanne’s painting: in the brightest zones blues act as accents or 211
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activators of the more extensive orange patches while in the dark regions blues become dominant and profound, corresponding to rhythmic units of greater duration and fewer attacks. In fact, the displacement towards the dark regions of less ’luminic vibration’ corresponds to the disappearance of a part of the rhythmic content, specifically those attacks that by their closeness make the rhythmic unit more vibrant. Figure 5 is a simplified outline of how the rhythmic patch generates and utilises the above-mentioned variables. The example contains the rhythmic unit that corresponds to the colour orange (hue=30), saturation of 50% and Intensity of 80%. The as yet unquantified intervals between attacks are given in milliseconds.
Figure 5. Construction of the rhythmic unit corresponding to the colour (H=30, S=50, V=80)
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Thus, as shown in figure 6, the patch that gives the rhythmic variables consists of three main parts. First, the three entries corresponding to the colorimetric data in the Hue, Saturation and Intensity codification. This input is represented by the three upper arrows. Then there is the complex subpatch network that sequentially implements the transformation of a colour path into a rhythmic path. Finally there is an effective construction of the rhythmic units expressed in the form chord-seq , parametrized in milliseconds, and represented by the bottom arrow.
Figure 6. The rhythmic patch
Figure 7 is an example of the rhythmical musical tensions generated by the opposing colour pairs orange-blue and red-green, and the rhythmic sequences that result from the superimposition of the two corresponding rhythmic units. In the orange-blue case, the perception of extreme closeness and depth requires characteristic time values that amount to a deformation of the uniform flow of time. In musical terms these irregularities take the form of an initial energy propulsion (initial blue attacks) followed by a central development (orange and blue together), suddenly stopped by a second propulsion (blue ends) that gives way to the final expansion (orange alone). In the red magenta-green case, the pictorial flat colours, we have the superimposition of two regular patterns of different durations that express less energetic vibrations, and start at the same time. These interaction types between rhythmical units take place in the maquette . 213
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Figure 7. Two basical rhythmic sequences
From colour to pitch In parallel to the colour-rhythm association, I developed a system of patches in OpenMusic that, for each colour, give an aggregate of pitches or ’chords’ consisting of a maximum of eight pitches and a minimum of one. It is the interval relationships that are important here; and somewhat less important, the absolute value of the frequencies. The role of these pitch-groups is to provide a strongly characteristic and differentiated harmonic colour, even in a monodical disposition, as is the case for Strette . As the starting point for the computation of the chords I took the first 32 partials of a harmonic series whose fundamental pitch I altered several times in accordance with the formal structure devised for Strette . Thus, to the three continuous colorimetric indexes is added the fourth - external - parameter of a discrete and intrinsically musical nature (figure 8). 214
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Figure 8. Patch for the pitch
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Again, as in the case of rhythm, it is the Hue parameter that plays the dominant role in determining the idiosyncrasy of each pitch aggregate, defined at maximum saturation and intensity by means of the sub-patch represented in figure 9.
Figure 9. Sub-patch for the partials (hot colours)
Decreasing these parameters will modify the aggregate by reducing the number of elements and by homogenising the interval ratios. As we can see in the upper part of figure 8, small displacements of the fundamental of the harmonic sequence are carried out in such a way that the colours close to the yellow-violet axis are raised a half-tone, while those close to the green-red axes are lowered by a half-tone. This simple procedure is an attempt to avoid pitches belonging to chromatically opposed spaces coinciding too often. In figure 10 we see how the two named functions ’virtual-fundamental’ and ’bestfrequency’ belonging to the OpenMusic library Esquisse provide some of the pitches that will be used for a hot color and its complementary cold one. Together with other partials from the upper lines of this lower section, the ’cold colour’ aggregates will attract and acoustically complement those that correspond to the complementary ’hot colours’. 216
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Figure 10. Sub-patch for the partials (cold colours)
As saturation decreases the pitch aggregates lose notes until they are reduced to a single tone for saturation values lower than 20. The ’frequency-distortion’ function of Esquisse generates a reduction or compactification of the original range of the spectrum. It transforms the original irregular intervals defined in eighths of a tone at saturation 100 into regular interval progressions. For saturation between 50 and 75 the resolution is reduced to quarter tones and to half tones for saturation values below 50 per cent. To sum up, the progressive loss of saturation that describes the progression to gray is made to correspond to a process of homogeneization by reduction of the elements that characterize the idiosyncrasy of the initial chords. In figure 10 this process is represented for hue = 60o , intensity = 100 and saturation values of 100, 75, 60, 50 and 20. Finally, the decrease in the intensity parameter also reduces the number of notes as well as the range of the spectrum. However, in this case concentration does not take place around the central pitch of the chord, but rather in the higher frequencies in the case of the hot colours, and in the lower frequencies in the case of the complementary cold ones. 217
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Figure 11. Chords corresponding to successive changes of 15o in Hue, at the maximum level
of Saturation and Intensity
Figure 12. Progressive decrease of the saturation for Hue=60 and Intensity=100
2.3
Final steps towards the score
The maquette For each visual phrase of my aesthetic perception of C´ezanne’s Chˆ ateau Noir I constructed a maquette timeline along which I laid out the small rhythmic units corresponding to each colour present. Each maquette covers a 10 to 30 second timespan. The particular spatial layout of the different rhythmic units is inspired by the functions played by the corresponding colours, as mentioned above. On the right side of figure 13 can be seen the rhythmic patch analyzed above, integrated into the maquette, as well as the list of colours that constitute its input. I think this procedure is sufficient to accommodate a strong and flexible interaction between the output of the OpenMusic patches and the composer’s musical requirements. After transferring the maquette’s contents to the OpenMusic multi-sequence midi editor I carried out simultaneous filtering of the sequence to suppress all those attacks that seemed to me musically uninteresting, and also to implement the pitch corresponding to each colour in what was in fact the pre-composition of the vocal line. This work was done at the same time as the first manuscript drafts of the score and while thinking about the best means of processing the text. 218
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Figure 13. Maquette corresponding to the first 30 seconds of Strette
The process of rhythmic quantification The quantification of the musical phrases was carried out using the rhythmic quantifier provided by the library OMKant 3 . The figure 14 illustrates the three stages of this process: 1 Marking the sequence at those points where I want to start a measure or place a strong beat. 2 Triggering the quantification process, using the tempo I consider most appropriate at this point of the piece and which, at the same time, offers a quantification rather closer to that of the original sequence. 3 Displaying the result in the form of actual rhythms, with a fixed tempo applied to certain measures. It is necessary to stress that the specific characteristics of each phrase make this process different each time. There is no routine automatic processing. For instance, although I used the OMKant object to force the choice of rhythms that satisfied me more than those resulting from the quantification process of certain beats, I nevertheless strove to adhere to the derived material. The final creation of the fragment quantified in figure 14 is shown in figure 15. It is obvious that certain of the rhythmic characteristics proposed by OMKant have been 3
The OMKant library was conceived and programmed by Benoit Meudic.
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Figure 14. Quantification with the OMKant library
transcribed. In general their gesturality has been stressed and adapted to the text by combining various dynamic progressions and structured silences. In other places, e.g. the last part of the second measure, the entry point of the second articulation was considerably modified.
Figure 15. Exemple from the score (measures 18 and 19 of Strette )
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Bibliography [1] Carpenter J. and Howard F.: Color in Art . Fogg Art Museum, Harvard University, 1974. ´ [2] Gowing L. : C´ezanne: La logique des sensations organis´ees. Editions Macula, 1992, Paris. [3] Itten J.: Art de la Couleur. Dessain et Torla /VUEF 2001. [4] Lhote A. and Howard F.: Trait´es du Paysage et de la Figure . Bernard Grasset ´ Editeur, Paris. [5] Machotka P. : C´ezanne, Landscape into Art. Yale University Press – New Haven and London, 1996. [6] Meudic B.: Librairie OMKant 3.0. Edited by Karim Haddad. IRCAM, Paris 2003. ´ [7] Montchaud R.: La couleur et ses accords. Editions Fleurus, 1994. ´ [8] Szondi P.: Etudes sur Paul Celan: lecture de Strette, dans « po´esies et po´etiques de la modernit´e » . Presses Universitaires de Lille, France. [9] W¨ogerbauer W.: Analyse de Strette. 1991.
H` ector Parra Hector Parra is a Catalan composer, born in Barcelona in 1976. He studied music at the Conservatori Superior de Musica of Barcelona (composition with Carles Guinovart and Davis Padr´ o s, piano with Jesus Crespo) where he was awarded Honour Prizes in Composition, Piano and Harmony. He has taken active part in numerous workshops for young composers, among them those at Royaumont 2001, Takefu 2002 in Japan and Centre Acanthes 2002 and 2004. In 2002-2003 he followed the Composition and Computer Music Courses at the IRCAM, where he was taught by Brian Ferneyhough, Jonathan Harvey, Philippe Hurel, Philippe Leroux, Jos´ e Manuel Lopez Lopez, Mikhail Malt, Philippe Manoury, Tristan Murail and Brice Pauset. His compositions have been played at the international festivals of IRCAM R´esonances, Festival d’Avignon, Royaumont-Voix Nouvelles, Elektronische Nacht (Stuttgart), Madrid-CDMC, Mallorca, Ensemble Intercontemporain Tremplin at 221
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the Centre Georges Pompidou, Maison de la Danse de Lyon, and also broadcasted by France Culture, France Musique and SW-2 (Germany). Recently he was invited by the Stuttgart Opera House to give two workshop-concert sessions in the Forum Neues Musiktheater based on his monodrama Strette , and he has taken part in a composition stay with the Youth Ballet of the CNSMD Lyon as well as at the IRCAM. Several shows are scheduled in France, Hungary and Yugoslavia for 2005. His pieces have been premiered by the Ensemble Intercontemporain, the Arditti String Quartet, the Ensemble Recherche, Holland Sympfonia, the Duet Nataraya, among others. He was finalist at the Gaudeamus International Composition Competition 2005. In 2002 he obtained Composition Prize at the INAEM (Spanish National Institute for the Scenic Arts and Music) - Colegio de Espa˜na (Paris). He was awarded scholarships from the Foundation ”Agust´ı Pedro i Pons” at the Barcelona University (2001) and from the Catalan and Spanish Ministries of Culture (for a DEA in the Paris-VIII University in computer-assisted composition, under the direction of Horacio Vaggione). Since January 2005 he has been research composer at the IRCAM in Paris.
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Klangspiegel - Lu´ıs Antunes Pena Abstract. This article is based on the piece Klangspiegel for quarter-tone trumpet, tam-tam, and tape. It describes the use of the computer and OpenMusic using two different approaches: a) the spectral domain - the use and manipulation of a sample’s analysis data; b) the combinatorial - the interpolation process and rules dependent relations between pitch, dynamic, and rhythm. ***
1
Introduction
Acoustic reality – The beauty of the inner ”I have sought for myself” Heraclitus Modern tools of analysis allow us to explore a sound’s micro-time domain. We can extract specific information from a sample, and reduce the individual sound - a complex and somehow intangible entity - to a collection of concrete data. This information, representing only a limited reality of the sample, can then again be transformed back into sound via electronic resynthesis, creating a virtual image of the original sample. The result of this transformation, retaining an instrumental aura, is neither a copy, a duplication nor a simulation of the original, but rather a new entity. Through instrumental resynthesis of the original sample, we are then able to create another image, an introspective one: the information which has been extracted from the original sound, analysed and converted into pitches and dynamics is then played back by the trumpet, thereby projecting the previously imperceptible inner structures of the sound into the audible domain. Thus, the instrumental and electronic resynthesis enables two interpretations of a sound sample’s interior based on the same analysis. The piece Klangspiegel 1 (2002) for quarter-tone trumpet with tam-tam and 4-channel-tape, brings both representations to the foreground, and plays with the images that arise from the resynthesis: Virtual, Sound, Imaginary and Memory, corresponding to the four movements Klangspiegel I (for tape), Klangspiegel II (tape and trumpet), Klangspiegel III (trumpet) and Klangspiegel IV (trumpet and tape).
1
Sound Mirror.
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2 2.1
Virtual mirror Inside the trumpet
The mirror illusion is created through the resynthesis of various trumpet samples, some of them using breath sounds or ”normal”, but extremely short, tones with very unstable partials. The fact that ideal samples (having stable partials) for the analysis were deliberately avoided reinforces the idea that the resynthesis in this piece is not simply a reproduction of the original. At the same time, the autonomy of the image increases in proportion to the distance between it and the object from which it was generated. The mirror is thus a transformed image, which presents an interpretation of the original object. This interpretation is dependent on the nature of the analysis techniques used (limited by the technical resources at our disposal) and on the meaning imprinted upon this data (compositional decisions).
Figure 1. Patch used for the instrumental and electronic resynthesis of a sample
2.2
Manipulating analysis data - frequency and amplitude filter
When working with analysis data of a sample we are confronted with two problems: the large amount of information and its musical relevance. The analysis, in this case the result of a Fast Fourier Transformation (FFT), rapidly generates information in such quantities that we are able to work with it only with some difficulty - for each small portion of time (about 20µs), there are usually 1024 amplitude/frequency pairs. Furthermore, to use this information in a compositional context, we have to interpret the results of analysis 224
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which have thus far been neutral, musically meaningless. Selection is then a necessary means not only to make it humanly possible to deal with such a quantity of data, but also to give sense to an abstract collection of data. Here, the computer - and particularly the programming - can play an important role, by automating some aspects of the selection process. The reduction (transformation of the whole into smaller parts) and sorting (creation of hierarchies) effected by the computer are two possible ways to manipulate large-scale data. Considering a group of data as one entity is one way to reduce information. A first criteria would define boundaries to limit the information within a fixed range, while a second would create groups selecting the information with the help of a fixed rule. With these two selection principles we are able to use the same information in two different contexts, creating differing views of the same entity (figure 2). Criteria 1 corresponds to the traditional Bandpass Filter, selecting frequencies within the given limits, whereas criteria 2 is used in this piece to create a spatial division, where a, b, c and d correspond to speakers 1, 2, 3 and 4. Figure 3 represents the first 60 seconds of Klangspiegel I. Here, the bandpass filter selects 13 bands dividing the frequency spectrum of sample 1 between 320 and 3840 Hz, with each of the frequency bands having a different envelope.
Figure 2. Selection criteria for the FFT data
The third possibility to select large scale data is to sort the information using criteria which form a new order of the whole, that is to say, to scale the data between two opposed poles, from small to big, from high to low. This is the case of the amplitude filter. Here, the frequencies selected were those which were the loudest (figure 4). Another way to select large scale data would be to sort the information with one criteria to achieve a new order of the whole, that is to say, to scale the data between two opposed poles, from small to big, from high to low. This is the case of the amplitude filter. Here, the frequencies selected are the strongest. The third possibility is the one that does not depend on a pre-defined rule or criteria, but on an external factor in a specific temporal context. This is a complex selection 225
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Figure 3. Klangspiegel I, 0-60 seconds
Figure 4. Klangspiegel II. The tones selected from the Amplitude Filter of sample 1
method once it does not depend on any fixed rule, but it depends on the development of the musical discourse: what comes before and what follows. This selection method could be called organic criteria. With the two filter types we are then able to reduce the 1024-amplitude/frequency pairs of the FFT to usable data opening the possibility to differentiate it in a qualitative way. The use of the frequency filter in the first movement allows the whole spectrum of sample 1 to be divided in 13 frequency bands, each one with a different envelope. Consequently, every frequency band will appear in a particular order in relation to the others creating this way an internal melodic movement that mirrors the 13-degree-shape Gestalt (figure 3 and 5). On the other side, the amplitude filter selects frequencies from samples that will be interpreted by the trumpet as tones. During the last three movements different samples are brought to foreground by the trumpet: Klangspiegel II uses selected tones from sample 1 (melodic sequence D); for Klangspiegel III three sequences from sample 3 are extracted - sequence A, B, C, whereas Klangspiegel IV incorporates all the former sequences and adds sequence E (figure 9). 226
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3 3.1
Imaginary mirror Interpolation 1
The role of the computer in Klangspiegel is not restricted to the interpretation and modification of the micro-time domain (analysis and manipulation of spectral data). Its combinatorial potential is also present through the use of interpolation. This process is used to create a fixed number of equal steps between two different states. For example, the linear interpolation of the numbers 2 and 10 in 5 steps would be 2 4 6 8 10. This procedure can be applied to a melodic sequence to create a complex network of movements where several interpolations occur simultaneously, a number of strands overlapping one another. A further particularity of the interpolation process is its application to the time or pitch domain; both cases will give us the same final result, but the steps between the two poles (snapshots of the ongoing process) are quite different (figure 6). In the former, the movement of each tone in the temporal space presents us with a new order and rhythm, while the latter presents a purely melodic transformation - with no alterations to the rhythmic character, but with a new pitch constellation. Applying the interpolation to the time domain, or to the pitch domain, we perceive each variation as a continuous transformation process of the previous interpolation (without perceiving any break between them), as a variation of the original sequence, or as a new entity, depending on the type of the movement (direction and velocity) and on the duration of the pattern.
Figure 5. Gestalt and Gestalt mirror
Figure 6. Pitch vs. rhythm interpolation between Gestalt and its mirror
Time domain interpolation During the whole first movement there is a time domain interpolation of the shape Gestalt with its mirror. The internal movement of sample 1 changes gradually the melodic 227
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order of the frequency bands, i.e., the order of the highest point of the envelope each frequency band, which reflects Gestalt and Gestalt mirror . Each step of the time domain interpolation consequently creates a new rhythm, and the order of appearance of the frequency bands also undergoes a transformation. In Klangspiegel I the duration of each interpolation is also transformed, i.e., compressed or increased, and its order changed (figure 7).
Figure 7. Klangspiegel I. Each figure describes the envelope within the frequency band
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Pitch domain interpolation In the fourth movement, the tones played by the trumpet are the result of a pitch domain interpolation between the tone C and 75 steps of a melodic sequence, also starting on C (sequence E, figures 8). Each resulting pitch sequence runs its own course, starting with C and ending with B+, B, D+, E, F, B, C2 . The first sequence is from C to B+, i.e., a quartertone lower in 75 steps; the second is from C to B . The largest melodic movement is that of an interval of a fourth between C and F at the fifth tone in the sequence. This long process results in a very static field that resembles the opening of a bandpass filter’s bandwidth.
Figure 8. Pitch interpolation
iNtErP oLAtIoN 2 As the composition of the work progresses, the tones extracted from the FFT analysis acquire increasing autonomy, opening a further dimension. The focus shifts from the spectral transformations to the note-to-note domain and its combinatorial possibilities. Five melodic sequences are then extracted from different samples and form the main pitch constellations of the last two movements. In addition, the idea of reflection has been expanded, creating a new perceptual level through the dynamics: the mirror is now present in the melodic sequence through a dynamicly-varying relief that shapes the sequence by accentuating all its quartertones (figure 9). Consequently, the application of this rule instills in the melodic sequence a particular type of interdependence of pitch and dynamics, whereby each sequence has its own ’internal rhythm’ (the ff rhythm linked to the the quarter-tone pitches), which may be, or not, exteriorised, made apparent. From a single melodic line, a number of interior and exterior structures are rendered apparent: the pitch, the rhythm that emerges from the melodic contour, and the rhythm materialised through variations in dynamic. In the following example (figure 10) the same pitch series is repeated three times, each time with a different dynamic contour: in the first sequence, there are accents (notes with 2
The symbol ’+’ is used here to indicate the raising of the pitch by a quartertone.
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upward stems) on all the quarter-tones; the second sequence is a quasi-inversion of the dynamic contour of the first; and in the third sequence, the accents occur on only one pitch.
Figure 9. Melodic sequences A, B, C, D, and E. Dynamic/pitch relation
Figure 10. Klangspiegel III, bars 128-133
In a further development of what was already implicit by means of the distinction between notes having and not having quartertone inflections, the same idea - the internal sub-structures - is expanded through an interlocking of two or more melodic sequences. This procedure is, in fact, a different type of interpolation with no steps between them (in OpenMusic it would be achieved with a matrix transposition of two lists). In bar 27, the interpolation of two melodic sequences occurs (with slight variations): the 13-note sequence C with the 11-note sequence D (figure 11). The same interpolation will appear again in bar 70, but this time the accents are the result of the interpolation AD (again with slight modifications, see figure 12). The combination of both structures - the pitch sequence CD and the rhythm AD - creates a new melodic structure that emphasizes both quarter tones and 12-tone equal-tempered tones. At the end of the piece a new interpolation passage emerges containing three of the melodic sequences already played in the former movements (figure 13): D (all the notes 230
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of the second movement), C (from the third movement) and E (sequence appearing in the fourth movement). Here, in addition to the already-mentioned inner structures - the pitch, the ’quarter tone rhythm’, and the dynamic itself - a further temporal structure emerges through a ritenuto applied to the quartertones (upward stems).
Figure 11. Klangspiegel III, bars 27-38
Figure 12. Klangspiegel III, bars 65-77
Figure 13. Klangspiegel IV, bar 76
4 4.1
Memory mirror Inner connections
The reinterpretation of the mirror idea leads to a reflection upon the time axis of particular aspects of previously-occuring elements (single notes or rhythmic events, phrases or whole sections). A certain amount of continuity in the composition is assured by allusions to these elements, in the form of partial repetition. In this context, the role of the computer is one of an interface between different musical representations of abstract structures, assisting in bringing into relief otherwise inaudible structures and thereby bridging the electronic and the instrumental worlds. 231
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Memory mirror 1 - Rhythm structure In the first movement, the resulting rhythmic proportions of all 13 voices, i.e., the summing of each frequency band’s highest amplitude point, build a one-voice-framework which is set into new contexts during the second movement. Both tape and trumpet reflect this temporal macro-structure with different proportions. For example, the durations of the rhythmic line of the trumpet are a diminution of the tape parts, while the tape part forms a new structure over the trumpet, but with several of its original aspects compressed (similar to a fractal structure that mirrors a pattern in different proportions). Each of the tape layers resynthesizes different samples with different settings for the various frequency bands.
Figure 14. Klangspiegel II, bars 1-9 (samples 1, 2, 4, and 5 use only frequencies 11 to 13, while
sample 3 uses all frequencies 1 to 13)
Memory mirror 2 – Pitch structure A new section at the end of the second movement connects this and the third movements. All the FFT information is resynthesized and filtered using a bandpass filter, where the central frequencies mirror the tones played by the trumpet during the second movement. The subsequent phrase introduces tones that will be heard in the next movement. Again, the tone’s durations mirror those of the former section compressed by a factor of two and four, respectively. 232
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Figure 15. Klangspiegel II. Section that connects both II and III movements. The Y-axis
represents pitch in Midicents, where 6000 corresponds to middle C, 6100 to C and 6050 to C quarter-tone sharp. The lozenges represent the envelope of the sound, while the triangles inside the lozenges represent the time-varying bandwidth of the filter (the Q)
Dynamic and pitch mirror In the fourth movement, the pitch and dynamic information of all the 527 tones played during the previous movement is reinterpreted in the electronic and instrumental parts. All the information concerning the third movement - the grouping of tones, the duration of the pauses, articulation, tempi, dynamic fluctuations, use of breath or percussive sounds - is now reduced to a melodic sequence containing pitch and dynamic data. The vascillation between two levels of dynamics found in the third movement ( f / pp) is now transformed into a timbral change between senza sord. pp and con sord. p in this new melodic sequence. Reflecting all the dynamic information extracted from the third movement, the tones played by the trumpet are the result of an interpolation between the note C4 and the 7 tone sequence E (figure 8). In the tape part, the fundamental frequencies played earlier by the trumpet will now define the central frequencies of a bandpass filter selecting the FFT data. The chosen amplitude/frequency pairs centred on a specific frequency will be able to distinguish between pitches, each individual pair having a particular spectral structure and envelope (figure 16).
5
To Conclude
We could resume the use of the double process of analysis and resynthesis in Klangspiegel in two different ways: - the spectral manipulations, - the combinatorial work. 233
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Figure 16. General structure of Klangspiegel IV
The spectral manipulations of trumpet samples and their resynthesis aims to create a new entity that does not attempt to substitute the trumpet sound, but rather to establish a spectral fusion between the instrument and its synthetic mirror. This is particularily evident when the instrument and tape are heard simultaneously. The tam-tam, which stands unplayed near the trumpetist, and whose surface is excited by the trumpet playing with its extremely differentiated dynamics, functions as a filter for the trumpet sound. The timbre of the tam-tam’s resonance is situated somewhere between the sounds of the tape resynthesis and of the trumpet itself, thereby contributing to the successful blending of acoustic and electronic sounds. The combinatorial work in the third movement appears in this context as a natural consequence of previous sections. The reinterpretation of the analysis information already used in the tape part in Klangspiegel I and Klangspiegel II makes it possible to use this data as pitch constellations that are not dependent on interval logic; the semitone chromatic division of the octave, and its quarter, sixth, and eighth-tone extensions, are foregone in favour of a thinking which considers frequency from a micro vs. macro perspective. Finally, the conscious confrontation between these two aspects of the composition – the spectral and the note-to-note domain – represents then an irresistible temptation that the legacy of both serial and spectral music has left us. The d´emarche of the spectral composers in the 1970s offered a new way of considering pitch free of the interval 234
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hegemony that prevailed after WWII. Today, about 30 years after the first spectral compositions, the attention placed on the sound and its internal spectral structure, timbre and envelope still affords us an exciting world to exploit, but the ubiquity of the computer and increasing awareness of its combinatorial potential has opened up a new dimension, creating bridges between two historically-opposed approaches to composition.
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Lu´ıs Antunes Pena Luis Antunes Pena, composer born in 1973 in Lisbon, Portugal. He studied composition with Evgueni Zoudilkine, Antonio Pinho Vargas and attended the composition seminars of Emmanuel Nunes in Lisbon so as various summer courses in Paris, Darmstadt, Berlin and Brescia. Particularly important was the course ` with GErard Grisey in IRCAM in 1998. In 1997 he was one of the creators and artistic directors of the annual contemporary music festival Jornadas Nova M´ usica at the city of Aveiro, Portugal (1997-2002). He went to Germany in 1999 to continue his composition studies with Nicolaus A. Huber at the Folkwang Hochschule Essen. At the same time studies electronic music at the ICEM with Dirk Reith and later with G¸nter Steinke. In 2004 he concluded his composition studies and wrote his dissertation on Helmut Lachenmann’s Music. His music has been played in Portugal, Germany, Holland, Sweden and USA. ´ He won composition prizes at the contests ”Oscar da Silva” and ”Lopes Gra¸ca”, at the 11th Summer Seminar from Vienna, and his music has been distinguished and selected for the ISCM Festivals in Miami and Stuttgart, and at the 32e Concours International de Musique et d’Art Sonore Electroacoustiques de Bourges. He was granted the Rotary Club Scholarship, and between 2000 and 2004 the scholarship of the Foundation for Science and Technology from the Portuguese Ministry for Science and Education. 2005/06 he was awarded the ’MozArt 250’ scholarship from the Jeunesses Musicales Deutschland and the ZKM (Karlsruhe). Work selection: Anatomia de um Poema Sonoro (2003-2004) for Soprano, Speaker, Saxophone, Percussion, Piano and Live-Electronic, following texts from Jorge de Sena and Kurt Schwitters; Sonorous Landscapes I and II (2005) for Tape; Kippfigur (2004) for Saxophone Quartet; Klangspiegel (2001-2002) for Quartertone-Trumpet, Tam-tam, and Tape; ...Winterlich ruhende Erde...’ (2000) ” for Violoncello; Trajectories (1999) for 12 Instruments.
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Kalejdoskop for Clarinet, Viola and Piano ¨ - Orjan Sandred Abstract. This article begins by explaining how harmony is built in Kalejdoskop. It then describes the rhythmic structure and its connection to harmony. The harmony and rhythm were organized with the help of the OMCS and the OMRC libraries in OpenMusic. The main part of the article discusses the musical aspects of the piece and only briefly describes the computer implementations. ***
1
Introduction
Of all my pieces, it is in Kalejdoskop that I have gone furthest in working with computer assisted composition. The piece was composed after completing the OpenMusic Rhythmical Constraints Library (OMRC ) for OpenMusic. The ideas that triggered the creation of the OMRC library were used very consistently in the piece. The choice of a rule based system made it possible to force a rigorous structure to integrate ear-based decisions. The computer processing is based on building blocks designed by ear. The larger structures generated by the computer were evaluated with the ear and could be returned to the computer with instructions for corrections. By using the computer the structure was kept consistent with my concept even when changes were made by hand.
2
Harmony
The way we experience harmony depends on two parameters: the vertical chord structure and the horizontal context. The smallest vertical building block in a chord is the single harmonic interval. Only four harmonic intervals exist in Kalejdoskop: minor seconds, perfect fourths, tritones and minor sixths. By using this strict limitation to four harmonic intervals, a first step is taken in the creation of a harmonic identity. The intervals are superimposed so as to create more complex chords. The starting point for the horizontal context is local voice leading. The harmonic intervals are paired and the voice leading between them is fixed. Since certain harmonic intervals can only pair up in one way, the horizontal possibilities are limited and the pairs of harmonic intervals become pieces of a puzzle with which to build longer sequences. The greater the number of pieces to choose from, the greater the number of variations that will be possible in the sequences. Complexity increases significantly when a third voice is added. The middle voice functions as a lower voice to the intervals between voice 1 and 2, and as an upper voice 239
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Figure 1. Four pairs of harmonic intervals. The voice leading in each pair is fixed and can not
be changed changed
to the interv intervals als between between voice 2 and 3. An added third voice will consequentl consequently y give give the middle voice much less alternatives in its design. To avoid a dead end when building sequences, the pairs of intervals are designed so that the lower voice in one pair can work as the upper voice in another pair. In figure 1 the lower voice in the first pair can work as the upper voice in the second pair, the lower voice in the second pair can work as the upper voice in the third pair, the lower voice in the third pair can work as the upper voice in the fourth pair, and the lower voice in the fourth fourth pair can work work as the upper voice in the first pair. In this way there is always always a pair of intervals for voice 2 and 3 which has an upper voice that will fit in to the lower voice voice of the pair of interv intervals als between between voice 1 and 2. Only two two different different sequences sequences with three three voices can be created created from the four pairs of harmonic harmonic interv intervals in figure 1. Both sequences will contain two different chords that change places (see figure 2).
Figure Fig ure 2. The two possible possible sequence sequencess of three three part chord chordss built built of the pairs of harmon harmonic ic
intervals in figure 1
If the pairs of intervals are allowed to be read both from left to right and from right to left there is a greater number of sequences possible. To obtain a more varied harmonic langua language ge a larger larger number number of pairs pairs of inte interv rvals als are needed. needed. In figure 3 all 32 pairs pairs of harmonic intervals that were used in Kalejdoskop can be found. found. The upper upper and lowe lowerr voices in a group of four pairs have the same relation as in figure 1. I tried to avoid minor seconds as a melodic interval when I created the pairs of harmonic harmonic intervals. intervals. I often find that the chromatic chromatic voice profile profile has lesser clarity clarity than 240
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Figure 3. All 32 pairs of harmonic intervals used in Kalejdoskop
larger intervals. Figure 4 analyses the frequency of different melodic intervals in intervals pairs. It is clear in the graph that the prime is the most common melodic interval followed by the minor third. Two of the minor seconds and three of the major seconds are identical 241
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(10 is identical to 23, and 16 is identical to 20 and 4 if read backwards). All minor and major thirds, perfect fourths and fifths are unique.
Figure 4. The graph shows how frequent different melodic intervals are in the pairs in figure 3
The pairs of intervals are formalized into a rule in a rule-based system in OpenMusic. The rule pair only allows for harmonic intervals and the voice leading between them that can be found among the pairs of intervals. The pairs of intervals can be read both from left to right and from right to left. Pairs of intervals may be transposed.
Figure 5. The OpenMusic patch that generated the harmony fore Kalejdoskop
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The rule is applied to all chromatic pitches in a range of three octaves. Five voices are generated. generated. The calculation calculation is carried carried out by the PMC-engine in the OMCS the OMCS library (developed for PatchWork by Mikael Laursen at the Sibelius Academy in Helsinki). Figure 5 shows the OpenMusic patch. On the left is an open window containing. The PMC-engine generates generates five-part five-part chords. Every Every fifth pitch in the answer belongs to one voice. The above described system is somewhat lacking in global control of the harmonic developm development ent.. Ths can be b e improved improved by rules that for example force chosen chosen chords at strategic points in the sequence. In figure 6 the first 24 chords in the piece can be seen.
Figure 6. The first 24 chords in Kalejdoskop
3
Rhythm ythm and form orm
Different Different sections sections of the piece use different different strategies strategies for the rhythmic rhythmic structure. structure. To simplify, one can say that the piece starts with a minimum of control over the rhythmic structure and then arrives at a more clearly defined rhythmic language. The piece can be divided into three sections, with the subdivision of each section follo followin wingg the same patte pattern, rn, where where two two rhyth rhythmic mic struct structure uress chang changee places places.. The first rhythmic structure (A) is homophonic and the three instruments rhythmically support each other and the second rhythmic structure (B) is polyphonic while the clarinet and the viola play their own rhythmic rhythmic and melodic line. The middle section section is a mirror of the surrounding surrounding sections sections as A and B subsectio subsections ns change places. places. The middle section’s section’s pizzicato and staccato playing contrasts with the surrounding sections.
Figure 7. The form for Kalejdoskop
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4
Rhyt Rh ythm hm an and d stru struct ctur ure e
As mentioned in the introduction to this article the ideas that led to the OMRC OMRC library were central when I composed Kalejdoskop composed Kalejdoskop.. I investigated different methods for creating a rhythmic identity in the piece. There are two possible ways of doing this in the OMRC library: rules for the rhythm are either applied to a number of allowed note values or to a number number of rhythmic rhythmic fragment fragments. s. In the first solution solution the rhythmic rhythmic identity identity is defined defined in the rules. In the second second solution solution the rhythm rhythm fragments fragments already contain contain some rhythmic rhythmic identity and the rules serve more as tools to build longer sequences out of the fragments. Both methods are used in Kalejdoskop. Kalejdoskop.
Figure 8. The three hierarchical layers in the rhythmic structure
The rhythm structure is built hierarchically. The most fundamental hierarchical layer represents the most abstract level and is closest to the form of the piece ( the form layer ). layer ). The harmonic rhythm is an intermediate layer (the (the harmony layer ). layer ). The third third layer layer is the performed rhythm in the music (the (the rhythm layer ). layer ). The connectio connections ns between between the layers layers are based on the onsets (i.e. (i.e. the starting starting points) of the events events.. The onsets of the events in the slimmest (or sparsest) form layer also have to serve as onsets for events in the harmony layer. The harmony layer may however however contain onsets for events events betw b etween een the onsets in the form layer. The form layer can be seen as a rhythmic simplification of the harmony harmony layer. layer. The rhythm layer layer has the same relation relation to the harmony harmony layer layer as the harmony layer has to the form layer i.e. the onsets for events in the harmony layer have to serve as onsets onsets for events events in the rhythm rhythm layer. The rhythm rhythm layer layer can contain contain onsets for events in between onsets in the harmony layer. The hierarchical structure is the fundamental rule for the rhythms and constitutes a fundament fundamental al concept of the piece. Each Each hierarch hierarchical ical layer layer also has its own set of rules. There are two two types of rules: rules: strict strict rules that do not allow exception exceptionss and rules rules that will be followed when possible (referred to as ”tendencies” ”tendencies” in the text). The rules for different sections in the piece are described below. The first first A1 subsec subsectio tions ns in the piece piece are all built in the same manner. manner. The f orm orm th layer layer consists of an even pulse that returns every 9 quarte quarterr note. This This pulse pulse is not emphasized in any instrument but it is still present since it influences the phrasing and the rhythmic gesture (see below). The harmony The harmony layer is based on four note values: values: a whole note, a dotted quarter quarter note, a dotted eighth eighth note and a sixteenth sixteenth note. The note values values can come in any order and they can be repeated (see figure 9). There is however a tendency for the harmonic rhythm to start with the shortest note value (the sixteenth note) and proceed step by step with 244
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increasing increasingly ly greater note values values thus creating creating a ritardando ritardando in note values. values. After this ritardando ritardando the tendency is in the opposite opposite direction, direction, i.e. an accelerando accelerando in note values. values. This rhythmic gesture takes place within one pulse in the form layer (nine quarter notes) and then starts starts over again. again. The rhythmic rhythmic gesture gesture exists as long as it is not in conflict conflict with the hierarchical structure discussed above.
Figure 9. The basic note values in the A1 subsections
The rhythm The rhythm layer is based on six note note values: alues: an eighth eighth note tied to a eight eighth h note note triplet, a dotted eighth note, an eighth note, an eighth note triplet, a sixteenth note and a sixteen sixteenth th note quintuple quintuplet. t. The hierarchical hierarchical connection connection to the harmony harmony layer layer is a constrain constraintt for the choice choice of note values. values. There is one tendency tendency and one rule that work together in the rhythm layer: the tendency is for note values to be immediately repeated but the rule forbids more than three repeated note values in a row, with the exception of the sixteenth sixteenth note quintuplet quintuplet that is allowed allowed a maximum maximum of five in a row. row. Triplets riplets and quintuplets are not allowed to start offbeat.
Figure 10. The form layer, harmony layer and rhythm layer at the beginning of Kalejdoskop .
The final score for this section can be seen in figure 17
To summarize summarize the rhythmic rhythmical al language language in the A1 subsection subsections: s: three three identica identicall note values values often succeed each other. other. There There is a hidden hidden rhythmic rhythmical al gesture in the harmony harmony layer (a ritardando followed by an accelerando). This gesture affects the phrasing in the rhythm layer. There are no other controls over the rhythmical language. 245
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The rhythm in the piece becomes increasingly directed, and in greater detail, by the system. The rhythmic layer in the last A3 subsections are based on pre-composed rhythmic motifs (or parts of motifs) instead of single note values. In this way the rhythmical language is more predefined. Just as in the A1 subsections, the form layer in the A3 subsections consists of an even pulse that returns every 9 th quarter note. The note values in the harmony layer are expanded to seven: a whole note, a quarter note tied to a quarter note triplet, a dotted quarter note, a quarter note tied to a sixteenth note sixtuplet, a quarter note triplet, a eighth note triplet and a sixteenth note. The note values are allowed to come in any order and can be repeated. As with the A1 subsections, there is a tendency for a rhythmical gesture to form in the harmony layer. In the A3 subsections the gesture consists of an accelerando that starts over at every new pulse in the form layer.
Figure 11. The basic note values and motifs in the A3 subsections
The rhythm layer is based on eight rhythmical motifs or fragments of motifs (see figure 11). Because of this, the hierarchical connection to the harmony layer becomes a harder puzzle to solve than in the A1 subsections. Two more rules influence the choice of motif: a motif cannot be immediately repeated, and triplets and quintuplets are not allowed to start offbeat.
Figure 12. The form layer, harmony layer and rhythm layer at measure 78 (the beginning of
the first A3 section). The performed rhythm is marked with gray. The final score for these measures can be seen in figure 18
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To summarize the A3 subsections: the rhythmical language is more complex but also more controlled than that of the A1 subsections. The language is mainly defined in the pre-composed motifs. The system builds longer sequences of the motifs, taking the hierarchical structure into consideration. The only exception from the strict structure in the piece can be seen in figure 12 and 18: since the music makes sudden jumps between rapid passing notes and sustained chords, the performed rhythm originate alternately from the rhythm layer and the harmony layer. Opposite to the A subsections, the B subsections have two polyphonic voices. Because of this there are two rhythm layers. Both rhythm layers have a hierarchical relation to one single harmony layer (see figure 13). The B1, B2 and B3 subsections that exist in the piece have a similar construction. The B1 subsection is used as an example below.
Figure 13. The hierarchy between layers in the B subsections
The form layer contains one single pulse that has the same length as the length of the whole subsection. The harmony layer is based on six note values: a whole note, a dotted quarter note, a quarter note tied to a sixteenth note in a sixtuplet, a dotted eighth note, a eight note triplet and a sixteenth note. The note values can come in any order but there is a tendency to avoid immediate repetition. There is no rhythmical gesture similar to the gesture in the A subsections. Instead, the much more complex hierarchical connection to the two rhythm layers affects the choice of note value.
Figure 14. The basic note values and motifs in the B subsections
The rhythm layers are based on eight note values and seven rhythmic motifs (see figure 14). The note values and the motifs are allowed to come in any order with the exception of the immediate repetition of a note value or motif. To some extent, the two 247
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layers are built independently of each other. There is however a tendency that at a point where a single note value is chosen for one of the rhythm layers, a motif is preferred in the other rhythm layer and vice versa. The interplay between the rhythm layers will create a counterpoint, where one voice has longer note values while the other voice has a clear profile with more elaborate rhythmic motifs in shorter note values. The two rhythm layers are connected since they are built on the same harmony layer.
Figure 15. The form layer, harmony layer and two rhythm layers at measure 17 (the beginning
of the first B1 section). The final score for these measures can be seen in figure 19
Figure 16. The OpenMusic patch for the computation of the A1 sections
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The rhythmical structure was completely created on the computer for the entire Kalejdoskop piece. If the computer reached a dead end during calculation, it was not decided in advance which layer should be changed. It is possible that the harmony layer was adjusted to fit the rhythm layer as well as the reverse. The rules cannot be broken but it is always possible to compromise with the tendencies. In figure 16 you can see the OpenMusic patch that was used for the computation of the A1 sections. In computer parlance tendencies are called heuristic rules. The form of the piece influences the choice of single note values since the hierarchy and the rules link the form via the harmonic rhythm to the note values. The rhythmical system was very strictly applied in Kalejdoskop. A somewhat freer use of the system can be found in Amanzule Voices for violoncello and live electronics.
Figure 17. The beginning of the piece (see also figure 10)
Figure 18. The beginning of the A3 section, measure 78 (see also figure 12)
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Figure 19. The beginning of the B1 section, measure 17 (see also figure 15)
A more general description of the ideas behind the OMRC library can be found in the PRISMA review no.1.
5
Summary
The method of composition described in this article has as its starting point a single musical building block as a single interval or a single rhythmic motif. The method differs from methods used by Xenakis for example. Xenakis focuses on the total effect of the musical parameters. Single pitches and rhythmic motifs are left to mathematical formulas. In Kalejdoskop there is a relationship between elaborate details (sometimes designed in advance) and the overall impression. Kalejdoskop was commissioned by the Swedish Arts Grants Committee, was composed in 1999 and premiered on October 2 of the same year at the Modern Museum of Contemporary Art in Stockholm. The piece is recorded on the CD ”Obscura” (dB productions 2002), and the score is available at the Swedish Music Information Center.
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Bibliography [1] Laursen, M. : PATCHWORK: A Visual Programming Language and Some Musical Applications . Doctoral disertation, Sibelius Academy, Helsinki, Finland, 1996. ¨ Kalejdoskop. Swedish Music Information Centre, Stockholm, Sweden, [2] Sandred, O.: 1999. ¨ OpenMusic RC library version 1.1. IRCAM, Paris, France, 2000. [3] Sandred, O.: ¨ OpenMusic RC library version 1.1, tutorial. IRCAM, Paris, France, [4] Sandred, O.: 2000. ¨ [5] Sandred, O.: Searching for a rhythmicla language in PRISMA no 1. EuresisEdizioni, Milano, Italy., 2003
¨ Orjan Sandred ¨ Orjan Sandred (born 1964) grew up in Uppsala, Sweden. After having studied Musicology at the University, he moved to Stockholm to attend the composition program at the Royal College of Music 1985-97. He took private lessons in Copenhagen and London with Poul Ruders and in 1994 - 95 he studied composition at McGill University in Montreal, Canada. In 1997 - 98 he attended the annual course in composition and musical computing at IRCAM in Paris. Among his teachers are Sven-David Sandstrˆm, Magnus Lindberg, Per Lindgren, Daniel Bertz, Bruce Mather, Bruce Pennycook (computer music) and Bill Brunson (electro-acoustic music). As a composer, Sandred has regularly received commissions from Swedish and foreign music institutions. He has written music for different types of ensembles, including symphony orchestra, ensembles with live electronics, chamber music and electro-acoustic music. Among his pieces are Polykrom (for chamber orchestra), Cracks and Corrosion I and II (I for piano quintet and II for guitar and live electronics) and Amanzule Voices (for cello and live electronics).
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Sandred taught electro-acoustic music and composition at the Royal College of Music in Stockholm from 1998 - 2005. Since 2005 he has been professor in Composition at the University of Manitoba in Winnipeg, Canada. He was guest lecturer at several institutes, for example the Sibelius Academy, Helsinki, the Conservatoire National Superieur de Musique, Paris and the Bartok Seminar in Szombathely, Hungary. He is a member of the international musical research group PRISMA (Pedagogia e Ricerca Internazionale sui Sistemi Musicali Assistiti). PRISMA is formed by composers and was created within Centro Tempo Reale (Florence).
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Flexible Time Flow, Set-Theory and Constraints - Kilian Sprotte Abstract. This article presents several examples of my use of OM as a compositional tool in the process of writing the piece Fernweh. It was useful in the domains of harmony and rhythm, sometimes as a simple and rapid scratchpad, but also for solving constraint satisfaction problems, allowing me to investigate a comparably large space of combinatorial possibilities. ***
1
Introduction
How can two poles - a great distance apart - be made to meet? Each pole has its own timeflow. If neither changes its tempo, they will simply run in parallel and meet in infinity. Only a flexible flow of time will enable them to approach each other. Acceleration and deceleration will bring them closer and move them apart respectively. This is the initial idea for starting the piece Fernweh for cello, accordion and percussion, which I completed in February 2003. It was premiered on April 4, at the Fr uh¨ jahrstage f ur Musik in Weimar, by the ensemble Klangwerkstatt Weimar. ¨ zeitgen ossische ¨ The title Fernweh brings together distance and grief, which can be described as the ”opposite of homesickness”. It was the notion of farness and nearness that interested me, a notion that can also be regarded as a play of dependence and independence between the two poles. As for the instrumentation, the cello mainly plays the role of one pole, while accordion and percussion represent the other. From time to time however they contribute to the layer played by the cello. On the most obvious level of the form, the piece is divided into two parts (the beginning of each part lasting 4 and 2 minutes respectively, see figures 1 and 14. I will refer to them as the first and second part. Since this essay deals mainly with complex aspects of CAC - this has been my first in-depth contact with CAC - my approach has been somewhat like a patchwork, without a great deal of global formalisation. In the process of getting to know the various CAC procedures, I became increasingly aware of a possible categorization into two groups that in my opinion show a distinct difference in quality: whereas some CAC tools can be considered as a useful but simple extension of ordinary means, there is a second category, in which the actual algorithm is automatically generated on the base of a set user-defined constraints, and as a result of which one enters a very different domain, going far beyond the mere use of the computer merely as a faster scratchpad. It enables the composer to solve problems of great complexity, and opens up new possibilities, exceeding what can be done with pen and paper, all thanks to technology. 253
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Figure 1.
2 2.1
First part Rhythmic aspects
Flexible time flow The sujet of two dialectic poles has first of all found its expression in the time flow domain. It exists by superimposing different constant tempi, but also by combining a constant and a (continuously) changing tempo. 254
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OM showed itself to be a very helpful tool especially when working with this flexible time flow, allowing me to lay down rhythms as if they were played with constantly changing tempo (whether ritardando or accelerando) thus making it possible for me to superimpose them on other, differently treated layers. The possibility of rewriting a given pulse in a different tempo, while retaining the same sound and pitch, is obviously of great interest. This principle is shown in figure 2: Tempo 90 is being represented in tempo 60.
Figure 2.
What happens when the tempo of the rhythm being transcribed needs to be flexible? An example of this is shown in the accelerando that leads from 60 to 90 in figure 3. The note durations in tempo 60 have increasingly shrinking durations.
Figure 3.
In order to deal with these rewriting issues, I created two functions for OM, namely notdur->realdur and realdur->notdur that are able to convert between the notated duration values and the sounded duration values. A mathematically smooth accelerando as required in the second example will be defined as a linear interpolation on a logarithmic tempo scale: the ratio between different tempi is more relevant than their difference (Stockhausen, 1963). Figure 4 shows a patch in which a rhythmical fragment from Fernweh is converted from the notation of the desired sounding result in tempo 60 to its notation under a ritardando curve. The list (125 1875 667...) shows the desired durations in ms that get converted to the following list with increasingly shorter durations (125 1755 567...) that can now be notated with a a 60 constant tempo quantization. The second parameter (60 11000 30) is used to describe the tempo curve as a break-point function with alternating tempo value and inter-point duration. 255
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Figure 4.
Hierarchic rhythm For the general rhythmic structuring of the first part, I have used a top-down approach. Starting from a framework of time points covering the first four minutes, I have inserted between them ”complex rhythm cells” that have were also constructed by hierarchically combining different ”simple rhythm cells”, chosen from a pool of about 80 cells. A patch that allows the combination of those simple cells into a more complex structure can be seen in figure 5. I use the input in the top left corner to insert a list, which describes the resulting rhythm. In this case: (28 (37 (76r (2n 37r 4n)) 75)). Or more clearly in figure 6.
Figure 5.
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Figure 6.
A number represents an index of one simple rhythm of the pool. The elements used in this example are shown with an arbitrary eighth-note pulse as their unit. In the notation a list ( ( )) is used to describe a subdivision of the rhythmical pattern from by the patterns that are listed in ( ), in which succeeding elements refer to the durations of , where they are filled in. As in this example, expressions can be nested. If an ”r” is added to a number, it means that the pattern is reversed. A notation like ”2n” means that 2 duration values of the super pattern are not subdivided. The result of this description is shown in figure 7. By anchoring this and other patterns in the time points framework, they are once more treated like a sequence of proportions that are to be individually stretched. Finally, the KANT library has been used to quantify the resulting (polyphonic) rhythm.
Figure 7.
Aperiodicity In this section, I examine hierarchic rhythmic structures anew. I describe a rhythm as aperiodic if it does not contain repeated duration values and if this is also true for any other abstract level. The (aperiodic) structure (1 3 2 4) can be seen in figure 8 with all its related super structures. None contain direct repetitions. I have taken advantage of this property in writing a short sequence for temple blocks (first staff of figure 9). Each of the 5 blocks can be thought of as one continuous voice (staffs below). All the voices are aperiodic. This sequence has been generated using the pmc-engine. In addition to the aperiodicity, some rules concerning playing possibilities were applied (see Second part, Harmonic aspects). 257
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Figure 8.
Figure 9.
2.2
Harmonic aspects
Selection of an initial set Many of the harmonic structures of the piece are based on one initially chosen set of five pitch-classes: (0 1 3 6 7). It was selected from the list of all possible prime forms of Z 12 (see the table in figure 10 for a list of prime forms. Consecutive sets marked a and b are inversions of each other, symmetric sets are marked s). Prefiltering has been carried out according to two criteria: 1 The set should contain all the interval classes. 2 The set should be combinatorial. Combinatoriality for sets of cardinality other than 6 has been defined, following the concept of combinatorial hexachords. In this sense, a set is called combinatorial, marked 258
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Figure 10.
c if it is a subset of its complement and inverse-combinatorial (marked inv − c), and if its inversion is a subset of its complement. Interestingly, no all-intervallic set is combinatorial and vice versa. Therefore, I have chosen to use the inverse-combinatoriality property (given for every set, except (0 1 3 5 6)). From the remaining possibilities, I intuitively chose to use (0 1 3 6 7) and its inversion (0 1 4 6 7) as initial sets. In figure 11, you can see a circular representation of (0 1 3 6 7) and its complement. Using these features, a twelve-tone-row can be constructed.
Figure 11.
Constrained based harmony A 148 chord progression has been established as a harmonic framework for the first part. It is based on the sets (0 1 3 6 7) and (0 1 4 6 7), as well as their complements (0 1 2 3 6 8 9) and (0 1 2 3 6 7 9). 259
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For each of these four sets, all the possible registral distributions in the space of two octaves have been generated. Figure 12 shows as an example all the 46 possibilities for the set (0 1 3 6 7). Starting from these, I have made intuitive selections (marked with *), which I used as a pool of chords that can be transposed, but not changed in their registral layout.
Figure 12.
I have used the PWConstraints pmc-engine, in order to generate the chord sequence based on this chord pool, applying the following rules:
• no octaves in outer voices, meaning no pitch-class duplicates, whether in the succeeding pitches of soprano or bass, or crosswise, • in a sequence of 16 chords there must be no chord-duplicates (regardless of transposition), • in neither the soprano nor the bass voice may any pitch-class be duplicated in a succession of 4 pitches, • common pitch-classes between adjacent chords must be close to predefined values, • there must always be as many common pitches (not pitch-classes) as possible between adjacent chords (as a heuristic rule). Figure 13 shows the first 9 chords of the resulting sequence, used as a framework for figure 1.
3 3.1
Second part Rhythmic aspects
The second part (for its beginning, see figure 14) is entirely notated using two superimposed tempo layers ( / ). The predominant rhythm on the faster layer is a 260
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Figure 13.
continuous sixteenth-note pulse; it is equivalent to a quintuplet sixteenth division in the other tempo.
Figure 14.
Formally, this part can be subdivided into four sections of equal length (see figure 15). The A sections share the same rhythm. For their changing characteristics see below.
Figure 15.
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In the other layer, there is again a process of continuously changing time flow, but much longer in its total duration. Section C consists of a rhythmic ostinato, with a steadily increasing tempo. Because this accelerando is so spread out, it is actually incorporated into the written rhythm, being played at the constant tempo of . The shape of the ostinato pattern itself is also changed in such a way that at the end of the process it becomes a completely regular pattern, coinciding with the other layer.
3.2
Harmonic aspects
The pitch structure of the A sections consists of a common sequence of pitch-classes based on the twelve-tone row created from the initial set of five notes (see figure 11). An excerpt of this is shown in figure 16, which relates to a former version of the piece for cello and piano. Some of the pitch-classes are missing in the piano part. They have been filtered out and have served as a framework for the cello part. The registral distribution of the pitch classes of the piano were controlled by a sequence of changing pitch fields.
Figure 16.
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When I transcribed this sequence for new instruments, I wanted it to be played by marimba and accordion. My idea was to change only the registral distribution in order to make it playable for these two instruments. At the same time, I wanted to keep to the idea of only gradually changing pitch fields, a rule which I expressed as follows: Each pitch-class has to stay in its register at least four times before the register of a recurring pitch-class can be changed. This rule (as a musical constraint) was confronted with a set of rules modelling the playing capabilities (as a technical constraint) for each instrument.
• For the marimba, the system attempts to use alternating strokes for each hand (assuming only two hammers), but also allows the crossing of hands and double strokes, if certain conditions are fulfilled. • For the accordion player, who like the marimba player, splits the monodic line between hands, the jumps in each hand are kept to a minimum. The case of the woodblock described above (see First part, Aperiodicity) was treated similarly to the marimba. A set of simplified rules was used.
4
Conclusion
The more I worked with the various techniques presented above the more I felt the need to unify them into one system. I believe it would be ideal to use a constraint-solving engine as a kernel algorithm, around which all the other tools can be developed. An encouraging starting point for me was the example of the marimba described above. I think the most natural approach would be to formulate rules in different domains such as rhythm, harmony, playing technique etc. and ”solve” them simultaneously in one system or at least, ”find the best compromise” between conflicting rules (irrespective of the domain to which they belong!) Unfortunately, this would not be an easy task. Even if one were to limit the application to generating polyphony and to controlling the harmonic and rhythmic structures of each voice (as well as those of the whole score), there would be considerable difficulties. The pmc-score engine of the PWConstraints library (Laurson, 1996), for example, only works on predefined rhythmic structure. There are, however some new developments in this field (Anders, 2002). In connection with the constraint solving strategy of ”propagate and distribute”, it has become possible to generate a score even where the rhythmic structure is not known beforehand. When the system is in the middle of a search, the next score element to be generated would be the one with earliest starting time.
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Bibliography [1] Anders, T.: A wizard’s aid: efficient music constraint programming with O . ICMC 2002. [2] Forte, A. : The structure of Atonal Music Yale University Press, New Haven, Connecticut, 1973. [3] Laurson, M.: PatchWork, PWConstraints . IRCAM, Paris, 1996. [4] Lester J. : Analytic approaches to twentieth-century music Norton & Company, New York, 1989. [5] Sprotte, K. : OMGroups 1.0 IRCAM, Paris, 2003. [6] Stockhausen, K. : ”...wie die Zeit vergeht...,” DuMont, Munich, 1963.
Kilian Sprotte Kilian Sprotte, born in 1977 in Hamburg, started violin studies at the age of seven with Isabella Petros jan. Later, he spent a year at the Brockwood Park School founded by J. Krishnamurti. He has studied composition with Younghi Pagh-Paan since 2000 and has attended various master-classes with Klaus Huber and Brian Ferneyhough. He was strongly attracted to the field of CAC, spending a year at IRCAM as guest researcher. Following this experience, he has worked constantly to improve a number of software tools, among them generational applications employing constraint programming techniques. He is also working upon music notation applications. The group PRISMA has on several occasions invited him to give talks on his research. His works have a strong focus on instrumental music, but include electronic sounds and video (museum Weserburg 2001). He received an award for his composition Fernweh at the Weimarer Fr u ¨hjahrstage 2003 and obtained a grant from the DAAD.
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To Touch the Inner Sound, Before it Becomes Music; to Dream About Dreams, Before they Become Real - Elaine Thomazi-Freitas Abstract. This paper describes a composer’s approach to her use of OpenMusic’s tools during the various stages in composing a musical work ( Derri`ere la Pens´ee, for nine instruments). Rather than engage in a deeply technical discussion of the software, the present article is more concerned with the intuitive aspects, and the intricacies of human/machine interaction in music. ***
1
Introduction “Le dernier mot sera la quatri`eme dimension. Longueur : elle en train de parler Largeur : derri`ere la pens´ee Profondeur : moi en train de parler d’elle, des faits et sentiments et de son arri`ere-pens´ee Je dois ˆetre lisible jusque dans le noir” (Lispector, 1998).
The starting point for the composition presented here was the analysis of recorded sea and wind sounds. Seeking for a more personal approach, I included processed versions of these sounds (by convolution), an approach that is close to another personal current field of research, the marriage of ambient sound colors with musical material. After the first step, the resulting groups of sounds were combined and translated into instrumental language by means of alterations made to their spectral content. In the course of this process, I abandoned the direct approach towards musical form and content, and decided to work with individual groups of sounds as they were being created, one at a time, controlling them directly more or less in a ’concrete’ way, before ascribing any musical meaning or context to them. Much of the underlying context for the compositional process is based on the idea of the moment of volition that precedes actual thought, or rather the initial idea that becomes the act of thinking. This concept is taken from a book by the Brazilian writer Clarice Lispector, Un Souffle de Vie 1 (Um Sopro de Vida ). I was determined to maintain 1
The choice of a French translation of the book has had a certain impact upon the composition, being the title of the piece extracted from this short passage referred to above. So far, I have not been able to find an English version, so all the references in the present paper are from the French edition.
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this concept throughout my work and closely examined every single sound, with a view to extracting the more primitive aspects of each. Because the sound sources come from nature the material is essentially primitive, as is the meaning, at least in the form that they are used in the music under discussion.
2
Musical source
The choice for the musical source of short samples of recorded sea and wind sounds is linked to the idea of extracting musical gestures out of extremely rich sound spectra. Although these nature sounds have a rather chaotic content, they are more like white noise spectrum than inharmonic (or inharmonious) spectral data. To extract music out of the latter was to run the risk of making a commonplace interpretation of the movement of the sound itself, and not discovering any new material. One way of avoiding such an outcome was to process the samples by convolution with voice sounds, which contributed to the enrichment of their spectral content. The resulting sounds can be described more or less as a sort of sculpted white noise, as if some of the specific inner parts had been emphasized in color without losing the richness of the overall chaotic character. The lengths of the analyzed samples ranged from less than 1 second to 7 seconds. Initially, these samples were analyzed with the software AudioSculpt, and the resulting data was interpreted in OpenMusic by means of the ’Audiosculpt to OpenMusic’ function (as->om, repmus library). This incoming data, arranged as a sequence of chords representing a simplification of its spectral content, was filtered by the seq-extract function (om-tristan library), subsequently resulting in a bank of chord sequences that constitutes the raw material for the composition. The final piece is written for nine instruments: flute, B clarinet, oboe, French horn, piano, violin, viola, cello, and double bass. This instrumentation was displayed in OpenMusic by MIDI instruments, a very useful resource that provided an approximation of the real ensemble in the process of conception of the work.
3
OpenMusic source
OpenMusic has been used in my composition via om-tristan library, created for work on spectral data, conceived by the French composer Tristan Murail, with whom I worked during my doctoral studies at Columbia University, in New York City. Once the connection between AudioSculpt and OpenMusic is made, the retrieved data goes through a series of manipulations using specific functions from the library. The om-tristan library communicates with other applications mainly via the AudioSculpt spectral analysis data import function (using the ”export partials” command). A single OM object, as->om (Audiosculpt to OpenMusic), reads the incoming data and converts it into a specific format to be processed by other OM objects. The data includes a text module of the analysis data; minimum and maximum amplitude values, scaled as MIDI velocities; a delta value that forces the grouping of close events into chords; limit values (max and min) in midicents, defining the allowed pitch range; microtonal approximation (i.e., whole tone, semi-tone, quarter-tone, and eighth-tone); and a value that reduces the polyphony, by retaining louder partials as the most significant content. After processing all this information, the object outputs a list of chords, which can be read by 268
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a chord sequence module. om-tristan’s objects work by means of procedures that can be grouped into the following domains:
• Frequency • Control • Intervals • Files • Combinatorial • Functions • Chaos • Arithmetics • Objects
• Conversions • Groups • List’s treatments • Board Operations • Numerical series • Treatment of functions • Aleatoric • Midi
In my composition, I focused chiefly on frequency manipulation. The main steps, carried out with the sample analysis data, start with the extraction of the melodic motives, the selection and manipulation of harmonic content, and the manipulation of these two bodies of musical material in order to generate the musical content of the piece. The function diamanter was used thoughout the compositional process, and was responsible for the earlier data manipulations that generated the melodic material of the piece (cf. figure 1). This function executes a calculation of the incoming chord-seq data, processes each of the chords in the list (an aleatoric function, in accordance with a percentage value expressed in the function parameters) and produces a corresponding nth harmonic, creating a new chord sequence. This function was used here in such a way as to allow me to extract a single melody from the complex polyphonic sequences contained in these first steps. Subsequently, the diamanter function was employed to generate complex arpeggio-like gestures that caracterize a second type of structural material, more obviously present in the second half of the piece. Regarding the harmonic materials, the imported analysis data was passed through a set of distortion fuctions, such as: freq-distor , ch-distor, ch-modif, densifier , fshift-proc (cf. figure 2), besides being subjected to my personal choice when simplifying the resulting contents, according to purely subjective musical criteria. A further step was the creation of harmonic fields for the structuring of bridge passages between sections. This was done by means of the fq-interpol function. When all this musical basis was structured and ready to go, the individual materials were processed several times through the above set of functions, in an empirical manner, until a satisfatory musical result was achieved. It is difficult to decide whether or not the final result is faithful to the initial raw material. However, the guiding line for the entire composition was that these sounds all come from nature. Another set of functions, such as: deformer% , stretch, l-distort/3 , l*curb, besides diamanter, were occasionally applied to a whole chord sequence, and at other times to a single specific chord, allowing for wide variations along both the horizontal and the vertical dimensions. These processes became more evident towards the second half of the piece , where I was working with increasingly complex material, and the final results were quite unexpected. Another group of aleatoric functions was used earlier in the composition, affecting only the horizontal domain. As I mentioned above, the main concern during the compositional process was to avoid an approach based on musical form and structure, and instead focus upon individual musical cells. A later stage in this process was that of assigning the instrument’s colors 269
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Figure 1. Melodic extraction from imported AudioSculpt analysis
Figure 2. Distortion functions on harmonic materials
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to these little gestures, even before positioning them on the time scale of the piece. It is of some interest to look at an orchestration example, carried out by MIDI representation of the instruments (figure 3).
Figure 3. Example of orchestration inside a multi-seq
4
Maquette
Another important feature of OpenMusic was the maquette . This resource made it possible for me to apply a continuous back-and-forth (or empirical) procedure while experimenting with the newly created musical material and situating it in musical space (an aspect that is more obvious in the final stages of the composition). When all the main calculations for the musical content had been carried out, the various types of material were structurally placed on the first maquette, using an empirical approach. During this stage a very important aspect was the maquette’s flexibility. At last I felt as if I was getting to the core of the piece, that my preoccupations were less technical, leaving place for musical experimentation, where ”real thought” began (to borrow Lispector’s imagery). Also during this stage of the process, the maquette2obj function was used, acting as a bridge between the initial sketches and the new material used in the final piece. Here are diagrams (figures 4 and 5) of the first version of the maquette (with a fragmentary internal structure) and the final version (in which the blocks constitute the main sections of the piece). 271
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Figure 4. First version of the maquette
Figure 5. Last version of the maquette
5
Finale
In the final stage, the interface with Finale was another important tool, providing an easier way of writing the final score directly from OpenMusic’s workspace. The interfacing was carried out via the ETF (enigma transportable files) resource, directly from either voice objects or poly objects. After the whole piece had been assembled into a final version maquette it was imported (via the maquette2obj function) into a fairly complex patch and broken down into smaller fragments. Each of these fragments had been individually quantized (for purposes of simplifying the rhythmic notation) and exported to a 272
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poly object, which enables the finished material to be directly transferred into Finale, the
musical notation application. A few minor adjustments were needed when reassembling the music in Finale, but considering the level of complexity of the score I was dealing with OpenMusic, they were almost negligible. The reader is invited to compare the two following figures (figure 6), one showing the excerpt in its final musical notation in Finale, the other showing how it looked inside a poly object in OpenMusic. The minor rhythmic adjustments were made for purposes of simplifying the musical notation. In the Finale application, this process of score simplification had already been carried out. Nothing was changed or lost in the course of the transfer between the two applications.
Figure 6. OpenMusic to Finale’s transfer
6
Aesthetic aspects
Notwithstanding all the preceding discourse, organized in neat logical steps, based on content that has undergone profound transformation, as well as generating forms out of the relationship between time and space, not to mention the act of taking nature as a model - none of this would be worth anything if it were not music. Now that the most difficult task is over, that of making music, it is time to try to understand the process with the help (or in spite of the interference!) of the written word. I would like to take the liberty of drawing a parallel between my work Derri`ere la Pens´ee and the poetical reference borrowed from Lispector’s book, Un Souffle de Vie , that provided the structural guideline for this musical composition. Lispector’s work has a deep poetical structure and an imagery that is exemplary in its richness of metaphor and variety of subject and situation. I often find myself drawn into a strange, different world when reading it, a world where the flow of time almost always joins the present. I get the impression that the author has been jotting words down on paper even as the act of thinking unfolds, in a deeply intuitive way. I believe that much of my work is created in the same intuitive manner. In addition to the poetical reference, I also borrowed a structural reference taken from the author’s questions on the process of artistic creation and its relationship to intellectual thought:
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“Je suppose que le compositeur d’une symphonie a seulement la ‘pens´ee avant la pens´ee’, que ce qui se voitdans cette rapidissime id´ee muette est un peut plus ` vrai dire c’est une atmosph`ere qui, d´ej`a color´ee qu’une atmosph`ere? Non. A avec le symbole, me fait sentir l’air de l’atmosph` ere d’ou vient tout. La pr´epens´ ee est en noir et blanc. La pens´ ee avec des mots a d’autres couleurs. La pr´e-pens´ee est le pr´e-instant. La pr´e-pens´ee est le pass´e imm´ediat de l’instant. ` vrai Penser est la concr´etisation, mat´erialisation de ce qui a ´et´e pr´e-pens´e. A dire, la pr´e-pens´ ee est ce qui nous guide, car el le est intimement li´ee ` a ma muette inconscience. La pr´e-pens´ ee n’est pas rationnelle. Elle est presque vierge. [Are we to suppose that the composer of a symphony experiences nothing other than ”thought before thought”, something that can be discerned in the extremely rapid silent idea that is little more than an atmosphere? No. In truth, it is an atmosphere that, already coloured by the symbol, gives me the impression of the air of the atmosphere from which all things flow. Pre-thought is in black and white. Thought with words is made up of other colours. Pre-thought is the pre-instant. Pre-thought is the immediate past of the present instant. Thinking is the realisation, the materialization of that which was pre-thought. In truth, it is pre-thought that guides us, because it is intimately linked to silent unconsciousness. Pre-thought is not rational. It is almost virginal.]” (Lispector, 1978) It was with this idea in mind that my work Derri`ere la Pens´ee was conceived, it was almost a feeling that precedes the musical idea itself, that subsequently was transformed to music. To speak of raw material that is sampled and then transformed and rebuilt with a new meaning, sounds so much like a causal chain. How can causality be applied to playing with colours and raw elements, how can it describe the steps that led to a final finished musical work? Music carries its own silences, and it is the music within music that is the metaphor of pre-thought, the music that touches inner sound, before it becomes music. The simplest way to summarise this is as follows:
7
Conclusion
One of the most important aspects when working with OpenMusic is the flexibility and the multiplicity of interfaces. More than just software for Computer Assisted Composition, it provides sufficient resources for a dynamic composition process, allowing empirical experimental data manipulation. The maquette and the direct link to Finale, via ETF, 274
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are important features that make OM into a complete package. Another important aspect is Tristan Murail’s research on spectral materials. The use of om-tristan library opened up for me a new approach to sound in acoustic composition, helping me to move forward in my work in computer music. Derri`ere la Pens´ee was commissioned by Speculum Musicae , Ensemble in Residence at the Music Department of Columbia University. It was composed in 2001-02, and premiered in May 2002 at Miller Theatre, New York City.
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Bibliography [1] Lispector, C. (1978), Un Souffle de Vie (Um Sopro de Vida). Traduit du br´esilien par Jacques et Teresa Thi´eriot (1998), Des Femmes – Antoinette Fouque, Paris.
Elaine Thomazi-Freitas Composer Elaine Thomazi Freitas was born in Brazil in 1970. She received a Masters degree from the Federal University of Rio de Janeiro, and completed a doctoral program at Columbia University, in New York, 2003. In 2001 she worked at IRCAM, Paris, under the direction of Gerard Assayag and Andrew Gerzso. Working with Tristan Murail as an advisor during her studies in the USA, she started to focus more on computer music, computer-aided composition, and multimedia. Her works range from the acoustic repertoire, including solo, chamber, and orchestral pieces, to pure electroacoustic music. She is a recipient of several scholarships from the Brazilian Government, as well as from Columbia University. In 2003, she was short-listed for the Prix SCRIME, composition prize, in Bordeaux, France. Actively engaged in the musical scene in Brazil, she developed an international carrier throughout Europe and North America after moving to NYC in 1998. In Brazil her last work has been on a teaching program funded by a governamental agency from Rio de Janeiro, to conduct a research on music and multimedia within the music department of University of Rio de Janeiro, from August 2003 to September 2005. At the present, Elaine presents her work in festivals and concerts as a free-lance composer. In 2005, she had her work performed in Rio de Janeiro - Brasil, Valpara´ıso - Chile, and Dublin - Ireland.
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Appendix
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OpenMusic
OpenMusic (OM) is a visual programming environment developed at the Ircam and dedicated to musical composition. It allows the user to create and to experiment with compositional models through programming, and by means of a graphic interface that represents musical structures and processes. Many of the chapters in this article refer to that environment. In order to understand these chapters more easily as well as the illustrations, the basic OM concepts will be dealt with in this appendix.
1
Patches
Patches are graphic representations of the programme. The composer uses them to connect graphically represented boxes. Each box represents a function. Each box has a set of inputs (at the top of the box) as well as a set of outputs (at the bottom of the box) for connecting them to other boxes. These connections define the functional layout of the programme i.e. what it will do. OM possesses a number of functions of varying complexity and specialisation. Others may be created by the user. Figure 1 shows a very simple patch using the functions for the addition and multiplication of integers. It is mathematically equivalent to (3 + 6) × 100.
Figure 1. A patch that is the mathematical equivalent of (3 + 6)
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×
100
2
A Patch in a patch
If the number 3 in the expression (3 + 6) × 100 is made into a variable, the result is a single parameter function defined as follows: f (x) = (x+6) × 100. Figure 2 shows a patch corresponding to this function. Graphically speaking the variable x is represented by an arrow shaped box (at the top of figure 2). The output arrow (at the bottom) specifies the value that results when the patch is calculated.
Figure 2. A patch that corresponds to the function f (x) = (x + 6) × 100
The patch in figure 2 can in turn be considered as a function call, and can be used in the form of a graphical box in other patches. This makes it possible to create patch abstracts, which can then be used in various contexts. Figure 3 shows the patch from figure 2 in the form of a box, with the number 5 as its argument. The result of the (5) calculation will therefore be f 10 = (5+6)10 100 = 110. ×
Figure 3. A patch in another patch
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Within the limits of what can be set down on paper, the articles in this book contain various illustrations for purposes of explaining compositional processes. These illustrations will refer to the main patch in this process as well as to the various internal patches.
3
Objects
Data structures (classes) can be used in the patches in order to create and manipulate objects (particularly musical ones). This kind of structure is also shown as a graphical box, with inputs and outputs that give access to its programme content. Figure 4 contains a note type box. In addition to the first input (and the first output) that correspond to the note itself, this box has 4 other inputs (and outputs). From left to right, these correspond to pitch, duration, intensity and Midi channel. The upper note in this patch receives the value 6700 as a pitch argument (in midicents this is equal to G3). This value is transmitted to the + box that increments it by 1200 (one octave). The box at the bottom of the patch receives this new value and creates a new note (G4, one octave higher).
Figure 4. Musical objects in a patch
Figure 5 shows a more elaborate patch, algorithmically generating a musical sequence. It contains BPF type objects (break point function), chord-seq objects (chord sequence represented in absolute time values) and voice (chord sequence in musical rhythmic notation). Among the most frequently used ob jects in this book, the reader will also find a number of other musical classes: chord, poly (polyphony made up of several voices), midifile, sound (audio file) etc. 283
Figure 5. An example of a musical sequence being created in a patch. The pitches are gener-
ated from the data in a break-point function, and the rhythm is created out of duration value proportional relationships
4
Editors
Each object class possesses a graphic editor, enabling the display and manual editing of musical data. Figure 6 shows the graphic editor of the voice type object that was constructed in the previous example.
Figure 6. Musical editors
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5
Control
Control structures, usually written in conventional programming language (loops, conditional expressions, etc) are also in the form of boxes, and are used in visual OM patches. The example in figure 7 uses a conditional box ( omif) that checks whether the variable x is equal to zero. If this is the case, the result of the evaluation (or calculation) is the note C3. In the opposite case, the result would be the note G3.
Figure 7. A conditional box
The example in figure 8 uses a loop ( omloop) that carries out an iteration on a pitch list (6000 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000 7100 7200), and then generates a chord sequence from the pitches.
Figure 8. The omloop box carries out an iteration of a pitch list in order to enrich each element
by two additional pitches
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Figure 9 shows the programme carried out by the omloop box. The pitch list is represented by the input0 box (the arrow at the top of the patch). The listloop box receives this list and sends back the elements in the list one by one at each iteration (6000 for the first iteration, 6100 for the second iteration, etc.) Each pitch is transformed into a chord by adding a minor third (300) and a fifth (700). The result of each iteration is collected into a list by the collect box. Once the last value in the list has been reached (7200) the collected list is transmitted to the finally box, which will be the result of the omloop box.
Figure 9. A patch linked to the omloop box from figure 8
6
Maquettes
A maquette is an original interface designed for the purpose of uniting the programme and the score in a single display.
Figure 10. Example of a maquette
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This is a 2-dimensional space in which graphic boxes may be laid out and organised. A box may contain an isolated musical object, a programme (patch) that generates an object, or it can contain an internal maquette. Boxes may be connected to each other and calculated as in a patch. Internal maquettes enable the user to construct hierarchical time structures. The horizontal axis of the maquette represents time, in such a way that the position and size of the graphic boxes can correspond to offset and duration values. The vertical axis (called y) is a parameter that may be used in different ways in calculations. Figure 10 is an example of a maquette in which 3 notes (C3, E3 and G3) are laid out along the time axis. These notes are used as calculation parameter for a fourth musical object (a chord sequence). The box that contains this chord sequence is linked to a patch.
Figure 11. A patch calculating a chord sequence in a maquette
The patch in figure 11 shows the programme that calculates the chord sequence. The three notes are represented by input boxes. The repeat-n box takes a note at random 6 times from among the 3 notes, in order to make up a chord by adding major third and fifth intervals. After evaluation, the maquette can be played in linear sequence as a score.
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The reader requiring more information on OpenMusic can consult the following reference works: [1] Agon, C.: ”OpenMusic : Un Langage Visuel pour la Composition Assist´ ee par Ordinateur”. PhD. Thesis, Universit´e Paris VI, 1998. [2] Agon, C., Assayag, G., Laurson, M. and Rueda, C.: ”Computer Assisted Composition at Ircam : PatchWork & OpenMusic” Computer Music Journal 23(5), 1999. [3] Agon, C. and Assayag, G.: ”Programmation Visuelle et Editeurs Musicaux pour la Composition Assist´ee par Ordinateur” IHM’02, Poitiers, France, ACM Computer Press, 2002. [4] Bresson, J., Agon, C. and Assayag, G.: ”OpenMusic 5: A Cross-Platform Release of the Computer-Assisted Composition Environment”. Proceedings of the 10th Brazilian Symposiuml on Computer Music, Belo Horizonte, Brazil, 2005.
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