BOGUSLAW SCHAFFER introduction to composition
1976 (PWM EDITION
Translated from the Polish original by JERZY ZAWADZKI
Edited by Ludomira Stawowy and Stefan Ehrenkreutz
1976 oy PWM Edition, Krakow, copyright assigned to ZAIKS, Warszawa. Printed in Poland.
Contents
From the Author 1. What is a composition? How does it come into being? What is a composition's basis? . . . 2. Yesterday, today and tomorrow. What attitude should a composer adopt towards these three time bearings? 3. What are "possibilities of music"? Where are they to be found and how are they to be treated? . 4. Is there a new method of teaching composition? If so, what is it like? . . . . . . . . 5. What are the methodological foundations of this manual? What does the composer's craft consist of today? 6. Who can be a truly creative composer? What should his attitude to creativity be? . . . . 7. What are the conditions for authentic creative work? When can we compose in fact but not just "write music"? . 8. What can be the impetus to creativity? Nothing but play in the imagination? . . . . . . 9. Is originality an important factor in creativity? May it be p u t forward as a programme, as the first item of the artist's programme? . . . . 10. To what extent does the problem of choice exist in today's music? 11. What attitude should a composer assume to tradition? 12. What constitutes the essence of new music, the essence of new composition being created today? 13. A marginal, but important question in this state of affairs: what is the contemporary composer? . 14. How has the social status of the composer changed and what is the nature of his social activity? . 15. What are the characteristics of contemporary composing craft?
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10 11 11 12 12 12 13
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27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
16. What factor seems to be the most important in new music? . . . 17. Analogy and change — the opposition of these notions to each other and the possibility of connections between them in a composition . . . . 18. Elementary study of the factor of change in music. On what does musical change actually depend? . 19. Further compositional expansion of our research
in the method of employing the factor of change in music . , The consequences of the limitation of components to a few symbols Simple and complex values Is there a progression of rhythmic values from the simplest to the most complex ones and how is it expressed? The composer's work on rhythmic models . . The limitation of rhythmic values to a few a bar threatens us with a rapid exhaustion of movement; how do we prevent it? Possibilities of a new divergent way of treating music written in simple metres Possibilities arising from modern compositional usages of metre. Playing by means of metre, further development of metric techniques . . . Metre today Ametric music Are there any new time models and, if so, what do they look like? Complexity of rhythmic models Changes and superimposition of metres and rhythms within metres Rhythmic complications Metric complexity Concepts of pitch-rhythm relationships . . . Compositional consequences of the repetition of the same pitches Relationship between the idea of constant variation and the formation of rhythm Rhythmic-dynamic relationships Rhythmic "harmonies" appearing as a result of new co-situations The restriction of composition exclusively or primarily to the range of r h y t h m . "Articulation of time" .
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41. Linear motion. The attitude of the contemporary composer towards linear motion and its role in the structuring of music 42. Foreground and secondary status of linear motion 43. Range of possible change in linear motion . 44. Compositional reading of linear motion pitch collections .
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45. The dependence of the structure of chords upon the contents of vertical arrangements of linear motion 46. Compositional application of chords . . . . 47. Microstructural organization 48. Intervals and their role in contemporary music . 49. Intervallic notation . . 50. Intervallic analysis of linear motion . . . . 51. Selection of intervals and its consequences . . 52. Five-note models enclosed within the major third 53. Work on six-note models enclosed within the fourth 54. Contents analysis of the variants of the chromatic six-note universe . 55. Harmonic models 56. Intervallic studies . . 57. Study in diagram — the idea 58. Study in diagram — the realization . . . . 59. Codes 60. Approximate linear motion
84. Technique of deschematization . . . . . . . . 85. Technique of the reduction of elements inducing monotony in serialism
31 32 32 33 34 34 34 35
86. Transformation of structures into textural formations .87. Study of textures 88. Series and their textural break-up . . . ' . . 89. Series and their rhythmicization (horizontally-conceived texture) 90. Possibilities of textural melodization of series or horizontal pitch combinations 91. Examples of four-part textures (string quartet) . 92. P i a n o ^ e x t u r e 93. Possibilities in the handling of textures in music for larger ensembles 94. Texture and density . 95. Possibilities of thickening vertical structures through an increase in the quantity of material employed 96. Dispersal of material . . . . . , . . 97. Influence of mechanical composing on texture . 98. Combined constructions .'• .99. Textural results of the application of group technique 100. Texture of large forms
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III 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71.
A new way of treating the orchestra . . . . Selection and particularization of tone colour Preparation of instruments Preparation in vocal and instrumental ensembles Changing pitch The transformed note . . . . ' . . . The gliding note . . Composition with one note Timbral intervals Deformations . . " •. Denaturalization of sound
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39 39 40 40 4 1 42 42 43 43 4 4 44
Series — problem of variability Forms of the series Series that determine the sound language . . . . Multi-intervallic series Further models of series Serialization of rhythm and dynamics . . . . Serial articulation . . . Serialization and pointillism "Oscillatory" and "modulating" serialism . . . Modal serialization . . . . . . . - . Total serialization — interchangeability of serialized elements . . 83. Problems concerning total serialism . . . .
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51 52 52 53 53 54 54 55 55 56 56 57 57 58 58
VI 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120.
IV 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82.
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Alphabetical index of examples
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True composition of music Precomposition Composition of time . . . . Abstract and concrete Aesthetic problems . . . . Canons of composing Counterindications and prohibitions Choice of techniques, antinomies Discontinuous composition Automization of composition Aleatorism Composing of co-situations Multimotivic work . . . . Break-up of the model Multidimensional composition Ambiguous music . . . . Multitechnical canons as models Polyversional music . . Composing musical actions Final remarks .
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72
from the Author
In the didactic work which is herewith placed at the disposal of the curious reader, the author set himself three essential goals: 1. to show methods of composition from the still difficult and not readily accessible technical aspect, 2. to acquaint the reader with individual solutions in the various parameters of music, by means of examples drawn (primarily) from the author's own compositions and the works of those composers who most extensively influenced the metamorphoses of contemporary musical language, 3. to awaken and encourage the creative imagination and the capacity for formulating ideas of the apprentice composer. Someone with no talent for composition cannot learn to compose. Not much can be attained by someone who has inherent or acquired prejudices against new music. Neither can there anything be gained by someone who will treat the entrusted didactic material in a superficial, cursory fashion. Nevertheless, compositional talents in themselves do not today suffice: contemporary composition is a difficult craft, but control of it must and ought to be gained if we deem musical language a language in which we wish to express something. The Introduction to Composition is a manual from which it is possible to study contemporary. composition. It should be studied slowly, in stages, with exceptional care being given to the achievement of results which make artistic sense. In this handbook the author has made an effort not to repeat elementary information dealing with the notation of music, or the capacities of instruments and the human voice, since the reader can find these for himself in relatively numerous publications. The author commences here without preliminaries at a level which to many readers may seem rather high but which, after all — at least taking into
account musical training in the author's own country — is essentially not excessive. Perhaps a certain amount of information pertaining to new music ought to have been recapitulated, although a totally different prescription emerges on the basis of the author's teaching experience. Composition should begin from the very first exercises and assignments — t h i s cannot be left till later. The Introduction to Composition consists of a concise text and of a very extensive set of musical examples (in progress, the work even went under the working title of an "Atlas"). The textual part contains 120 short chapter-problems and discusses in detail the issues of rhythm, melic motion, timbre, serialization, texture, as well as composition proper. Each chapter is subdivided into short segments, as indicated by the headings: q i d e c
— — — — —
question information discussion exercise composition.
The texts of these segments are quite brief and concise. Together with the pertinent examples and diagrams they ought to give a rather clear picture of the problem under discussion. Translation into English of this advanced specialized musical treatise brought about a special set of difficulties in its wake. The problems were of a higher order than is usual in translation because the text requires a meticulously employed, complex technical language that truly and effectively deals with the issues of new music. In this regard, many thanks are due Roy Wightman (musicologist from England), Stefan Ehrenkreutz (composer from the United States, fluent in Polish) and Adrian Thomas (English com-
poser residing in Northern Ireland) for their work on the verification of the text from the linguistic and musical points of view.
Each musical example is only identified in brief. Their full titles together with information regarding scoring and publication is given in the "Alphabetical Index of Examples".
The written text is illustrated in the examples by numerous diagrams (rhythmic models, rhythmic series, graphic models, juxtapositions of results emerging out of the application of open forms, a list of all the multi-interval sets, analysis of the contents of series, permutational listings of chosen models, listings of possibilities for differentiation of musical material, analysis-graphs of compositional means employed in a given work, etc.). The written text is further illustrated by compositional exercises as well as musical examples from 170 scores of the 60 most outstanding contemporary composers, from Bartok, Webern, Stravinsky and Messiaen to Cage, Stockhausen, Kagel and Bussotti. The length of the listings, the size of the diagrams and the musical examples depended here on the significance of the given problem as well as on the potential of the possibilities contained within the problem. (Thus, for instance, a complete listing of all the multi-interval sets is given here because contemporary composers regularly take advantage of only a limited fragment of the collection, as if unaware of the immense, attractive sum of possibilities Of the complete collection; such an extensive juxtaposition precisely illustrates such foregone opportunities in new music.)
At this point the author would like to express his warm appreciation to all the editors and publishers who so graciously consented to the inclusion of examples taken from the works of composers published by them as well as to those composers who made their manuscripts available for presentation in print. The author would also like to express his appreciation to the Polish Musical Editions (PWM) for their sincere encouragement and for undertaking the difficult labour of editing the Introduction to Composition and to all those who personally were instrumental in helping this work appear in print, namely: Felicyta Glen, Elzbieta Miinz, Anna Zoga, Maciej Kowal6wka, Adam Kusiak and Andrzej Watala (preparation of musical copying materials), to the team of the Polygraphic Laboratory of PWM for slides of musical examples, to Aleksandra Mitka (retouching and technical preparation of musical examples). Miss Ludomira Stawowy deserves separate words of thanks for the editing of the whole. Only the author can have some idea of the problems she had to face. Without her patience, endurance, hard work, and various efforts this work would not have attained its ultimate shape. Krak6w, January 15, 1976
What is a composition? How does it come into being? What is a composition's basis?
A composition is an a u t o n o m o u s artistic creation,, impossible either to evoke or discuss apart from musical matter. A composition's basis will always be that of our purely musical experiences and, above all, our experiences of the range of possibilities of musical material in itself. And even if we can occasionally employ experiences from beyond the sphere of music in a composition, we must remember that these external impulses can have compositional significance for music only after they have been translated into musical language.
very essence, but the most important experiences in the experience of music are those contained within music itself and restricted to it, even if we use methods acquired through contacts with other domains, e. g. fine arts, architecture, mathematics, psychology of aural reception, and the like. Moreover, if we are to talk about music, then let us talk only about its future. The future of music is exclusively determined by its potentialities, not by ideas. Ideas that are not fit for musical realization are not ideas at all, since they lie beyond the sphere of the very matter of composition. Having no support in the past, a contemporary composer can imagine the music of the future only with regard to its potentialities. Tomorrow's music ought to be composed by us today! This is also the case as regards the pedagogy of composition — we teach composition for the f u t u r e .
d A Fundamental Question: to what degree in contemporary musical creativity is it possible to conserve the autonomy of a musical composition? Music is constantly "endangered" by impulses from the outside; it always seems to be tied to the time in which it appears. Yet if we consider what these dependencies in fact have been, in terms of their historical background, we shall come to the conclusion that, despite all the common labels which we bestow upon music as a result of confronting musical activity with artistic trends and scientific discoveries contemporaneous to it, music conserves its own range even when the ties to other domains are strong. Contemporary music, which interests us here in a very wide sense, certainly has not as of yet sufficiently matured to be subjected to a process of generalization, let alone to a process of the discovery of links connecting it with other domains. Developing along many lines, music cannot be reduced to one stylistic or technical model, and observations concerning music will always be fragmentary. From such particles — in this manual they will be used as the basis for concrete tasks — we build up general information about music without resorting to forms of classification, without any desire to discover certain definite preconceived categories in it. In other words, we intend to build up general information about music from such particles following the way it originates immediately before us. No doubt music originates against the background of different discoveries not related to its
Yesterday, today and tomorrow. What attitude should a composer adopt towards these three time bearings?
Up to this time, the exposition of composition has been retrospective in nature. The basis of teaching composition has always been music from the past or, more strictly, music of the past. Such didactic thinking could engender a better understanding of music composed earlier, but it could not provide the future composer with what he hoped to obtain from this mode of thinking. To be sure, we do say that one should learn from the greatest masters whom, as is only natural, we view as exclusively in the past, but at the same time we are aware of the fact they have n o t h i n g to tell us as regards the fundamental problems of new composition. Moreover, one cannot today draw comparisons with the old masters for whom our times formed but a very vague future.
What are "possibilities of music"? Where are they to be found and how are they to be treated?
"Possibilities of music", should not be understood as being restricted merely to the number of techniques available. Multiplication of the number of techniques is a difficult problem; such a multiplication is often only apparent. Dazzled by quantitative richness, we might readily forget that it is q u a l i t y , just the opposite of quantity, that plays a decisive role in art. The great innovator, Anton Webern, did not write one new note and yet he achieved a great many important solutions of the problem of new composition in his works. The significance of his solutions became evident only to those who observed the subsequent course of events in music. In other words, it will not be our aim here to make a huge catalogue of compositional techniques, but to encourage the composer to slove — as independently as possible — real problems of composition, and these can easily be found in all possible internal relationships in music.
Is there a new method of teaching composition? If so, what is it like?
Composition cannot be taught, but in the present state of affairs it can be d e m o n s t r a t e d . It must then be assumed that the young student of composition is so mature a musician that the whole of this demonstration in composition may be addressed to both his intellectual skills and artistic sensibilities. It is only under such conditions that real interest in the subject of composition itself can be aroused. The subject of composition when treated in the whole wide range of intellectual and imaginational problems can' become not only functional but also attractive to the composer. The author assumes, in addition, that the student of composition is endowed with powers of criticism and counts on his skills in making his own choices. Finally, in order not to return to this question further, the student, if he is to go .through this course in composition successfully, must have confidence in the author who, before publishing this manual, thought -carefully not only about the subject itself, but also about its expression in didactic terms.
d In discussing the possibilities of music,. those of new music, we must not overlook the fact that although they are virtually unlimited, they do not lie within the reach of every composer's imagination. Certainly a great many of the possibilities of new music, or even most of them, are quite beyond the imaginative range of a contemporary composer. The possibilities of new music do not constitute a definite repertory of new techniques (although it might seem so to most musicians). The greatest changes in music were not brought about by the addition of new compositional techniques to the conventional stock, but were due to changes in the very conception of composing procedure. In order that such changes may occur, the»composer must frequently delve to the very elements of music, verifying the existing stock of techniques (once again, for his own use) from the view-point of the inherent possibilities of making changes in them. Otherwise the material in itself will constantly dominate the composer, whose creative activity will be reduced merely to the reproduction of his own personal variants to which, after all, most contemporary composers confine themselves. Overcoming this hitherto so important determining effect of the material may be hailed as the greatest achievement in contemporary composing. We can now see how small the role played by technical progress is for composition. In this situation it is now all the more obvious, that all things considered, real composition begins only from the point of a r r a n g em e n t of musical material.
The problem of how to teach composition needs further explanation. Composition, like sculpturing and painting but contrary to the writing of poetry, is taught up to the present time. It might seem that now, after so many years of practice, expertise in the teaching of composition has attained a level that satisfies current demands. This however is not true. The teaching of composition cultivated in our times is one of the most horrifying anachronisms in new music. What is the source of this disparity between composition, so advanced nowadays, and its teaching? Above all, this situation arises because the composer in his own work makes use of his own experiences, while the same composer when he is teaching avails himself of somebody else's experience, experience of a kind which is often very remote from his own talent, temperament and also his critical judgement. The composer's own experiences are the more valuable because they have been gathered very slowly and only with the most intense activity of both intellect and inspiration, of the musical imagination and the systematizing process of the mind. Moreover, and 8
here we perhaps approach the most important point; the. huge disequilibrium existing between style and technique in new music brings about a situation which resembles none of those met with so far in the history of music. Today, when the stylistic layer of a musical composition is not so closely related to the technique adopted and when technique has, so to say, outrun the style, even the most ambitious teaching of composition must stop within the bounds of technique itself. Despite these difficulties the contemporary method for teaching composition, even if confined to the demonstration of music, is capable of disclosing many of the regularities that appear in new music, some of which may bear the features of more general, stylistic regularities.
The issue of contemporary craft needs more detailed explanation. Today's craft is based, as it were, on contacts with the potentialities of music rather than on learnable canons. In any case such canons would be impossible in new music, since it lacks even the most general intimation of some system. The systematization of technical-compositional phenomena and problems is hampered chiefly by the large number and diversity of techniques applied by composers. In this respect the traditional teaching of composition has already lost its old sense. It can no longer be the teaching of craft, as it once was in the past. Once, when the teaching of composition consisted in passing on a set of rules to students, such a method was reasonable and even of some significance. Nowadays, when compositional technique has moved so significantly ahead of previous practice, both pedagogy and its fruits must be focused on one and the same task of posing and solving compositional problems, and thus more on the extension of the range of vision than on the classification of new phenomena, which in any case escape classification in some respects.
What are the methodological foundations of this manual? What does the composer's craft consist of today?
This manual of composition is not a genuine manual. Perhaps it does not deserve to be called a manual at all. Although written with a definite didactic purpose in mind, it is intended to demonstrate the fallacy of the notion that art cannot be taught. Teaching is possible where we are concerned with craft. In the last few years craft has ceased to be what it had been before and consequently it must now be conceived in a different way, not in the sense of rules for putting the voices together in a composition ("to compose" is semantically associated with the Latin: componere — to put together), but in a new sense, that of the compositional utilization of the potentialities of music. Moreover, the contemporary craft may be interpreted as a specific kind of readiness for authentic composition, for the original, in its essence, posing of compositional problems and their individual solution. For this reason also, disinterested work, the only aim of which is to get to know the potentialities of music, is desired in the first stage of study. The suggestions received should be transformed individually in the second stage! The author attaches no importance to the studied repetitions of what he propounds, but advocates the actual transformation of his suggestions so that they will meet the composer's own requirements, in particular the suggestions which have a good chance of becoming his intimate property in course of time.
6 Who can be a truly creative composer? What should his attitude to creativity be?
The author assumes mastery of craft in the old sense of the word. Here, in its place,, there appears a specific theory of compositional potentialities of music. We know (if not, we can easily see for ourselves) that everything expressed in musical categories i s music (this may be exemplified by all the radical movements in new music, e.g.,, those of Ives, Varese, Haba, Webern, etc.). There is thus no justification* for ignoring all the possibilities that arise from a new, unconventional attitude to music. However, broad intellectual horizons and aesthetic openness are required in order to deal with this issue. A musician who confines himself to the narrow categories of present-day utilitarianism cannot foe a creative composer. He will turn out secondrate products. These sometimes give a composer the illusion of interrelating with respect to the evolution of new music, but they have little in common with authentic creativity. 9
In addition to what we should call the authentic necessity of creation, play in the imagination may also became an impetus to creation. Thanks to such play, we can obtain very interesting results, and the rules made up by the composer may become a specific system in course of time. In great measure, the very playing of a game (not establishing the game's rules) becomes transformed into composition. At moments of reflection we can enrich play in the imagination by the contemporary achievements of science and thus assume a new critical attitude to composition, so necessary in authentic creativity. Creativity may be treated as a sort of information; then the problem of expanding the media of artistic expression achieves primary significance. Both imaginative play and learning contribute to the formation of situations which otherwise would never have been attained, and this indeed is already saying a great deal. Generally speaking, we may adopt the principle that it is worth our while to compose if we obtain results that could not otherwise be achieved were it not for creativity. In this respect creativity aims at the disclosure of the truth a'bouf music, its potentialities and new responses effected by it. If we repeated stereotyped entities and solutions, such as may justifiably be described as contaminations or repetitions, in so doing following after other composers (or falling in together with them, which by no means improves the situation), then, to be sure, we should enrich, the repertory of the given stereotype without enriching music itself. "Play the imagination" usually occurs in the sphere of values that we have already come to know and do not care much about. Far more important to new creativity are compositional results that contribute to the expansion of what we know about music and, consequently, of our imagination. Known stereotypes can be developed only when the play is begun at the beginning (this is why most of the sections given to concrete tasks start from elementary composing principles).
What are the conditions for authentic creative work? When can we compose in fact but not just "write music"?
More often than not, composers act in the conviction that creation occurs at a certain point in the maturation of a musical idea. In other words, they feel that they need only to begin work with some sort of musical idea to have an artistic work spring into being. Nothing could be more illusory! An artistic work makes sense only if it has resulted from a necessity of creation. Such a necessity of creation does not appear until the musical work "sets itself" together, from the elements chosen by the composer. At the same time we know that the musical work must have its authentic beginning. This is why' care must be taken that a composition always begin at the z e r o p o i n t without any preconceptions. This will well nigh have to be a principle while the present manual is being used. The sum of ready knowledge acquired before may perhaps be necessary in realizing a compositional idea; however, such knowledge ought n o t to be used above all. The Composer should know how to attain humility within himself before music, whose very source material is already aesthetic. Guiding the material according to the state of your ideas, try to obtain suggestions from the material already produced. Make the material contain information and then draw guidance and information from the material — this is one of the main principles of contemporary composition and perhaps the most important didactic principle of this manual.
What can be the impetus to creativity? Nothing but play in the imagination? All too often, out of play in the imagination, out of fancifulness come conventional stereotyped creations, which have already been heard somewhere (by someone else); in' what way are.such stereotypes to be expanded?
Is originality an important factor in creativity? May it be put forward as a programme, as the first item of the artist's programme? What must an artist do, if he is not ingenious or capable of original creativity? 10
Although it has never been emphasised, history proves irrefutably that one of the fundamental canons of true compositional creativity is originality. The awareness that, at the same time that you are reproducing your impressions, derived from knowledge of previously existing modes of composing, a few hundred other composers are occupied in a very similar manner (and to a similar- artistic effect!) should encourage you to action in another, even in an opposite direction. For this reason originality in creation should be brought into the foreground. Assuredly, originality alone, when not underpinned by the composer's awareness, is insufficient (in any case, in spite of appearances, it is often simply u n a t t a i n a b l e in this situation), but in creativity it is a sine qua non. If in a couple of years you find that you have not managed to attain authentic originality, stop composing. Leave it to others. In order to resolve this, one must be not only a good musician but a keen critic as well. Compose indiscriminately, but later have a lodk at your work with a different eye — as if you were a stranger. Let nobody forestall you in criticism; always be the first.
techniques, pieces composed "chaotically", are of no value. It cannot be denied that music, like any other branch of art, demands exactitude, well-ordered reasoning and differentiation of material. It cannot however be denied either that for many years music was developed within ranges so narrow that composers could not become aware of its great potentialities. It would be indecent to compose chaotically in full consciousness, but I venture the statement that future generations will find orderliness in many situations which we regard as chaotic now. This orderliness will be of a different, higher rank. Let us repeat it once again: selection (whether we like it or not) always accompanies a creative act. We can make sure of this, if not otherwise, by observing the "selection of techniques" in the composers who not so long ago were considered to be heedless of any principles and norms.
11 What attitude should a composer assume to tradition? What is traditional music to him and must he necessarily set himself up in opposition to it?
10 Present-day music has been determined to a great extent by its history. History has really formed presentday music and set bounds to the imagination of coinposers of new generations. Be an assiduous researcher of its history, especially as regards the development of music, of instrumental and vocal techniques (bear in In the course of composition, we are constantly making mind the fact that all the musicians with whom you acts of selection. The element of choice is inherent' may have dealings still dwell almost entirely within already in decisions regarding the kind and range of this climate). Do not imagine, however, that tradition information to be employed. In short, it may be said will be in a state capable of teaching you anything. that selection is part and parcel of creation, even when Great composers did not look back to tradition, they we do not consciously take this into account. On the created it t h e m s e l v e s . Thus, the musical tradition other hand, deliberate selection, as a restriction already should have the import of a n e g a t i v e m a g n e t imposed in the initial assumptions,' is nothing but the i c f i e l d for you. One thing more: do not despair restriction of music itself, and nobody can approve over losing contact with tradition, this cannot happen. of this. Remember that even if you manage to attain maximum originality, you will enter the zone of that only seemingly lost tradition. Being conscious that whatever The problem of selection (it will be dealt with in more you do automatically merges into tradition, try to only detail in Section 108) needs a special comment. A great think of tradition in terms of that negative field. many musicians claim that selection is the most (Staunch anti-traditionalism has however nothing in important law of creation; the source of this opinion common with creativity. One always creates for and may be the axiom that pieces based on unselected not against something.) To what extent does the problem of choice exist in today's music?
11
12 What constitutes the essence of new music, the essence of new composition being created today?
Composition based on reproduction, that is, composition originating at the point of intersection of convention, tradition, schematism, and vague concepts concerning the essence of new music, is increasingly coming into prominence dn new. music. Do not attempt such reproductive composition anfl do not recommend it; in part, art has always been used by petty manufacturers. Creativity must not rely on reproductive elements, otherwise it ceases to be creativity. If you succeed in finding appropriate masters for yourself, learn to study in their work the p o t e n t i a l i t i e s of music but not music itself, which cannot bear repetitions and, as a matter of fact, c h a n g e s continuously (for such is the nature of art).
There is a contradiction here, which should be explained. Certainly, composition hitherto has to a great extent been based on the principle of reproduction, and yet that which is the most valuable in music looks how different. The question arises whether these two tendencies can be reconciled. No doubt they are reconciled by art itself, in which the revelatory element borders upon the reproductive one, but the contemporary composer must not assume this in advance. Even if we are anxious to go beyond eonnmitting certain reproductive stereotypes, we shall commit them continually; we are still victims to either yesterday's or today's tendency to stereotype. This is why, governed by ethical principles of a higher order, we ought to avoid everything that might bring us into the disrepute (pitiful with regard to creativity) of being replicative composers.
13 A marginal,, but important question in this state of affairs: what is the contemporary composer?
The contemporary composer ought to be a discoverer, an inspirer and dictator of aesthetic taste. If he lacks ambition in this respect, he will descend to the level of the "also-ran" producers of music (easily replaced by other producers, etc.).
d Let us consider these aspects individually. The composer as discoverer. In music, as in any other field, discoveries occur constantly. "Occur" is not the right expression. The composers are the ones who make them. It is to them that this role has been assigned (if it is true). To be a discoverer in music does not mean to disclose the regularities contained in it (for this task may be undertaken by a contemporary analyst), but to produce material characterized by such relations that it becomes possible to uncover hitherto unknown possibilities in music. Associated with this task is the composer's role as an inspirer. The creative composer should incite others to act in spheres of which they have scarcely any presentiment. Any kind of new music is inspirational, both at the time when it is being created and presented and — for this may also happen — when it becomes the centre of concern for others. The last of the composer's roles, the dictation of aesthetic taste, is the most difficult. It must be emphasized here that the composer himself, and not the reviewers of music or the audience, is to decide what is good, to decide about aesthetic issues. After all, our artistic taste today has also been moulded by composers, not reviewers.
14 Social changes have lately affected everyone. How has the social status of the composer changed and what is the nature of his social activity?
Most certainly, the activities of the contemporary composer cannot be assessed by the standards of the previous century. Nowadays his activities are more introvert than extrovert, concentrated more on the object than on its effect, and enclosed in a model which he moulds himself, not in a- model imposed on him. 12
,
v •^ S
Here there is a problem calling for explanation: to what degree is the composer dependent on his environment, on the circles in which he displays his activity? These relationships are treated in many different ways. In some social systems the composer is one of many people engaged in co-creation, subordinated one to another by the very fact of their being put on an equal footing. It happens — and today we feel it more keenly than at any other time — that in a world of different contradictory interests he has moved right out to the margins of society, where, after all, he can act so much more easily and independently, because he has been debarred from his previous role, verging on a mission (nineteenth century!). In various systems of our times the composer assumes different roles; however, it may be stated in general that his social activity is not direct but transcendent. To serve one's society means to compose as well as possible.
15 What are the characteristics of contemporary composing craft?
The contemporary composer's craft is not restricted simply to composing. From the practical point of view composing is an easy action — assuming both the musical talent of the composer and his authentic need for creativity — and it bases itself on a craft which can be conveyed in a short time to anyone, on condition that he is a fully mature musician. However, correct composition does not suffice today and most certainly it cannot be the motivation for creative activity. In order to achieve anything in composition one must know how to introduce values which are unknown to it. For this purpose, the composer's consciousness must be expanded by a number of experiments which may become the basis for a continually augmenting ideational superstructure of new creativity. The aim of this book is to encourage the contemporary composer to action in directions which have hardly been indicated in music. The potentialities of music are enormous, their realization up to now relatively small. To remedy this state of affairs it is necessary
to think over and creatively transform a great many problems that arise in connection with the. present situation of contemporary music. For that which art uses least to its advantage is freedom.
16 What factor seems to be the most important in new music?
The most important factor of contemporary music, music which has been evolved over a few decades and has enjoyed various successes in individual fields, is the change of material and its change in relations. Change has existed since the remotest 4imes; however, in new music it has simply become a governing principle and its absence brings about situations which are obscure in many respects. Change results in a very natural manner from the only formal principle that has survived up to now, namely, that of variation.
The foregoing problem is not quite unequivocal. Change can be attained with a high proportion of elements left unchanged. There need only be a partial change, not a total one. It is not certain whether the very perceptibility of variation is important here. Perhaps it suffices that this rule shall be observed in composing only.
Compare Examples 1, 2, 3 and 4. Find where these pieces resemble each other and where they differ (each example is to be compared with each of the remaining ones,, there being 6 comparative juxtapositions altogether). Establish which examples bear the greatest resemblance to each other (in the largest number of facets!), and which differ most. This is, however, only a preliminary task. In the further course of analysis of the examples find to what extent we can speak of change in each of them and whether it is sufficient in all of them; moreover, see what the composers observe to avoid monotony when they use elements little capable of being changed and how they compensate 13
for restrictions in some facet. The solution of these problems is not simple and, therefore, the secrets of the factor of change must be divined intuitively. In coming to know further the functions of the causational factor of change, these functions will no longer be as inaccessible as they were at first contact.
17 Analogy and change — the opposition of these notions to each other and the possibility of connections between them in a composition
the techniques of new music as spontaneously, as possible, "unconsciously". Some time later, subject this piece of music to a very scrupulous examination for mechanically applied analogies and tendencies to change the material (naturally it cannot be, for instance, a typical dodecaphonic piece in which the change of pitch is, althought it should not be, the point of departure for composition. Compare Schbnberg's music with that of Webern, who did not compose dodecaphonically, but went above and beyond dodecaphony). Taking detailed notes, find the point your present compositional consciousness has reached and its distance from the problems that you have got to know from Examples 1—4.
18 Up to the present time music has always been based on both these factors. However, in new music analogy has had to make room for the factor of change. In the first place, the factor of analogy has lost much of its formative power. So far as composition is concerned, analogy puts music to death: when, for example, there occurs a repetition of a passage of music, composing ceases to be what it ought to be. Therefore, analogy had to be abandoned in favour of the variational principle with all its consequences. Music is now ruled by the principle of constant but not mechanical change.
Re-examine closely the functioning of the individual elements of music from the examples (1—4) you already know. Find in which elements the principle of variation prevails and in which that of analogy. Now establish to what degree analogy is mechanical (neutral, indifferent, conventional, simply not perceived by the composer as potentially changeable) or how far it results from special selection, the deliberate surrender of change, and, on the other hand, to what degree change is non-imeehanical (and therefore applied intentionally, not because change is possible but because its introduction brings about such an animation of the musical substance as cannot be attained in another way).
Compose a short piece for piano, at first without considering either the meaning of analogy or the functions of the factor of change; compose it in the same way as you composed everything before, reaching for
Elementary study of the factor of change in music. On what does musical change actually depend?
The essence of change in music depends on the presence of internal changeable relationships. In order to demonstrate this, we ought to make use of the musical consequences of assuming the binary system. Handling the numerical symbols 0 and 1, we can perform a number of operations, which will excellently illustrate this problem (never hitherto taken seriously). Real change, such as we are concerned with in music, cannot be formed mechanically. It suffices to take a look at the result of the simplest method to make sure of that. Let us take, by way of example, only two symbols (they may represent, e.g., two percussion instruments differing in pitch): 0 and 1. If we decide that our model will be the formula 01010101 etc. (Example 5), the most elementary analysis of such a process of variation will show that although a change occurs at each moment, the whole process is marked by superior analogy, which ruins the change, which we have otherwise so perfectly programmed. What are we to do to avoid this? To answer this question we ought to inspect the very process of change somewhat more closely. In our example there are only two pairs of symbols, 01 and 10. We experience the absence of the pairs represented by 00 and 11 as a lack of information regarding the possibilities of structural changes. This is why, for instance, the arrangement 10011, or the like, will satisfy us much more than the previous mechanical juxtaposition of contrasting values. In 14
musical terms, the alternation of two symbols stands for an ordinary tremolo on two percussion instruments,, which by no means can be regarded as satisfactory either aesthetically or technically. However, let us try turning the next sequence into musical language and it will appear much more attractive than the structurally reduced tremolo (as will other similar sequences). Let us draw from this observation as many compositional consequences as possible. It should be kept in mind that only the translation of such an arrangement into musical language may be of didactic significance. There is no reason to fear that such an analysis of the possibilities of music leads to something in the nature of musical abstraction. Each abstraction can be changed into the concrete, if only we turn it into musical language and ideas. This remark also concerns many of the subsequent sections.
Mechanical change should be contrasted with internal change. How to do this is shown in Examples 5—8, which are to be analysed very closely (Example 8a presents the universe of possibilities and Example 8b presents a long digital sequence composed spontaneously; the attainment of the full universe requires rational complementing — the composer should not aim to attain this universe but ought to be aware of its existence).
e/c Develop as accurately as possible the ideas given in Examples 5—8 by using new categories. Now that you are familiar with the principles of real internal variation in m'usic, try to compose a number of musical pieces for percussion instruments of non-defined pitch. They may be pieces both for one performer, who plays a number of similar or different instruments, and for two or more performers, in which case the number of different instruments may be proportionally smaller. In these compositions you must not go beyond the boundary of chamber music, but lay stress on the virtuoso treatment of the instruments. At this stage you should not yet attempt to write extensive pieces; they should rather be concise forms, each time treated differently in respect of movement and metre. The handling of a fairly large number of instruments necessitates the extension of the binary system into a multi-digital one. However, the digital system should not be developed to consist of more than a few symbols, otherwise we lose our grip on the whole stock of variational possibilities of arrangements. This is why
it is better to employ stratification —• very characteristic of composition — in which there is an overlay of several programmes.
19 Further compositional expansion of our research in the method of employing the factor of change in music
We can work with three or more elements: Examples 9—12. Example 9 illustrates the variation of internal two-note cells built at four different pitch levels and Example 10 the configurations of three-note cells at three different pitch levels (10b — note: there is a possibility of exchanging the pitch elements). Example 11 shows the variation of cells of several notes with an inner division defined beforehand (and thus with the number of repetitions of the given pitch determined in advance); as a result, here too, the factor of change observed by us comes into prominence, though in another form. Example 12 combines the experiments from Example 9 with a new problem of change up to four places (internal change: the digital sequence in the order: 1—4, 2—5, 3—6, etc., cf. also, Example 6b and c) and at the same time illustrates the possibility of the translation of abstract structures into musical ones.
Handling pitch material of various numbers of elements (e.g. from 2 to 5) and applying different methods of internal variation for it, and therefore, as it were, putting different demands on it as regards variation, make 12 different successions varying internally in different manners. Basing yourself on the given models (Example 13), examine minutely the possibilities of internal differentiations (in the first case it is to be a series of six-note cells, in which three notes are the same and three are different; construct also your own models).
20 The consequences of the limitation of components to a few symbols 15
Such a division will be musically complex just as a division of a | bar into halves (Example 15) will also be complex. Complexity occurs if we contradict an originally accepted principle. In Example 16 we find further details concerning superstructural musical complexities. The values set together in this way are called — customarily though perhaps not quite reasonably — irrational values.
In this section we are no longer concerned with the vast multitude of general compositional possibilities, which in any case music never fully utilizes, but are concentrating upon the problem of exclusively internal change. This is work to be done "in depth" and — if well executed — it may bring about a marked extension of the awareness of composing techniques. In the course of cognisance of the laws governing music, such "work 'in depth' " may lead to a better understanding of the essence of music.
Scrutinize Example 17 carefully for places where irrational values have been used and find out what the. consequences are for the general impression of motion and movement in the music. Find those places where the music is animated by the introduction of irrational values, those places where it need not be enriched by this method and, lastly, where the introduction of irrational values is immaterial to the process of music. Undoubtedly, owing to the introduction of irrational values the text becomes visually richer, more difficult to read, and at the same time makes the performer provide at least approximate equivalents to the complex structures. Examine the example for the places where we may speak about expressive benefits involving musical movement resulting from the application of irrational values.
A decision to accept limitations in components after having worked through the foregoing exercises immediately gives rise to the following question: isn't there a risk of confining ourselves excessively to a minimum on making such a choice? Assuredly, such exercises, as have gone before should not be treated mechanically but, on the contrary, should be understood from the outset as musical models. This is not difficult since in music abstractions, as we know, turn readily into concrete phenomena. For this reason, it should be possible to obtain many different consequences from even the fewest juxtapositions. So far, the element modelled here is rhythmically conceived motion, but the symbols, which are subject to the laws of change, can also be translated into other musical elements.
Compose a short piece (abounding in rests) in two versions, one based on simple values and the other one with irrational values superimposed on them. Compare both versions and find what sort of methods of transforming simple values into complex ones suit you best.
In Example 14 find traces of the consequences of a thorough-going analysis of the problem touched upon in Sections 17—19.
22
21 q
Is there a progression of rhythmic values from the simplest to the most complex ones and how is it expressed?
Simple and complex values
Rhythm is apperceived on a logical not an auditory basis. We may therefore safely say that rhythm includes both simple and complex values.
We can arrange a progression of rhythmic values, having at our disposal an increasing number of values which differ f r o m e a c h o t h e r in richer and richer numerical relations. In comparing rhythmic values with each other, we endeavour to find a common denominator. The more disproportionate the differences occurring between the values, the more
We must be aware that the division of a bar composed of two quavers into three equal parts is a procedure of superimposition. 16
complex is the logical structure of the whole. Example 18 shows how such progressions can be produced (18a — the method of finding proportions and the first orderings of the material obtained; 18b — the full system of values obtained not only by dividing them but also by combining different values, owing to which the range is gradually widened still more and the arrangement of the rhythmic system undergoes a still greater enrichment; 18c — the close analysis of two extracts from the table of rhythmic progression; 18d •— the possibility of arranging a series of different rhythmic values only slightly distant from each other: naturally, in practice values which lie so near each other do not have much of a practical application; nevertheless we should get to know them).
In practice, the compositional consequences of such a progression may to some extent contradict the existence of an equivalence between the complexity of a musical picture and that of the complexity of the effect on the listener. This, however, should not obscure the fact that only notated relations are of objective value to us. The antinomy between the image presented by notes and its expressive effect has always existed in music; we must put up with it and simply take little notice of it. What is more, such antinomies ought to exist, for they create in great measure what we might term—• the enigma of art.
Closely analysing Table 19 (19a is based on simple values, 19b on combined, conjoined, values), try to find for your special favour several dozen "two-voice" succession whose development might enliven the monotony of the rhythmic models used so far.
20b shows a series of developed rhythmic processes, whose inner variety is more emphasized by differentiations of melodic motion (in the approximative sense of the word melodic) and articulation. Finally, Example 21 illustrates the process of the gradual complication of rhythmic material, being based invariably on one series of pitches (in order to obtain comparative material). The use of one and the same series for very different rhythmic models makes it an element of minor importance. The example visualizes a change in the composer's way of thinking. Note that, as regards movement, consequences of a higher order can be obtained even from the simplest models (Example 21, passages 3, 4, 6, 9., 10, 12, etc.). -
Only the piano has been employed in Example 21. All the passages exhibit similarity in the method of procedure itself, but differ nevertheless in texture. (Observe, that increasing the quantitative number of techniques as well as bringing various irrational additional values into interaction enriches the rhythmic material only in certain aspects, as we already know from the previous chapter.)
Using simple and irrational values, make up 6 different juxtapositions of rhythmic models in <» £> u> «> I and l metres. Arrange the models together in a progressive succession keeping in mind the rhythmic result (the models must not be arranged on the mechanical principle of asymmetrical complications!). Make up, independent of metre, a series of 24 rhythmic models and space them out within sections lasting approximately half a minute each. Take care that no mechanical repetitions of similar situations appear in them.
23
24 The composer's work on rhythmic models
q The limitation of rhythmic values to a few a bar threatens us with a rapid exhaustion of movement; how do we prevent it?
Example 20a presents possibilities of composing rhythmic processes on the basis of selected values. Each choice of values, having an effect on the composition of rhythms, determines the homogeneity of the rhythmic style, which is the more closed and particularly individual the more suggestive the choice is. Example
Exhaustion of a sense of movement is a phenomenon which inseparably accompanies the repetition of 17
rhythmic models which were narrow in scope. The restoration of the rhythm cannot be attained by a mere permutational reshuffling of models, but it can be achieved by setting together opposite models. Compare Example 22, which clearly shows the compositional mechanism of restoration of a stable model. Other examples of this type: 23—28. Example 23 — the placing of an identical figure (and similar material!) in various points of time in a simple process; Example 24 — the opposition of simple piano sounds, modelled according to the rule known from Chapters 22 and 23, to an internally complex structure of movement; Example 25 — a play of antinomies, consisting of placing similar sound groups in different positions in the metre and of placing changes in the sound content of the rhythmic figures positioned identically (the numerals given beside the rhythmic values indicate successive repetitions); Examples 26 and 27 — the juxtaposition of different rhythmic groups; Example 28 — a simple model of movement serves here to obtain an ingenious formal structure, which extends beyond the model itself, and which prevents the exhaustion of movement, inevitable in the case of ' 'mono-rhythm".
Closely analyse the problem of exhaustion of movement in Example 29. Compare the four sections of the piece with each other in respect of the development of movement technique. On the basis of Example 30 study in detail the consequences to be inferred from the canon in movement and accent. Analyse the way in which movement is treated in Example 31. Taking as your example the procedure in Example 29, compose a four-section piano piece, using the simple model for pitch as your basis.
25 Possibilities of a new divergent way of treating music written in simple metres
we contribute only to its consolidation, but this is of no importance as a help in imparting dynamism to movement. In order to prevent this situation, changes of arrangement, displacements of so-called "accents" (nowadays metre has lost much of its original accentual nature), and changes in the model of movement are continually applied e v e n within simple metres or perhaps a b o v e a l l within them. Example 32 shows a method for the overcoming of mechanical usage of metre (Example 32c is a consistent development of the models from Example 32b). Metrical or metred time can be added and divided. The perpetual alternation of these two composing procedures and, above all, the simultaneous superimposed use of addition and division (feasible in music) make it possible to evolve interesting solutions to the difficulties posed by even the simplest metres. Naturally, the greater the complexity of the metric matrix, the greater the results to be obtained in the articulation of movement, although this does not happen automatically of itself. Example 33 illustrates a simple means of enriching the metre by setting up contrasts between rhythmic cells. This example is a "living illustration" of the methods of working on motivic models. We came to know these imotivic models in the chapters dealing with rhythm from the point of view of its internal properties. Example 34 shows the dialectic between continuous motion and pointillistic motion, a motion divided by rests; here the metre fulfils another function, chiefly that of welding together a motion whose flow had been disintegrated by the application of serial technique. Example 35 depends on an elementary duality of metre: I and ° (kettledrums) are run simultaneously to contrast in such a way with each other that neither of these metres prevails over the other in the process of their parallel formation. The metre is imposed beforehand in Example 36. Such a precompositional choice enables the composer to designe (construct) the movement. No other choice would have allowed him to achieve this. Lastly, in Example 37, we are concerned with the successive joining of very different metres (the differences are augmented by changes in tempo), which makes the metric text ambiguous, and this may be just the effect intended by the composer.
Simple metres automatically bring about simplifications in movement. They are, so to say, the confirmation of the scheme that has been adopted. Writing in a metre,
Compare the various consequences resulting from countering the established metre (Examples 38—42 and 18
also Example 43 in the convention of contemporary jazz). Find to what degree the final text is related to the fundamental assumptions, in what way it is possible to obtain, if at all possible, similar result by using other means, and whether it is possible and, as regards legibility, remunerative to bring about a reduction to simple metres (various forms of creating uniformity in this respect, alteration of the text in favour of a similar but simpler text, etc.). Taike Examples 40 and 41 as procedural models. Animating metres adopted in advance, compose only in rhythm, a fairly long passage of music (lasting about 2 minutes). (The "example-models" should not be copied. This is possible but goes quite against the principles of the ethic and the inner nature of creativity. Such prescribed examples, at any rate rare, relieve the present author of the responsibility of picking all compositional facets from their beginning level.)
tions should "support" the metre in the form in which it has been adopted and not fully contradict it!). The methods of metric handling are not uniform. Examples 45—47 present only a very few of the general possibilities in this respect.
Music moulded on the principle of changing metre presents the composer with problems, some of which involve sharp antinomies. This is shown in Example 48. With the almost continually changing metre we observe a discrepancy between the metre adopted in advance and its rhythmic formation (bars 3—4 and 8—9 are particularly critical). Such antinomies should be picked out and a thorough understanding of them achieved, but they should not be treated as errors since, all things considered, the composer has the right not to attach major importance to a given element (in this case it suffices for us to obtain the information that the composer composed o v e r changing metres and n o t : changing metres).
26
Following the pattern of Models 49—51, make up 6 to 8 of your own well-developed conceptions of this type.
Possibilities arising from modern compositional usages of metre. Playing by means of metre, further development of metric techniques
Write a passage of about 3 minutes' duration based on as variable a metric model as possible in three versions: a) in a version confirming variable metres, b) in a version decidedly negating the system of metres, and c) in a neutral version, as if bypassing this problem (despite this the metres must vary markedly).
Contemporary music tends clearly towards ametricality. Metre, however, even if treated only as a matrix, may have great inspiring and constructive significance. The introduction of playing by means of metre throws new light upon the text (in order to make sure of that, it is enough to subject a musical text to complex metrification). The tendency to ametricality renews the idea of time in music, but simultaneously loses the possibility of its being endowed with'dynamism, at least in the present sense of this word. Composition in metre alone does not suffice and, to go further, for this reason we resort to metric game playing. Such game playing is the more dynamic, the more fully the dynamic possibilities inherent in metre are employed. Example 44 illustrates the possibilities of moulding metrically divided time in a manner complex enough for composition to remain interesting, but at the same time not so complex as to negate the metre {the musical text, no matter how brought about, should support the chosen method: in our case even the greatest rhythmic complica-
27 q Metre today
Eight examples (52—59) of contemporary music have been chosen. Let us consider what the compositional bases are for creating metric lay-outs in these examples; wherein the composers fully justify the use of change in metres, and in which metric change creates something more than change which is only modification of the point of departure. In other words, in these examples metric change brings about certain results — 19
and what is important! — results not to be attained in any other way. Metric change has multiple applications. In the simplest examples it will be the driving force behind creation of constructions, whereas in more complex ones it becomes — as we already know — a matrix over which new lay-outs, often contrary to the adopted metre, are superimposed (Examples 57 and 59). Upon attaining a full consciousness of the significance of metric change, this procedure may come to be applied intentionally in full consciousness, as a means of achieving the above-mentioned, otherwise unattainable, ends. Nevertheless, it may also happen (and the last three examples prove this) that the purposefulness of such a lay-out is merely apparent. Example 60 shows an authentically intentional way of operating with metric change for the sake of compositional ends of a higher order.
Analyse carefully in Examples 61—66 the way metres are filled and the results obtained from the juxtaposition of different rhythmic values (a model analysis of selected measures is added to Example 61).
of accents from metric interplay. In Examples 67, 68 and 69 the composers inteijftionally used accents in the division of time to produce arrangements which cannot be reduced to metre. One of the important composing factors here is the intentional (67) or apparent (70) stoppage of time. Examples 71—80 indicate that despite the use of rhythmic values the 'moulding of time depends upon general proportions (typical examples: 75, 77 and 79). The next examples of this series (81 and 82) illustrate the replacement of the metred rhythm with approximate values; their arrangements result from a practical, performer's way of understanding notation and thus from the functional (intermediary) nature of the new ametric notation.
Write three different proportional time schemes with 1 second equalling every 4 centimetres,. Transcribe these schemes into several such ametric notations as, in your opinion, are the most functional from the point of view of execution (Model 83).
29 Compose a longer piece of chamber music for 6—8 instruments, applying at the same time metrical techniques that you have learned. Observe strictly the principle for the proper filling-up of the metre in this piece i.e., respond above all to the metric course pre-established metric.
28 Ametric music Ametric music springs from two sources. One of them is opposition to metre and its persistence as the primary means of organizing time. The other is the notion of time freed from imetric orderings. Here, we are concerned with establishing where we stand in relation to this problem today.
Are there any new time models and, if so, what do they look like? •
Time can be measured in ametric proportions. This can be achieved by adding up minute particles each of which is treated independently of the remaining ones even in metric arrangements (Example 84). This is the simplest way of presenting the material; raised to the rank of a primary rule, it can give rise to a specific dialectic concerning the forms of movement. Example 85 demonstrates the method of splicing a process together from small particles. Examples 86 shows rhythm dependent on the proportion model (the proportions themselves arise here from the practical possibilities in the realization of processes; the rhythm is thus the result of a process and not its basis). These three examples prove the existence of a constant dependence of the process of time on the structure imposed by the composer.
If we analyse closely the increasingly ametric modes of moulding time (Examples 67—82), we find that at their bases there lies a tendency towards disengagement
In Examples 87—91 tendencies to go beyond the hitherto existing limit in the moulding of time are apparent 20
'
The proportions that occur in these examples are various: strict, mathematical (87), co-situational (88, 89), some are programmed in vertical asymmetries (90), some are intentionally regular (91), others burst the imposed scheme (92—94). (In Example 94 we are concerned with a combined two-fold disruption of the scheme on account of the variable metre and the disproportionate distribution of rhythms). Finally, there are even proportions that impose a definite formal type based on the formation of a process from particles whose profile is distinctly structural (95—98).
In order to become fully aware of the fact that, as regards rhythm, we have today at our disposal completely different material as our point of departure, we must return once again to the very act of moulding time. Obviously, the results are the more interesting, the more the lay-out of the material is susceptible to change; but also, ,the dispersal of material is all the more attractive, the less it resembles a statistical distribution; in other words, decisions concerning the lay-out of material must have characteristics of a clear disposition. For instance, two different lay-outs, in themselves 'exhibiting change to the highest degree, may give a result which exhibits much less change. This is to be avoided. All methods of mechanical planning are injurious to the result. Schematic methods may be applied only when they ensure particularly individual final results. A method does not exist for itself but to serve some other purpose (in our case to serve time disintegration rather than complementary reduction). It is possible to obtain an effect of very subtle time shading by very simple changes within the given proportions. The complexity of the rhythmic models arises from the simple handling of proportions (this type of procedure is contained in Examples 112 and 113).
Analyse independently the possibilities arising from the conversion of one method of organizing time into others. See to what extent the adopted methods of timeorganization restrict the range of composing activity in other respects.
Compose a short chamber piece —• about two and a half minutes in duration — marked by its unconventional time projection (rhythms, metre, proportions, time divisions).
30
Take Example 117 as your point of departure. Write about 20 similar combinations, penetrating exactly the nature of the time proportions between the individual rhythmic values.
Complexity of rhythmic models
Write a rhythmically complex passage of music of forty seconds' duration for six different instruments, applying at least three of the given thirteen patterns (Examples 104—116); avoid the use of different patterns in one and the same voice.
Examples 99—103. Time runs differently in each of the five examples. As will be seen from the examples, it can be built up of unequal particles (99), by taking account of changes in the tempo, which cause different structures to become "similar" (100), by sharpening the dynamic articulation (this is more logical where uniformity is preserved in other respects — 101); lastly, it can be put together compositionally from different particles in a perfectly asynchronous time scheme (102— 103). The complex rhythmic models (104—112) prove that there is a varying method for moulding time using the conventional notation system (this is most strongly opposed by the arrangements in Examples 109 and 112). Only further stratifications of the process (113—116) make it possible to obtain a wider scale of differentiation from rhythmic substance.
31 Changes and superimposition of metres and rhythms within metres The vertical and horizontal juxtaposition of different rhythmic values creates co-situations in which a state of affairs hitherto unknown in music occurs. Example 21
118 shows to what extent the pointillist isolation of rhythmic values adds to the new articulation of time. The more the rhythmic values are bound together into groups (Examples 119 and 120), the less we may speak about the emancipation of the rhythmic element within established metres. The vertical accumulation of complex rhythmic structures often results in the following of a diametrically opposite, simple scheme (carefully analyse Examples 121, 122 and 123). Changes in metre may differ in character. There is a kind of metrical change which does not play a major part either as a means of energizing the movement or as a constructive means. Example 124 is typical in this respect; here, both the dynamics of movement and the construction are very convincing, but they do not belong to the metrical sphere; they are achieved in spite of a lack of dynamic and constructive functioning in the metre. In Example 125 the first three models of movement are abstract and do not suggest a further course for the rhythm, nevertheless affective potential arising from real and accidental changes in the metre is large. Example 126 shows a neutralized metre (nearly all the bars are connected by syncopation), 127 an ordering metre, and 128 an almost barless metre (accelerations and stoppages of movement provide a thorough recompense for the amorphous movement adopted in advance).
Analyse closely the examples of change in metres and the results of their rhythmically complicated composition (Examples 129—134; Example 134 comprises a model of a preliminary analysis on which the close analysis of composing techniques should be based).
Example 135a reveals the possibility of the existence of two types of complications in so far as rhythm alone is concerned. In bars 81—82 we deal with a group of different irrational arrangements. It is worth noticing that working with a common denominator does not suffice for irrational values. We must also — even in the absence of simple values, as in the example given — take into account the initial elementary values (Example 135b, common denominator — 504). Towards the end of Example 135a, a model of a septimole occurs. The same model appears in all five parts. The model is however composed in a different manner each time (cf. 135c). Between these two extreme models there is a whole range of intermediate rhythmic complications.
The problem of rhythmic complications is not an easy one. In the first place, the very complexity of notation is not always reflected in the aural effect; richly written music may seem to be simple to the listener. This is unambiguously shown in Example 135c; here a new model of movement (3'2 ), which is not complex in itself, simply appears in the middle of bar 82 (we shall see what happens, if we "transcribe''' this text in greater values — Example 135d; it is clear that we are then concerned with a new metre, which fact shifts the rhythmic problem beyond its autonomous aspect!). Thus, the composer's task is to use rhythmic complications in the autonomous sense of this procedure, without simplifications but always keeping in mind the need for rhythmic complications whenever it would be impossible to attain a particular desired effect in another, simpler way.
Using the course of affairs in Example 135 as a basis, compare the ways of juxtaposing rhythms in Examples 136—140. Find to what extent the occurrence of a large number of different rhythmic forms actually enriches the music and, in addition, what kind of connections with metrical handling and with changes in tempo have an effect on the delineation of rhythmic character. From the numerical equivalents in Example 141 deduce your own, even general, analytical principles for Examples 142—144 (simple realizations) and 145—147 (complex realizations). In analysing the first group of examples,, concentrate on the problem of the interplay of rhythmic forms. It is also worth considering here
Compose a short four-minute piece of music for string trio. The problems of changes and stratified accumulation of metres should be at the forefront compositionally. Scrutinize it after the fact to see what the possibilities are for avoiding or neutralizing metrical problems in seeking to approach this kind of music. Attempt several tests of such an arrangement.
32 Rhythmic complications 22
I
3
the influence of additional factors on the evolution of the rhythmic picture, e.g., the influence of articulation, which, as it were, shortens the rhythmic values, or the bearing of the very nature of an instrument on rhythm (for instance, the harp has to be dampened very accurately in order that, in the case of strictly written rhythmic values, the instrument might fully render the composer's rhythmic intentions). There are other similar instances; note them constantly and make the appropriate personal technical inferences. While analysing the second group of examples, consider the possibility of transposing the problem of rhythmic complications into textural terms. (Example 147 accurately illustrates the value of the use of the rich forms of rests; owing to them, the impression of richness in complex rhythmic forms can be enhanced. An impression of richness manifests itself more fully against an "open" time than it does in a continuous, compact version. In continuous, compact time rhythm loses its autonomy and, by the way, resembles lumbering part polyphony.) Design your own analytical solutions for at least two of the four rhythmically very complex examples (148— 151).
Compose a musical passage (about 40 seconds in a medium tempo) for eight instruments, based on a gradually condensing summary effect as regards rhythm (you should: 1. avoid shifting the centre of gravity from the rhythmic element to other elements, 2. take into account the closed stock of means of rhythmic complications, and 3. give the whole a readable form, without an excessive complexity in the external picture). In compositional exercises of this type one should always keep in mind the necessity of speaking about the whole by means of a fragment; thus, the assigned musical passage must contain suggestions of the possibility of further development (expansion) of the music on the basis of the assumed method of procedure or, in other words, one should have the impression that the continuation of such a game might be interesting, easy, instructive and encouraging for the composer (composition is not the solving of given problems, but rather a game played with problems in which the problems are treated playfully).
Rich results may be obtained even within simple metres by incessantly annihilating their supremacy. So-called polymetre has turned out to be only a partial solution in the present state of composition. Based on monometric foundations, it has functioned for many years as an antidote to the "rhyming" simplicity of rhythm and movement. Polymetre, characterized by accentual irregularity, was employed to counter invariable metre with its constant, symmetric distribution of accents; however, polymetre acted only as a "counter" in terms of the monometric system. In the music of today, in which rhythmic values are already emancipated in full, the play of accents — their various distribution and treatment — has lost its advantages, if for no other reasons than to apply the play of accents it would be necessary first to demonstrate — optically, systematically and aurally — the initial elementary model. Only then could contrasting passages by built. Nowadays polymetre may only be regarded as one of the factors of change in material, and the effects it produces (for instance when polymetre is combined with other techniques such as the serialization of other elements) are slight even in respect of the dynamics of movement alone. This notwithstanding, it can be useful as a matrix for rhythmic values for inspirational, if no other, reasons (more interesting co-situations emerge out of a metrically complex groundwork of movement than out of a simple one). It may be said, in general, that metric complexity has now taken on the task of deconcentration — not concentration — of the element of movement and that it is introduced by composers chiefly to intensify the ambiguity of the musical process. In order to become aware of new metric possibilities, one should set together vertically, single bars filled with rhythms which compose the metre, as it were, "from inside". (Example 152 presents the modes of filling time with metric proportions — from 3 to 10 units).
One may employ methods of great complexity in connection with metre, yet these lead to no major results. This is because today metric results are obtained in a different way. Nevertheless, as has been said above, they can be used and are worth using, if only for the enrichment of the vertical and horizontal process. Examples 153—155 show some compositionally valuable metric schemes. In all of them the changes of
33 Metric complexity 23
metre and the various ways they are filled up take on the functions of changes in material. Processes may be rendered dynamic by the horizontal (Examples 156—160), vertical (161—163) and combined vertical and horizontal (164—168) confrontations of metres. The horizontal confrontation of metres is more palpable than the vertical one, but from the view-point of construction and texture it "says" less. The vertical confrontation of metres may give various results; much depends on what is confronted vertically (an excessive number of parts can cause information to pass by chaotically which is dangerous from the metric point of view; however, such a chaotic effect might sometimes be desired). This is also the case with verticalhorizontal confrontations — Example 168 is typical of them. Owing in a way to the very fact of two-sided relations, they lead to different results, often unforeseen and hardly even sensed by the composer (it is worth noticing how partial composers are to this type of set-up, through which otherwise unattainable ideas are undoubtedly released for them).
Analyse Examples 164—168 for metric complexity. Find at what point vagueness of metric information begins to appear and in what respect this vagueness may be regarded as compositionally advantageous. Try to locate and point out the differences between Examples 167 and 168 as exactly as possible.
Compose a short piece, based on the principle of vertical and horizontal change, for a chamber ensemble (directed by a conductor) in such a manner that it will express a point of view on the dependence of the musical process on metrical assumptions. (Find out after the fact to what extent you succeeded in building formations on the predetermined metres,, which, to say the least, did not result from the predetermined metres directly.)
other. Our receptive system, is prepared, as it were, for immediate perception of pitch, whereas rhythmic values require a conscious intellectual act of recognition of each value and of the proportions between rhythmic values. The reception itself of rhythmic values proceeds, in general, on a logical, rather than auditory, basis. Some relationships exist between pitches and rhythmic (time) values. These we can ascertain, if by no other, by simply observing what happens to pitch when the speed of a magnetic tape is doubled.
In new music we can fully avail ourselves of the interchangeability of parameters. Examples 169 and 170 show to what extent such relationships can be utilized in composition. Example 169 demonstrates parallelism of internal changes with the use of 5 rhythmic and pitch components, this parallelism being based on the principle of ascribing a time value to each sound value. These relations are naturally the result of a convention and the adoption of another model of pitch-rhythm dependencies might be equally good and compositionally workable. Example 170 shows some more highly developed associations of pitches and rhythmic values. Here I should include a note: there is no doubt that the interdependence of these two parameters is not natural, despite the capacity of all the pitch intervals to be converted into time intervals. It is not natural, but can be n a t u r a l i z e d comparatively easily. The ability to do this can be achieved only by practice; here we confine ourselves to the statement of the possibility alone.
Work out your own table of correlations between pitches and rhythmic values. On this basis construct a fairly long musical passage (fairly long, because we are unable to realize all the advantages and shortcomings of the adopted composing procedure until we have studied the results for some time), which in its consequences will be far more complex than the assumed points of departure (Examples 171 and 172 may serve as rhythmic patterns).
34 Concepts of pitch-rhythm relationships
Assuming the experiment carried out in the exercise above as the starting-point, compose a piece which, without being the mechanical product of adopted principles, will still bear certain characteristics of a composition that has arisen in this very manner;
Pitch and rhythmic values are perceived on a different basis and as such they arise independently of each 24
compose spontaneously, only slightly stylizing the previous kind of music (one absolutely should not attempt to achieve a perfect coincidence of previous and new results). Chamber ensemble, at least five-part texture, well-developed form (up to 4 minutes).
35 q Compositional consequences of the repetition of the same pitches
The possibility of replacing change in the hitherto most important parameter of pitch by the repetition of the same pitches or the same pitch complexes with the simultaneous activation of change in other parameters is a discovery of the new music. Example 173 — reduction of the compositional problem to a minimum (note the role the composer attributes to the last bar, the arrangement of which thoroughly compensates for the lack of a compositional factor in the four preceding bars); Example 1V4 — composition of pitch material limited to W minimum (it consists of chromatic projections departing from each other in opposite directions), despite the repetition of fragments the whole is dynamic in nature owing to the special distribution of rhythmic stresses in time; Example 175 — reduction of the pitch problem (percussion) and rhythmic-dynamic construction of time; Example 176 — use of note repetitions as well as normal pitch variation in an interaction; Example 177 — utilization of one note as a point of departure followed by its dynamic (and textural) composition.
Composition based on the reduction of pitch variation raises the danger of bringing about an indifference to this parameter. It is good to use this method as a technique beside (Example 176) or among (Examples 177—180) other methods, but it must not be used for itself. Examples 181—186 present the developments of the technique of repetition of notes, their groups and complexes; 181 —• the repetitions, accented in time, complete the whole (the note lying motionless without repetitions, even if enriched vertically and intonationally, as in this case, would not suffice); 182 — the repetitions set together in an approximate way are structurally constructive; 183 — the dynamics and tone
colour complete the expressive aspect of reiterated rhythmic values whose repetition here becomes obsessive; 184 — the type of note is repeated but not its pitch (!); 185 — the construction arising from unequally distributed repetitions is combined with the stoppage of movement on a full chord; finally, 186 — the retention of the note (in other words, its continuous repetition) is compensated by changes in its tone qualities. The foregoing examples suggest that repetition need not be associated with the indifference to material, which occurs only when a process-moulding role is ascribed — as a rule ineffectually —• to repetitions. (Psychology of reception has something important to contribute here: "only he who has lost the thread repeats the same words". In other words, it is precisely repetition that demands to be specially composed!). One can however reduce repetition to a secondary role and move together with compositional ideas to another terrain, but such a move must be indicated clearly and unambiguously!
Construct eight different models of intentional composition by means of single notes and making use of change in some other fields.
Basing yourself on these models, compose a fairly long passage for string quartet. Ensure that the consequences of the composing process go beyond the principle of repetitions, e.g., textural consequences.
36 Relationship between the idea of constant variation and the formation of rhythm
In new music there are examples of grafting arrangements derived from note series on the rhythm. We already know that these two elements can be related to each other, that each can be mutually ordered in respect to the other by correlation. Example 187 affords a rough demonstration of such an ordering (we can define it simply as a patterning of the rhythmic series after the pitch series). The results of such a procedure are shown in Example 188, in which four distinct 25
strata make up a whole that cannot be reduced to any schematic pattern (this is why composing methods of this type are so valuable).
In comparing Examples 189—191 with each other, we arrive at the conclusion that the results of rhythmicserial patterning (or the results of compositional habits stemming from this type of technological approach) are structures characterized by constant change. Consequently these structures become similar to each other in defiance of the composer's initial assumptions. In order to prevent this, a peculiar mode of u n d e r s t a n d i n g patternings should be adopted (e.g. with the simultaneous use of a specific reduction of components — cf., dynamics and articulation in Example 187).
e Construct a few. examples of rhythmic derivation independent of mechanical serialism. Here you should a) maintain the impression of constant change in most elements, b) introduce richer relations into the rhythm, not only the mechanical ones resulting from the additive setting together of rhythmic units, c) produce textural effects of a distiictly rhythmic origin and d) emphasize composing on this material without confining yourself to the mechanical listing of results.
Compose three short pieces based on the principle of a relationship between the series and rhythm. In this relationship the series may be any ordering of notes and the material cf rhythmic values should be an arrangement of simple and irrational values set together in one plane, with the arrangement being different each time it is employed (the impression is then to be created that the simple values stand very close to the irrational ones; this is easily achieved when a remarkable predominance of the latter over the former has been introduced).
itself in composing practice is illustrated in the excerpts of a work written exclusively for a percussion ensemble made up solely of instruments of indefinite pitch (Example 192 a, b and c). Example 192b is the most instructive in this respect; it proves that the duration of a sound is directly dependent on the force of the stroke. Such methods of procedure are sensible only when they are associated with real performance practice. The development of these methods is shown in Examples 193 and 194. Example 193 is based on rhythmic structures directly dependent on dynamics and Example 194 treats dynamics in a complex fashion (the two lines are independent of each other). This results in the superimposition of chorda! structures whose saturation says something — also directly — about dynamics and about how decaying sounds last.
Rhythmic-dynamic relationships constitute very natural connections between elements. In the previous section we got to know rhythmic-pitch relationships or rhythmic pitch ordering correlations which, to be sure, can be naturalized but are not as direct and natural as the rhythmic-dynamic ones. This is why, in order to become familiar with elementary composing possibilities, we must take into consideration the possibilities of playing with antinomies, for instance, with opposites (in such a case, a small rhythmic value would correspond to forceful dynamic levels, a large rhythmic value to low dynamic levels, a still larger one to even softer dynamic levels etc.). The play of antinomies — treated as a system or routine — can be wholly naturalized (in other words, we can become accustomed to material behaving in just such a way).
Construct your own scheme of relationships between rhytm and dynamics, including the play of antinomies. Examine it for benefits arising from the adoption of the method of constantly changing reversible dependence. Write a short musical passage in two versions, one natural, the other antinomic, and compare them (textural and compositional conclusions are to be drawn from this comparison).
37 Rhythmic-dynamic relationships
Compose a piece, lasting at least 3 minutes, for a percussion ensemble (predominance of instruments with long pitch decay, using the procedural methods discussed above). Compose a short piece for instruments of
There may be a direct relationship between the intensity of sound and the rhythmic values. How it presents 26
definite pitch that have an easily damped a long decay time. (The play of antinomies, including rhythmic-articulatory ones, should be applied on a larger scale.)
38 Rhythmic "harmonies" appearing as a result of new co-situations
195 indicates that it is possible to equilibrate the vertical and the horizontal. The conversion of the horizontal change to a vertical lay-out, observed in the fourth bar of Example 198, is artificially superimposed on the modern system (this is best proved by its rare occurrence, and may be regarded only as a possibility). To be sure, there is still a long series of co-situationalharmonic models attainable in a simpler, not so mechanical, way. In order to get acquainted with them, it is necessary — paradoxically — to create them as if unconsciously, in a less studied, more spontaneous manner.
In addition to the possibility of bringing rhythmic values and pitches into a mutual relationship there also exists the possibility of an influence of rhythmic (rhythmicizing) processes on chords. Relationships of this type are illustrated by Examples 195—201 (different ways of obtaining new chordal co-situations, "harmonic" ones, by the use of rhythmic components). Example 195 — a harmonic vertical combination, richly and ambiguously composed, interrupts the neutral horizontal course and attracts our attention precisely on account of its structure; 196 — variants of the model from Example 195 developed "in groups"; 197 —• vertical structures, constantly changing thanks to the aleatoric openness and exchangeability of material; 198 — here the harmonic complex acts in a different sphere from that suggested by the notation (the separate and accurate composing of each note splinters the material and forms a highly anonymous whole; consequently, the result does not reveal much of its consistence); 199 — accidental harmony; here the harmonic result is an effect of the situation and as such is "less important"; Example 200 illustrates an even further possibility of multiformity in the vertical combinations, which we met in Example 197; lastly, Example 201 transfers us to the field of a new harmony; here, however, what the actual harmony consists of is important (in contradistinction to cluster-type complexes, in which the intervallic sum almost automatically reduces the whole to a structurally very restricted and in fact uninteresting "timbre"). In all these examples vertical synchronization creates a harmony of a higher order, perhaps less easily perceptible, but all the more ambiguous. Composers particularly desire such a higher order.
Make up four different patterns of rhythm-chord correlations. Solutions sought should be of textural, not only harmonic, importance. An unknown co-situation, not a "model for harmony", is principally to be sought (now harmony must not be treated as the foreground, as in the past, but as an accidental result or product of the composer's work in another area; it thus manifests itself in a highly "non-harmonic" manner).
Compose twelve different vertical combinations laying them out for a small chamber ensemble. Each of them should be based on a different initial principle and, consequently, should manifest itself in a different way. In this study the composer is expected to be prompted by the possibility of harmonic action without the creation of a harmony, in other words, the possibility of obtaining harmonic results by means very distant from the traditionally harmonic ones.
39 The restriction of composition exclusively or primarily to the range of rhythm
In the framing of rhythmical scores and scores in which rhythm is the foreground value, the mode of time division is immeasurably important. Each composition consists of a series of various rhythmic values, but it is only their selection and compositional shape that are decisive in regard to the importance of the rhythmic element in a work. This may be exem-
This is most certainly one of the forms of compensation for the no longer existing harmonic factor. Example 27
plified by an excerpt from a work by Schbnberg (202). Within 3 bars of 53 notes the author deals with as many as 10 different rhythmic values (a), which in addition are situated in various ways in the metre. This example is supplemented several variants which deform the situation present in the excerpt quoted (b). A procedure of this sort permits us to see how extensive a range of possibilities the composer had at his disposal; it suffices to change the value of particular rhythms or to change them in order to obtain a completely different result (c). This is however possible only with the wealth of initial material in Schonberg's music, whereas in music based on conventional rhythmic conceptions (Honegger), in spite of changes, the result will always be the same schematic rhythmic pulsation. There is a possibility of restricting oneself exclusively (203) or primarily (204) to working with rhythms, i.e., with material of generally indefinite pitch. Example 205 illustrates the method of proceeding in a rhythmic and quasi-linear fashion at the same time. Example 206 is a kind of transposition of the idea of rhythmical score into pitch material. Further examples of intensely "rhythmicized" scores: 207—210. Example 207 shows the possibility of forming a rhythmic process on the basis of seemingly varying tempi; Example 208 demonstrates a general textural effect produced by the vertical accumulation of parts with each part having its own structure, as if it were independent of the whole; the idea of Example 209 is the shifting of the centre of gravity from one part to another,, while Example 210 is its extreme opposite, since it is based on the perfect equivalence of parts, owing to which we reach a point where, however richly the rhythmic element is composed, the whole is anonymous and statistic in nature; in the present case this character is extended even further by a constant dynamic value, which, as it were, sums up all the elements.
ering different formulae of one and the same value (in this case — crotchets); further portions demonstrate some better-developed rhythmic forms in which greater irrational values are used (b), and subsequently free, as if approximate, systems (c). The two vertical arrangements of (d) indicate how much the manner of vertical composition of rhythm matters: in the first instance we are concerned with poorly perceptible and thus hardly significant differences, in the second case with significant differences which contribute to the fine division of time. Example 211e shows still wealthier vertical arrangements of rhythm (numerical proportions visualize the wealth of inner relations in the material composed in this way).
Write an intensely "rhythmicized" score and transpose it into pitch material (the model of the score should be so constructed that the transposition does not annihilate its original complexity).
40
'Articulation of time''
Rhythmically-moulded time may arise from special concepts, for example, from the conversion of spatial musical ideas into g r a p h i c images which suggest their concrete realization. The model in Example 212 contains twelve units of articulation of time, which can be read not only directly, i.e. copying particular models from the graphic representations,, but may also be read interpreting the graphic representations in a more complex manner (e.g., giving a fuller sound picture instead of one tied note).
The restriction of composition exclusively (or chiefly) to the field of rhythm calls for special interest in rhythmic problems in themselves. It is well known that rhythmic change is neither .easy to realize nor — later on — to grasp. In order to work with rhythmic change, we choose the method of handling rhythmic cells from the general method for the formation of rhythm by setting together its particles. This method and the consequences of its application are presented in Example 211. The first portion (a) shows the possibility of discov-
New rhythmic procedures require non-mechanical initial assumptions, compositional even within themselves. The consequences of such assumptions can be adopted as a method for rhythmic procedure and, when already recorded in the memory, applied as a programme for spontaneous activity in this field. Different attitudes of composers towards the problem of time articulation, ranging from strict measurement to aleatoric treatment, are shown in Examples 213—223. Example 213 — 28
measuring of time, on the division of selected time units; 214 — four different time processes occur in four parts; the rhythm seems similar but, in fact, owing to the introduction of different tempi, it constitutes richly differentiated material; 215 — possibilities of obtaining different forms of time articulation, using the same sound material; in each variant the textural result undergoes a change and the chordal and linear results are also different; the extent to which rhythmic material is a composing factor is here clearly demonstrated. Examples 216—223 demonstrate different approaches to time articulation, no longer understood as a result of composing with rhythms, but as the composer's fully conscious activity in the sphere of time. The first two examples, 216—217, originate from autonomous time conceptions; Example 218 presents a peculiar kind of time amorphism: in spite of the proportioned notation, time articulation will always be accidental here; Example 219 goes still further in this direction; Example 220 shows how far one can deviate from rhythmic proportioning towards an approximate graphic proportioning; Example 221 illustrates the translation of time articulation into the idiom of score shorthand; Example 222 demonstrates a certain systematization in the time scheme, although this is not reflected in the aural effect. Finally, Example 223, in which different interpretations of time are given, shows .the openness of time, which is however enclosed (since one must abide by something) within mutual proportions. Musical time, which in new music has been deprived of its quality of being measured and, consequently, of its logical mensurability, requires new methods of disposition from the composer. These may be discovered spontaneously (Examples 216, 217, etc.), yet the awareness of the necessity for constant regeneration and constant variation of rhythmically-moulded time should lie at their basis. Not all the methods of notation of time articulation can find a sensible reflection in performance practice and for this reason one ought always to start from time schemes verifiable by performance. At the same time, however, we should not worry that excessively complex structures may not be executed with perfect accuracy. In new music the very impulse to new action in the field of time articulation is more important than the strictness of realization.
Compose a piece with individually conceived time articulation (this should be a piece in which the way of approach to the problems of rhythm will come to the forefront).
II 41 Linear motion. The attitude of the contemporary composer towards linear motion and its role in the structuring of music
Derhythmicized melody is termed linear motion. It is a horizontal arrangement of pitch material abstracted from time relations. In new music linear motion is a substance detached from the originally important core. It is a mobile substance which is subject to transposition. Hence, it may also be conceived in the first place as an intervallic model and only in its compositional consequences as material. Today linear motion is void" of the outstanding importance that it had in previous developmental periods of music. Treated as an element subordinated to the new organization of musical time, it is also deprived of its past function of material that forms horizontal arrangements. Nonetheless, in composers' work it betrays its Own autonomous specific nature, which in the best case is that of a stylistic component. As music develops, linear motion loses its autonomy (Example 224, first'signals of this process), and in extreme cases may be replaced by linear motion-like formulations which are regarded as its full equivalents (Example 226).
A number of problems arise here and require a more extensive discussion. First, in contemporary music must we start from pitches material; secondly, is linear motion gradually losing its original significance as a horizontal ordering which can be transposed and, thirdly, to what extent can we dispense with linear motion nowadays? The answers to these questions will be found in the works of contemporary composers. Today we most certainly can assume any optional musical
Make up a universal model of new time articulation,, using a limited stock of rhythmic symbols, very different from each other. 29
parameter instead of the material of pitches as the starting-point of composing; as a horizontal ordering, linear motion is of importance only in that kind of music which is horizontally arranged (for example, in dodecaphonic music); whereas in non-horizontally, "nonthematically" programmed music it is devoid of a structural role and may very often be replaced by another (similar or otherwise) horizontal arrangement. The arrangement in the horizontal plane is therefore the result of activity in linear motion rather than a product of linear thinking. Example 225 illustrates the specific nature and also the anonymity of the arrangements used by composers (the arrangements presented have been taken from Examples 2, 4, 17 and 24).
instruments over other elements, still accompanying; Example 229 — harmonic polymelody, based on the principle of main and secondary parts (surrender of the thematization of motion); Example 230 — reduction of motion to a secondary textural role (notice the transposition of the linear arrangements); Example 231 — shifting of the centre of gravity from the horizontal arrangement to the figural vertical one (motion is losing its significance since it appears simultaneously with its variants); Example 232 — comprehension of music based on texture not on linear motion; this is also true of Example 233, in which vertical structure arises from the deliberate linear asynchronization of linear motion at the horizontal level; Example 234 — dispersal of points of linear motion in time, on account of which motion ceases to be important as a horizontal arrangement; Example 235 — reduction of the role of linear motion in favour of changes in instrumental timbres (here the change in instruments is an indicator of linear motion); Example 236 — replacement of linear motion with approximate arrangements.
Write a 240-note motional arrangement, observing the following rules: the first 60 symbols should arise as a result of traditional "thematic" linear thinking, the continuation as the product of a dodecaphonic approach (five different or similar series), the third part as the spontaneous handling of selected intervals, and the last section as a row of notes composed without any definite linear aims and structural ideas. Compare the four parts of the written arrangement with each other, subjecting them to material, intervallic (frequency of certain intervals) and aesthetic analyses. Correct the arrangement at its most drastic points and examine after the fact on w h a t criteria these corrections had been made.
Scrutinize Examples 227—236 for the significance of linear motion; find in what instances linear motion may constitute a point of support in the formation of a composition or, in other words, how the music is to be moulded to attain the change in material required in a composition.
43 42
q Range of possible change in linear motion
q Foreground and secondary status of linear motion
Since linear motion is treated as a secondary element, the use of the factor of change in it is possible only to a small extent. Example 237 illustrates the slight shading of the pitch of the linear motion (however, by using other parameters of change here the composer exposes linear motion more than he would if he actually worked by varying it).
Examples 227—236 provide a survey of the process of the shifting of linear motion from the foreground into the background. Example 227— predominance of the linear motive (the first four melodic notes are later repeated in a changed rhythmic form, which fact indicates the preponderance of linear motion over other elements; the whole is based on the harmonic substratum accompanying the upper line; the treatment is traditional in this respect); Example 228 — predominance of the melodic lines entrusted to selected
The following problem arises: the maximum change in linear motion (cf. Examples 234 and 235 from 30
the previous section and Examples 238 and 240 here) constitutes a kind of anonymity in the components of this element. In order to draw attention to linear motion, it suffices to change it within a specific narrow range (Examples 244 and 245). A close analysis of change in linear motion in all the examples given is necessary if we want to ascertain this. Example 238 — dispersal of the components of linear motion throughout various registers; motion as the derivative of a continuous line is here neutralized by being broken up between different registers in such a way that we shall not receive the impression of layers of linear motion,, for in such a case we should be concerned with a conventional polyphonic treatment; 239 —• deliberately non-complementary dispersal of material in six parts; 240 —• the optimum crossing of voices gives rise to a textural fabric composed of a mass of notes scattered in musical space and irreducible to the initial point of departure; 241 — the previous technique of break-up of motion raised to a still higher intensity; 242 — dispersal of single notes through various parts, owing to which the originally continuous line of linear motion must be "gathered together" in the same way as it had been dispersed by the composer; 243 — scattering of material throughout the various registers, intentionally obscure as regards the number and nature of parts; to all appearances this is one part passed automatically to different registers, regardless of consequences, but in fact it is a product of linear motion arising from the absolute equivalence of all the register ranges; 244 — four sections of this example show four different textural solutions and, consequently, the linear motion here can be reconstructed only analytically (nevertheless,, it is true that originally it could form the basis for such a process, even preserving the immanent character of its note successions); finally, 245 — shifting of motion to the background accompanied by the simultaneous exposition of its qualities (quarter-tones).
44 Compositional reading of linear motion pitch collections
Example 246 presents a number of readings of a selected four-note horizontal arrangement (also in its vertical aspect). In the "case of a larger number of notes the readings are no longer restricted to a small quantity of variants (for this reason it is convenient to solve this problem on models limited in components). The graph indicates a great potential of changes that can be made on identical material; in this situation linear motion is no longer a unequivocal structure but a stock of sounds rather than a horizontal ordering.
The tendency not to oppose the vertical and horizontal aspects becomes very conspicuous in new music as does the tendency to treat orderings only as results of a definite state of affairs, as the results of composing, rather than as consciously horizontal pitch handling. Example 247 points to the consequences of such an approach to motion.
Basing yourself on Example 246, examine the compositional potentials and consequences of the arbitrary reading of the vertical and horizontal combinations in Example 247.
Compose a piece of music based on six selected fournote motives, applying all, l i t e r a l l y a l l , modes of their reading. The piece should be written for such an ensemble that it makes it possible aurally to trace the composing work in this respect very exactly.
Write six short passages of music formed similarly to the music in Example 237; take care that the change in motion, however narrow its range, be clearly heard.
45 The dependence of the structure of chords upon the contents of vertical arrangements of linear motion
Compose a fairly long piece based on the foregoing principle. Different kinds of changes in linear motion are to be included. The performance of the composition should take about 8 minutes; chamber instrumentation (at least 5 parts).
Example 248 shows how we should understand the analysis of chords today. The point of departure is not 31
the sum of notes making up the chord but the structural sum, that is the aggregate of all the intervallic components (intervals are designated by the number of semi-tones, from 1 to 6, the inversions of intervals may be marked with dots placed by the figures; see also Chapter 49, "Intervallic Notation".
In new music the simultaneities, too, are only a result of the vertical combination of sounds, and this is why even the closest analysis of vertical groupings cannot explain anything; at any rate, it is not on this that the observation of composing methods should be based. Nevertheless, it is worthwhile investigating the type of chordal specificity we are dealing with and what sorts of "harmonies" arise from the combination of sounds. In Examples 249 and 250 we are concerned with accidental harmony; in Example 249 single parts are seemingly independent and as such cannot constitute a complex of parts that add up to form a harmonic common denominator; this is not the case, however, for the ultrachromaticizm applied here creates, in fact, a sort of harmonic climate which always be prominent. In Example 250 we can observe the neutralization of harmonies, if not in any other way, then by the use of different kinds of chords; and the harmonic climate, which after all can still be grasped, arises from a textural model rather than from the orderings of notes, in spite of the fact that in this respect a good deal of "accordance" might also be found.
Write three series (each of 24 elements) of and six-note chords and compare them other, giving attention to their structural how chords are related to each other symmetrically, read in inversion, e t c
four-, with sums. when
fiveeach Note built
46
appearance; it is worthwhile noting the transcendent presence of traditional harmonic thinking — the role of leading tones); Example 252 illustrates the tendency towards detachment from vertical relationships by the exposure of a) parallel intervals and b) atonal, polytonal and deliberately dissonant groups; Example 253 shows chords in autonomous action (note the specificity of the choice of intervals that make up the chords); Examples 254 and 255 — chords as a co-factor that enhances movement; Example 256 — chords as the "accompaniment" for a vocal part; Example 257 — handling of co-situational changes in chordal vertical structures.
In new music the chord no longer fulfils a formative or structural function. It is however sometimes used with specificity, and even (Example 257) creates situations which would not come about without its contribution. If we assume that chords may be an accidental concurrence of parts, we shall obtain an effect which will go far beyond our present experience in this respect. The models in Example 258 illustrate the specific "behaviour" of the sound material at the moment when the technique of free combination and crossing of parts has been introduced. In the accidental vertical structures we attain chordal consequences of totally different qualities. Evidence of this is provided in the structural sums underneath each model.
Following the pattern of composing methods presented in the above examples, construct three different models of a clearly harmonic nature but focused on the problems of a) the organization of movement and b) new texture.
Basing yourself on these models, compose three fairly long passages of music for a chamber orchestra.
47
Compositional application of chords
Microstructural organization
Examples 251—257 demonstrate the new functions of chords. Example 251 shows that the interval chosen "by the composer constitutes the centre of linear cosituations (the example is supplied with a diagram of notes employed and the range of the frequency of
A set of three notes, which in serial music constitutes a section of the series, in being closed from the point 32
of view of linear motion, can be worked with in such a way that we obtain results that merit more extensive discussion. Limitation to small three-note groups neutralizes, as it were, the importance of the factor of linear motion. To ascertain this it is enough to scrutinize the models of composing in music based on the principle of microstructural organization. Example 259a illustrates the dispersal of three-note material among different instruments. Here the composer was already quite unconcerned as to whether or not a given microstructure was the equivalent of a passage, motive, theme, chord, or combination of chords; Examples 259b and c indicate the possibility of development of this procedure. Examples 260 and 261 show the application of the microstructural technique in closed continuous structures; from the view-point of the organization of pitch material this is a great impoverishment and because of this different methods of internal variation of material have been adopted in the examples presented. Examples 262 and 263 provide some analytical material for the technique of working with four-note groups (Example 263 — in a freer form).
As the possibilities of handling small note groups become exhausted (only Web'ern's works gainsay this, but Webern uses the material of linear motion mechanically and, consequently, lays a far greater stress on the formal aspect of compositions), there arises the problem -of the non-schematic method in the organization of musical material. It seems that a law of dependence might be applied here: the more music is confined to microstructural groups, the more attention should be paid to the textural changes made on the material. The mere transformation of microstructural material by transposition, inversion, retrograde motion and retrograde inversion does not suffice. To avoid the inevitable monotony in this process, the methods of organization of sound material must be complemented with other elements (rhythm, texture, variation in instrumental timbres, etc.).
methods for the expansion of the factor of change beyond the sphere of linear motion. Instrumentation: 1. two pianos, 2. string trio, 3. wind quartet and 4. chamber instrumentation: 6—13 different instruments.
48 Intervals and their role in contemporary music
In new music intervals increasingly exceed the material of pitches in importance; there even exists a possibility of restricting compositional work to the disposition of intervals (see Chapters 57 and 58). Intervals contain much more information than pitch material. This may easily be shown if only by transposing music (the essence remains unchanged and therefore is not determined by the material). Intervals, selected or preferred, may also determine the harmonic climate of music (Examples 265—267). In Example 265 the music is based on two conceptions employed simultaneously, one conception, linear, and the other, harmonic; to what extent this duality is essential for the music is shown by the differences between the dynamic planes of the composition. Example 266 illustrates a more highly developed conception of the vertical and horizontal shaping of material. In this example the intervals play a much greater role than they do in the previous example for several reasons: first, the interval resources are brought to the forefront as an expressive (we may here use this word) stratum; secondly, all the chords,, mostly two-note ones genetically, also contain that intervallic quality of motion (their range is enormous from minor seconds up to the intervals exceeding five octaves!); thirdly, either of these concepts gives a very different textural effect owing to the richness of the intervals used. In Example 267 the intervals of motion are still further enhanced by both complementary and antinomic intervals with regard to dynamics and the very complex time values.
Scrutinize the composing methods in Example 264. Find how many different factors are involved in the formation of the musical process. Analyse the effect of intervals on the specific nature of the sound language in Examples 265—267. Find which elements are related to intervallic change and which are independent of it.
Taking your own microstructural models as a poiiit of departure, compose four short pieces, using different 33
Compose a fairly long piece for piano —• lasting about four and a half minutes — and carry into effect the possibility of compositional work limited to the disposition of intervals. On the basis of this piece compose another version, in which — on the principle of association but also that of antinomy —• other elements complete the over-all picture.
49 q Intervallic notation
All intervals are comprised in the semi-octave. The smallest interval is the semitone, the largest one the tritone; the intervals larger than the tritone are designated as inversions by adding a dot to the figure and the octave extensions of intervals (compound intervals) are marked with a stroke placed by the figure (Example 268).
This notation contains a number of structural laws essential for the shaping of music and independent of past habits in the field of linear motion. The restriction to the tritone and the treatment of all intervals exceeding this compass as inversions and octave extensions make it possible for us to have an all-embracing look at the musical material. In practice, all unfoldings of intervals, from minor second to tritone, are only interpretations of a concrete intervallic event.
second — to 6 — tritone) and changes in their direction are left to be notated (the direction of the first interval is marked with an arrow, changes in the direction with a stroke between the symbols of intervals; notation in Example 272).
This point requires close explanation: in the digital notation under discussion a very significant relationship occurs between the magnitude of an interval and its direction. The ascending major seventh ( | 1 ' , e.g., c-b) corresponds as regards sound to the descending minor second ( I 1, c-B), and the ascending minor second ( | 1, c-d \>) is something essentially different from the descending minor second (which is shown, if by nothing else, by the change in the name of the note: c-db and c-B). This is why, writing down, for example, a multi-intervallic series within the narrowest possible over-all compass (e.g., in an octave), we must mark the intervallic ambivalence in the notation. Taking down intervals together with changes in their direction, we record the essential, freely transposable, motion contents of ah ordered set of sounds without resorting to the use of the names of notes and, thus, in a state of some abstraction, indispensable in those instances in which we do not want to make a fetish of the pitch material.
e Notate the linear motion succession in Example 273 in note notation and check the result by comparing it with the solution given below the exercise. Notate the linear motion succession in Examples 274—276 in intervallic notation.
51
Adopting the method of notating intervals used in Example 268, write down the arrangement of material in Examples 269—271 in intervallic notation.
Selection of intervals and its consequences
50 The selection of intervals (the predominance of some intervals over others or, in extreme cases, the restriction of the process of linear motion to a few intervals) creates a sort of stable harmonic climate, which the composer may find desirable. Example 277 illustrates the method of selection of intervals and its sound and chordal consequences.
Intervallic analysis of linear motion
Sound material may be treated as a solely intervallic succession, in which only intervals (from 1 — minor 34
[n this connection a number of questions arise and call for explanation. In the first place, is the selection of intervals a necessity? It obviously is not. The deliberate restriction of the process of linear motion to selected intervals is not at all in conflict with changes in pitch material. There are intervallic groups which in a simple way make it possible to arrange innumerable series of constantly changing pitches (only some intervals, e.g., 2, 4 and 6, limit mechanically the possibility of handling all notes). Thus, the restriction to several intervals does not cause any essential restraints; instead it provides an opportunity for the disciplined formation of material in one respect at least, namely, that of intervals, on account of which the composition, subjected to highly diverse manipulations, still remains integrated in so far as intervallic elements are concerned.
Examine the vertical and horizontal consequences of the restriction of linear motion to the following intervals: a) b) c) d) e) f)
1, 5; 1, 4; 1„ 4, 5; 1, 6; 1, 4, 6; 1, 5, 6.
the notes). The material enclosed within the interval of a major third (in oiir case all the notes between d f smd g) constitutes a constant value irrespective of the order of notes. The structural consequence of change in the order of intervals in such a closed group is the various intervallic contents of the five-note models (e.g., 0220 indicates the absence of minor seconds and major thirds but the presence of 2 major seconds and2 minor thirds, and 4000 indicates the presence of 4 minor seconds only, etc.). Their analysis, in turn, allows the systematization of different models into groups with the same intervallic contents (Dt, D2, D20; model A appears only at the beginning — Aj — and at the end — A2 — of the list). The results of limitation of structures to five-note groups depend only on the method of compositional procedure.
The five-note model may serve as an experimental set; the effects on its material of the internal changes in the note arrangement are fairly obvious. In compositional practice there is no need to confine material to such a narrow range, but groups of this sort may be used and, at any rate, it is worthwhile using them, superimposing them one upon another in an aggregate of groups.
Examine the effects of the limitation of note groups to five notes. Find whether these models can be transposed to other elements.
Compose three short piano pieces based on a particular selection of intervals (vertical consequences of the selection may go beyond the selected scheme of intervals),
53 Work on six-note models enclosed within the fourth
52 The catalogue in Example 279 presents all the possible variants of the initial chromatic model within the fourth. The method of listing this type of model is already known from the previous section. Here — to avoid following the most conventional scheme — the reverse instrumentation has been used. In the catalogue of the 720 variants of the full chromatic universe the following characteristics are also given for each model: the direction of motion and size of successive intervals, the number of changes in the direction of
q Five-note models enclosed within the major third
Five neighbouring chromatic notes can be arranged in different variants (Example 278). A hundred and twenty variants of the five-note model are obtained by assigning a digit to each note and changing the order of the digits successively (and thus also the order of 35
motion, the intervallic contents, and the span between the first and the sixth note.
55 Harmonic models
Not all the variants of the model in Example 279 can be fully applied in composition; together, however, they . make up a wealth of comparative material, easy to perceive because of its limitation to a half of the chromatic scale. Example 280 demonstrates limitation to variants of a series with expanding intervals.
Example 283 illustrates the quality of harmonic models in the trope arrangement. We divide the trope circle into 12 semitone sections in the chromatic succession. By marking points for each sound of the harmonic model in the trope circle and connecting them with each other, we form a picture of the arrangement of sounds, which we may naturally transpose, reverse, etc. (a), while the harmonic model remains the same (b). Only a pattern for the shaping of harmonic models and a method (the programmed one) for examining all possibilities with the help of the ordinal system (c), which we have already got to know very well, are given in Example 283, which is supplemented with several detailed solutions (d: programme of the first three positions).
Compose a fairly long piece for piano on the basis of the idea given in Example 280 so as to exhaust the variants of the adopted model.
54 Contents analysis of the variants of the chromatic sixnote universe
Develop carefully the items of Example 283. Moreover, take an eight-note circle and then a nine-note circle as your points of departure and examine, respectively, five-note and four-note models on them.
The list in Example 279 permits the preparation of another catalogue,-281, which is based on the intervallic contents of six-note models. It is due to the very nature of the system that each ordering has a corresponding inverted variant, as exemplified by motives 347 and 374, of which the latter is the exact inversion of the former, and this is, in addition, connected with the fact that it can be read as the retrograde of the former. The law of correspondence of motives operates here to its full extent. Some of the motives are quite uninteresting, e.g., the motive 50000 (1 and 720), whereas some others are distinguished by peculiar features, e.g., the motive 11111 (all-interval series), very abundantly represented, or the motive 00320 (347 and 374), already mentioned above, based exclusively on thirds. By grouping the motives in categories we obtain a more complete picture of the differences separating the variants of the same initial model.
Compose 3 short pieces built on the models of eightand nine-note circles. Depart gradually from the models adopted; the first piece may be approached still in a very "harmonic" way, the last one should bear mere traces of the initial pre-formative arrangement of pitches.
56 Intervallic studies
Examples 284—289 present different ways of working with intervals and different results arising from operations with intervals. In Example 284 we are concerned with matter that seems to be simple only on the surface; in fact the intervals between the notes, enriched with interchangeable quarter-tones, cannot
Choose a few other five- and six-note models and examine them (limiting yourself to samples only) for the consequences — with which you recently became acquainted — arising from the ordered changing of places within a given set (Example 282). 36
be reduced to a simple structural sum. This is certainly an intervallic structure, though what is important in it is not intervals but the timbre of the internal sound relations. In Example 285 the individual parts are, to be sure, exceptionally transparent in their intervallic consistency, but the progress of the whole cannot be reduced to the material from which it has been formed (this impression is deepened still more by polymetre, that is, the realization of the whole process in three different metres). In Example 286 three lines are based on their own intervallic schemes. Thanks to the common agogic features that have been given to the process and also owing to the crossing of the parts, the intervallic substance loses its identity. Example 287 presents a musical whole composed out of motives containing all possible intervals. A tendency to fill up the musical space with a full supply of sounds is shown in Example 289, in which a complex of 24 different sounds is slowly formed from intervallic motives of a similar order. Finally, Example 288 illustrates the possibility of the variational construction of a musical text by lowering or raising its particles.
Example 290b provides comments upon the notation: element k (sound cell) consists of two notes, the arrow indicates the direction of the interval, and the figures designate the species of interval, the same figure standing for minor second and minor ninth, for minor third and minor twelfth, etc. Example 290c illustrates all the possibilities that emerge if we assume the sound a as the point of departure (there are therefore twelve times as many possibilities altogether!) The sounds given in frames are d i v e r s e and as such fulfil the very essential condition of change material; Example 290d presents a list of these variable sound arrangements.
Compose similar studies, taking your own ideas of infinite composition as the point of departure.
58 q Study in diagram — the realization
Carry out a close analysis of the foregoing examples and add some new ones of your own, in which different aspects are developed. Scrutinize the mode of intervallic lay-out in Example 288 and write a fairly long passage based on similar principles (it is necessary to retain the lay-out of some elements other than intervals).
57 q Study in
ram — the idea
The idea of study in diagram is based on the infinity of possible versions of the composition. Example 290 illustrates 'this idea and at the same time comments upon it by presenting a) notation of music, b) interpretative comment, c) model of procedure — study of possibilities and d) selection of variable material (non-repetition of notes being pre-established). Several important explanations: the notation of the composition under analysis (290a) consists of two layers, the musical text being given in the upper layer and the number of possibilities for the given group in the lower one.
The problems in realization of the study in diagram are demonstrated in Examples 291a, b, c, whereas Examples 292a, b concern a separate problem, that of the selection of possibilities from the view-point of broader change in sound material.
Analyse Examples 291—292, paying special attention to the problems of change in the material. Attempt your own realizations. Some examples can be solved in diametrically different ways and then the wealth of elements brought about by the adoption of the sole principle of studies in diagram will become evident. Studies in diagram carry us from compositional relativity to the sphere of concrete tasks. In our case these are interesting inasmuch as they have been formed over non-existent material. It becomes especially clear in realization that compositional ideas can be abstracted from the material of pitch level, some regularities being preserved for the sake of music. For instance in our example the existence of a definite harmonic climate is secured by the mere choice of the compositional idea, though in realization we can use our discretion as regards choice of intervals. We can read-
ily move from intervallic ideas to related ideas concerning other aspects of music.
Compose a fairly long piece in the form of a diagram, choosing different sound ideas for it. Keep in mind a concrete instrument, although the composition may be presented in a form dissociated from conventional textural thinking.
Write a short piece based on the idea of codes, applying methods of approximate treatment of sound material other than those known hitherto (this is to be a piece for a small chamber ensemble consisting of different instruments).
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59 q
q Approximate linear motion
Codes
Codes — an expanded version of study in diagram —• embrace an infinitude in which details are delineated. However, many elements of this infinitude are limited to such an extent a priori that, having no information about the sounds, we can gain information about the kind ("style") of music. Various versions of this music will differ considerably only in certain respects, remaining similar in others. Examples 293—294 illustrate the problems connected with particular dispositions. Such dispositions of music whereby we write codes instead of concrete solutions are particularly instructive in so far as the observation of the "behaviour" of sound material in different situations is concerned. Determining the limits within which the music is contained .— for the codes clearly limit music in some respects — the composer shifts the centre of gravity from conventional "concrete" activity to open activity, the essential feature of which is approximateness. These particular compositional experiences incline us towards a different understanding of music from that prevailing till now. If we take for granted that one element may be secondary and another one primary, we may assume that the form, hitherto an accidental result, may be the primary element and the matter that "fills it up" a secondary element, in our case written down by means of open codes. '
Using your own method, analyse Examples 293—294, each one from a different (selected) point of view. Scrutinize a small compositional unit rather than the realization of a large whole. One of the examples may also be examined for reversibility (interchangeability) of parameters.
In the preceding chapters we have been concerned with precise definition,, if not of pitches, at least of intervallic material. There is however the possibility of a still greater freedom in the area of pitch material. It may consist in approximateness. Examples 295—308 illustrate these problems well enough: Examples 295 and 296 show to what extent ever changing material, through this very fact, loses its identity and becomes neutral; Examples 297—298 display a still greater anonymity of material in spite of the role which the composers attribute to its variability; Examples 299 and 300 demonstrate translation of this state of affairs into the language of percussion and quasi-percussive material; Example 301 proves the possibility of the treatment of variable (neutral) material as an initial base in the handling of colour (Examples 302—304 also belong here); examples of approximation (and the sense of applying it) in vocal music: 305 and 306, in instrumental music: 307 and 308.
Approximate linear motion employs approximate material. Such approximate material makes an impression identical with or similar to that made by material written down precisely. Approximate material does not mean complete freedom in performance at all: the fact that pitches and intervals are not determined is counterbalanced by the determination in other aspects, e.g., that of form.
Analyse Examples 295—308 concentrating especially on problems which contain information about the possibility of avoiding making the pitch material explicit. 38
Compose a fairly long piece of chamber music, using only approximate linear motion (the composition should be supplied with extensive comments, explaining the particular methods of approximate notation).
Basing yourself on the instrumentation of Example 318, confront in a vertical arrangement those instrumental timbres that differ most from each other.
Draw up 10 different orchestral and chamber mental ensembles, and for each of them write plete musical passage, taking more than ten in performance. The should be in the nature positions of materials and timbres.
Ill 61
instrua comseconds of ex-
A new way of treating the orchestra
62 Two tendencies can be distinguished in new music, one towards the chamber form of orchestra and the other towards monumentalization. The classic instrumentation in the orchestra is practically unacceptable today and its place is taken by instrumentations independent of symphonic conventions, e.g., an ensemble of percussion instruments (see Example 309 — instrumentation, notation, and seating arrangement). The development of the sound language, consisting in the gradual atomization of material, contributed to basic changes in the treatment of the orchestral ensemble. Particular lines of the ensemble are treated in a soloistic manner and even if they all form a homogeneous whole, the full independence -of parts is maintained (Examples 310—313). Webern's compositions are typical models of the new soloistic treatment of the orchestra (Example 314)" The examples of pointillistic music (315 and 316) show other possibilities in the treatment of an orchestra with a solo-type instrumentation.
Selection and particularization of tone colour
The general possibilities of combination of tone colours and the confrontation of instrumental and vocal parts enable us to produce a particularization of timbre. This is accomplished by a peculiar kind of selection, consisting in the narrowing of the technical problems to a chosen phenomenon so that the distinct nature of material can be more fully, brought into relief. The distinct nature is not incidental but absolutely specific causing us to experience the work as a clear solution of a particular technical problem. The sense of the solution of the problem is created thanks to the exposure of the problem at the surface, foreground level of the score. It should be mentioned that such a specified timbre may take up a very short passage in the whole composition. Here are examples: 319 — the first bars of a well-developed composition, full of different solutions to the problems of texture and timbre, despite a total sameness of instrumentation; the tone colours are handled in vertical relation, the parts being simultaneously reduced from five to three (the sounding of the flute and clarinet together indicates the neutral quality of the beginning of music); 320 — the reduction of material to the smallest number of parts possible (string trio including two violins, with material of minor importance: tied notes, repeated motives, etc.); 321 — the reduction of musical substance to tied notes, the "neutral" behaviour of material in a four-second passage, etc. Here the reduction itself contributes to the specificity of both material and process,, but there
The atomization of sound material in the new orchestra aims at splitting the uniformity of music. The atomization of the individual particles of orchestral vertical structure dees not, however, negate the possibility of re-arranging them into a uniform whole. There is evidence for this in most contemporary avant-garde compositions. Example 317 illustrates the chamber treatment (since it is generally in four parts) of a large 40-instrument orchestral ensemble, resulting in continual changes in instrumental timbre; Example 318 shows a similar situation (in both cases we are concerned with the continual though unmethodical changes in the play of timbral intervals). 39
are cases of a still more careful selection (composition); Example 322 consists of two vertical structures which are very carefully composed internally, owing to which they form a fusion of parts unrepeated in this composition: motives of different instruments in the first vertical combination and dynamic projection of chordal particles in the second one. Example 323 illustrates the selection of timbre and its limitation to metal percussion instruments; the distinct nature of the music thus reduced is enhanced by far-reaching dynamic differentiations. In Example 324 the sound reduction is also audible in the restriction of the ambitus of the parts, thanks to which a specific emotional climate may arise from music "impoverished" in this manner. In order to create such specific sound climates composers use especially sophisticated combinations: the harpsichord against the background of a rich percussion instrumentation (325), the deliberate reduction of material to a minimum (326). It is obvious that the specifity of music can be more easily attained by the nonstereotyped treatment of instruments: instead of using a conventional tone colour, the composer applies a number of means of execution which shift the centre of gravity from the colour of sounds to their particularity. In Example 327 this will involve the utilization of a rich repertory of performing techniques on the alto saxophone. The sound specificity can however be attained more easily, if variation has been applied within homogeneity (Example 328).
63 Preparation of instruments
The timbre of some but not very many instruments, i.e. that of piano, strings and some percussion instruments, can be modified by preparation. Thanks to preparation we not only gain new timbres for these instruments, which finally do not suffice for long, but also move to the field of considerably expanded material. Consequently, the preparation of instruments is undertaken as an addition to their normal treatment: not to renew timbres but to acquire a wider range of material and intervals (a prepared sound beside an unprepared one forms a specific sort of interval; cf. Examples 331 and 332). Elementary and more ingenious preparations of instruments are presented in Examples 333 (piano) and 334 (string instruments).
Here we are concerned with a fundamental problem: preparation does not aim at the replacement of the original timbre of an instrument with a new timbre (in itself much worse, which is only natural, and less effective, though different), but to attain a new aural effect. Such an effect is always related somehow to the unprepared original.
d The question that arises here is that of the compositional utilization of textural ideas, which, so to say, automatically widen the qualities, of the new instrumental timbre. It suffices to combine even simple sets of sounds with each other in a specific medley to obtain an aural effect remote from the usual results arising from the very elements from which the whole has been composed (Examples 329—330).
Make up a short list of piano preparations, giving special attention to the timbre of prepared sounds.
Carefully analyse the effects obtained by the selection and particularization of instrumental colours, using the material of Example 330 for this purpose.
64
Basing yourself on the above list of means of preparation, compose a fairly long piece for piano, compositionally justifying the application of instrumental preparation.
Preparation in vocal and instrumental ensembles Compose a fairly long piece for 24 different instruments, concentrating on the selection and particularization of timbre in the ensemble.
In addition to the possibility of preparation of a single sound source there is also a possibility of preparation — 40
in various degrees — in larger ensembles. It may consist of a) homogeneous preparation, aiming at the obtaining of a new but uniform altered sound or b) polygenous preparation, in which each part is prepared in a different way in order that as wide a range different sound varieties as possible of obtained. The first steps towards preparation may consist in a new treatment of the texture itself (Example 335 shows vocal music prepared in such an elementary manner). Preparation proper requires a change in the existing performing techniques of particular parts (examples: vocal music — 336, instrumental music — 337).
Not all forms of special treatment of an instrument can be termed preparation. There are many examples of apparent preparation. In these cases the composers attempt to widen the range of timbre (it is known from the preceding section that such an opposition of the prepared colour to the original is effective for this very reason that we have both the original sound and its transformation; this however does not mean that this method is superior to the method of total preparation, which locates the composer in a completely new situation — and such location in a completely new situation matters a great deal in today's music).
of one note, one and the same pitch, is possible only when change (that is, such transposition) is shifted to other elements. One can, however, compose using only change in pitch. In this case, change of this sort must be applied intensively. We infer that in composing we cannot base ourselves merely on a succession of changing pitches since the result, though compositionally rich, would then be too one-sided. We know that if a series, as horizontal material, made sense, it did so only as an arrangement that releases the composer from the necessity of ordering material in this respect, thus making him use compositional procedures involving other elements (Examples 338 and 339 illustrate such multiparametric methods for the acquisition of change: 338 — by contrasting individual particles of the pitch succession and 339 — by freedom in interpretation within the limits of the given notation). Thus changing pitch is a result not only of transposing procedures but also of compositional co-situations. These phenomena are shown in Examples 340—341.
Analyse closely the examples given in this section from the view-point of the compositional extent of preparation.
Consequently, changing pitch is not an element that can be isolated. Appearing as a function of multiparametric variation of a particular sort, it contains not only its own parameters, i.e., the characteristics that appertain to it, but also indirect parameters, i.e., those resulting from its being placed in a concrete compositional situation. In this case, therefore, to compose means to "renew" the pitch by its permanently changing position in relation to other pitches and by continual changes in its function in relation to other pitches.
Write two short pieces employing the techniques of preparation, one for a vocal ensemble and another for an instrumental ensemble (up to 12 persons).
Construct two quite long examples of changing pitches, which owing to their multiple change will have the significance of changing textural components.
65 Changing pitch
Pitch material may be treated as material resulting from the transposition of a s i n g l e note and therefore it can be determined in relation to a constant point, in relation to which it is a transposed note. The treatment
On the basis of these models compose two fairly long pieces: a) for a chamber ensemble (polygenous, with instrumentation according to the type: flute, trumpet, piano, vibraphone, voice and viola) and b) for a large chamber ensemble (soloistic chamber orchestra, different instruments). Neither of these pieces should be congruent with the examples cited in this section, but they should spring, as it were, automatically from the assumed multiparametric variation of the models themselves.
41
66
apparent) and in the optimum case the method of apparent transformation and that of genuine transformation should concur, although we are no longer concerned with the separate audibility of each of these transformations.
The transformation of a pitch may foe effected in different ways. It is far easier to create the impression of a transformation of a sound mass than of a single note (Example 342: here is transformed conventional material by an uncomplicated operation of changing the material by means of a factor as simple as articulation). Special sorts of transformations — and it is such sorts that we are concerned with — are based on acoustic changes (343—344). Example 345 presents a true transformation of a note based on the intentionally asynchronic additional colouring of each string instrument entry by piano (the aural result suggests a new and unknown instrument) articulation.
67
The transformed note
If changing pitch is conditioned by the co-situation, that is, if it could be treated as variable just on account of the situation in which it occurred, the transformed note must,, as it were, attract attention to itself in itself (Examples 346 and 347). The transformed note should, consequently, speak for itself, but it can also be introduced as a co-situational component (in this case the text must be suitably arranged; Examples 348 and 349). Such instances belong to the category of apparent changes (a typical case, Example 349: here we receive the impression of the transformation of a whole mass of sounds, while the single note itself appears in a relatively natural form).
Closely analyse the methods of transformation of a note in simple systems (Example 350) and in cumulative ones (Example 351).
Write two short compositions for a) a small chamber ensemble without doubling of instruments and b) the most homogeneous possible orchestra of soloists (e.g., string instruments). In the first of them you should handle genuine note transformations, which must also be perceived as genuine transformations. In the second case the transformations may be apparent (or partially
The gliding note
It has been said in one of the preceding sections that a single note may be treated not only as a particle of a system (formerly — scale, in new music — series), but also as a note rising through transposition from another single note, to which it always remains related in some ways. These relations are intervals. Consequently, if a note can be passed over different intervals, we may just as well pass a number of notes over one interval. This procedure — expressed in compositional language — would however be intolerable, unacceptable. Therefore, we say that a note can move from one pitch level to another, passing through the intermediate notes without stopping at them (glissando). Such a note will be called a gliding note. Example 352 gives the simplest possible models of gliding notes, Examples 353—358 — their compositional application.
The question arises here of duality in the practical application of the above phenomenon in composition, for the gliding note may be treated as a complement of or as an antidote to a note treated conventionally (Example 354), but we may also regard it as an autonomous element, giving it some structural, formal characteristics (358) or, as if on the contrary, textural, motivic ones (253, 355—357). Some examples (e.g., 352) illustrate yet another problem: each musical element, determined by its angle of inclination, may be regarded as a separate musical component and, what is more (Example 357), we can deal with the full interrelation between intervallic and time distances. This last case however provides an instance of too mechanical a treatment of the gliding note. Hence, the methods of its treatment that go beyond the narrow circle of interval-time determinants are, of greater importance in the analysis of the phenomenon under discussion. 42
Make a set of models based on the idea of gliding notes, limited in their fundamental principles but as complete as possible. Scrutinize the examples that are relevant to the set obtained in this way.
Compose three short pieces for various instrumental ensembles employing gliding notes, using a different method of organization of sound material in each case. The first composition should be limited to simple instrumental arrangements (ensemble of the type: 4 trombones and 4 cellos) and contain elementary instances of gliding notes, the second composition should express the structural and textural ideas about the handling of gliding notes (they may be entrusted to a large group of instruments treated in a soloistic manner able to produce glidirfg notes either directly, as in the case of the above-mentioned instruments, or indirectly, e.g., using chromaticism —• in the case of instruments that do not produce glissandi) and, finally, the third piece may reach for spatial polychoral dispositions (a fairly large instrumental ensemble treated in groups).
to prove something by confining himself to such composition, like one who composes only string trios, but we do not know exactly what). Nevertheless we ascribe great weight to this problem for various reasons. Firstly, composition with one note demands an intensification of the creative process as regards non-pitch elements, and this already means a great deal. Secondly, this method permits the detection of equivalent limitations which applied under other circumstances might be of great importance in composition. Thirdly, such a limitation allows us to understand individually how the disposition of pitch material should be comprehended t o d a y .
Write six studies in such a way that their sound material is restricted to one note, each time intensifying change in other parameters or pairs of parameters.
Choosing a unison string double-stop as the point of departure, compose a fairly long musical passage on it, reaching for the non-pitch parameters that do not deform the essence of u n i s o n a n c e .
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68 Composition with one note
Timbral intervals
It is possible to limit the pitch material to a single note. Then, the composer's attention is, naturally, concentrated on other parameters and the restriction to one simple note is no greater a restriction for him than that with which he is well acquainted, i.e. a selected musical idiom or type of instrumentation. Composition with one note demands not only a shift of attention to other parameters but also skill in emphasizing the s e n s e of such a limitation (Examples 359 and 360).
Both prepared phenomena, as well as usages of changing pitch note, the transformed note, the gliding note or, even, the simple note confined to one indication, are, above all, phenomena of colour. However, they are methods of acquisition of colours in an indirect way. The handling of timbre directly is not possible until timbral intervals have been introduced in pairs (Example 361). Timbral intervals can be based on unisons or various pitch intervals.
This compositional problem should most certainly be regarded rather as a means of obtaining information concerning the behaviour of sound material than as a substitute for other methods of composing (it is hard to imagine a composer writing a piece of music predetermined exclusively in such a way; he might intend
There are a great many developments possible in the handling of a timbral interval.- Composers seem to carelessly neglect the consequences of the use of timbral intervals. The consequences are various and range from the renewal of the attitude held so far towards even such conventional techniques as instru43
deformation of music as understood in this sense (it should be added here that the deformation is the more easily achieved the more instrumental parts and colours are applied). The technique of deformation is excellently expanded by the modes of treatment of parts which deform the scale material: by "putting the sound picture out of tune" through false intonations as in Example 365 and by bringing the quarter-tone technique into play.
mentation, right up to the possibility of composing exclusively with instrumental colour — matters that in other respects are very much the concern of composers.
e Make up two different models for disposition of timbral intervals, using the largest possible number of different timbres (different voices in a vocal ensemble and different instruments in an instrumental one).
Sound deformations aim not only at the widening of the range of mean of sound and timbre but also at the expansion of the compositional ideas themselves. The more they suggest the necessity for the composer and performers to go beyond the standards established so far, the more they seem to be able to contribute to the development of new types of compositional thinking.
Compose a fairly long piece based on the technique of timbral intervals, assuming that in a big ensemble of instruments treated in a soloistic manner there is a definite number of different vertical combinations; both the given timbral interval and its inversion come into account here (the flute-bassoon combination is, for instance, something different from that of bassoon-flute, etc.).
Write three small compositions for different ensembles and use a different method of deformation in each.
70
71
Deformations Denaturalization of sound
Deformations are applied in order to achieve greater individuality in sound material. Roughly speaking, they derive from the new role of instruments and voices. This is connected with the fact that the performing apparatus has not undergone any changes or further development for many years and that composers are not satisfied with persisting modes of treatment of this apparatus in that they do not meet the requirements of all new music. The tendency towards deformation of music is' very old and dates from the time when composers became aware that invariable musical elements — cannot exist. Examples 362—363 illustrate the simplest instances of deformation, based only on a change in the function of instrumental parts. Now the instruments do not compose a unity according to an established initial form,, a unity which can be reduced to a piano score. These instruments, have as their goal the annihilation of what could have been recognized as being in common between them, and thus the sound of the whole has been deformed into a new structure. Under optimum conditions this cannot be reduced to the elements that made up the original composition. Examples 364—369 illustrate a further stage of the
Using deformation the composer creates new sound qualities. In new music, however, there exist ways of deploying timbres that result from the application of special transformation procedures. In the example of electronic music (370) and in the example of instrumental music which has been influenced by electronic systems (371), we are able to observe a range of denaturalizing techniques, applied in a composition not for themselves in themselves, but for a broadening of the sound-language. As may be seen, they can be perceived both "literally" and in terms of precisely measured parameters.
It is possible to discuss the term "denaturalization" itself. In essence it is not so much a question of describing new sound qualities as the emphasizing of a divergence from conventions existing to the present time (cf., the polemicizing surrounding the term "atonality"). 44
Analyse precisely the consequences arising from the application of the notion of denaturalization of sounds (Examples 370—371).
IV 72 q Series — problem of variability
Music based on series incessantly excites controversies. The main objection raised to the series as a musical model is that it lays claim to the inclusion of the whole set of linear motional issues, whereas, in fact, it introduces but a mode of ordering the material. The question arises whether ordering is necessary for music. Observations of pre-serial music show that the arrangement of material serves only as an initial model, on which new expanded models were repeatedly built as music evolved. The series is a very artificial organization, and for this reason in composing it one should have regard to its possessing the greatest possible susceptibility to change, change which is so necessary in music. The more "definite" a series is the smaller the transformations it may undergo in composition. And the more self-contained it is (this often impresses composers), the more limited are the possibilities of its compositional utilization (which quite evidently hinders free composition in practice). The fact is that the application of series that knit together too "perfectly" makes the composer shift the centre of gravity from pitch material to other elements (typical example: Webern's Opus 30). Example 381 illustrates the use of developments and repetitions, open series,, which provide possibilities of optional
In order to secure constant change in music the serial arrangement of material is applied. However, the very repetition of this arrangement raises doubt as to whether this is the right solution of the problem of change. The example of an analysis of the rhythmic element reduced to a minimum showed that the problem of variation does not at all boil down to the very arrangement of this element, to the very mode of ordering, but is based on the incessant need for change, the composer's tendency to acquire inner variability. The variability of material is also confined to the problem of this very inner variability, which can be attained by the parallel use of a certain number of methods concerning d i f f e r e n t aspects of change. .Using your own models, write 120 different series, of However let us approach the series itself first. Example which 30 are to be "closed", 30 "definite" in various 372 illustrates the possibilities of composing twelve- ways, and 60 optional open ones. Examine the horizontone series using the full chromatic range of material tal, vertical and diagonal results of the application of (in examining the series, one should play it not only these series. horizontally, as a linear succession, but also disperse it texturally in the vertical and horizontal planes in order to hear the practical functioning of all the elements Write a free composition for 3 wood-wind instruments, of material). Example 373 illustrates the possibility of using three different series in such a way that, in spite obtaining a peculiar type of resultant series. Example of repetitions of the series, the music satisfies the condi374 shows the functioning of a series in the vertical, tions of inner variability in the best possible manner. horizontal and diagonal combinations and Example 375 provides information about the possibility of giving preference to some intervals of the system, the struc73 tural sum of which does not undergo any changes (within the effective limits of the series); Example 376 demonstrates the use of variable intervals (in succession), resulting in the repetition of notes, whereas Forms of the series Examples 377—379 contain models of closed and open microseries and Example 380 presents the relationship between the model of a series and its possible develop- As we know, in addition to the original form of the ments. series we have at our command its retrograde form, 45
its inversion, and its retrograde inversion. These four forms differ from each other but are confined to the same intervallic relations, on account of which they are assigned functions of regular derivatives of the series (the theoreticians of twelve-tone music distinguish still other derivatives of the series, which fact is however of hardly any practical significance to composition). Example 382 shows the relationships between particular forms of the series. These relationships depend to a great extent upon the mode of ordering within the series itself. Examples 383—386 illustrate the methods of utilizing different forms of the series in a composition.
as regards the sound language, we first of all establish the intervals which will form the sound language, leaving the arrangement of the series behind for the present. Examples 387—389 illustrate the use of this method. In compositional practice its results are much better than those obtained by keeping strictly to an ordering, once it has been chosen.
This problem is obvious only to someone who has experienced the pains of strict, artistically unremunerative composition, since as a matter of fact it is not known exactly what is achieved by such composition. Strictness for the sake of strictness is a motto that signifies little for a composer; strictness for the sake of discipline — this means somewhat more, but even so it is not discipline that is important in composing. In observing the development of music based on series, we notice one important aspect. Owing to the definitive ordering of material, the composer's attention is shifted from the region of pitches to other fields and thus textural results are obtained, the existence of which we would not have been aware of unless this sounddiscipline had been applied. On the other hand, however, action permitting freedom in a field (let us say, the field of handling of series spontaneously derived from the choice of intervals) is much more attractive for the composer.
Here we come to the question concerning the equal status of the derivatives of the series. If we assume that the inversion or retrograde form of a series can hold a status equal to that of its original form, because they contain identical intervallic relations, we may just as well say that each series confined to similar intervallic relations will be fit to fulfil the functions (naturally, further ones) of the derivatives of the given series.
Write 12 different series with their derivatives and add 6 series related to them on the principle of intervallic similarity.
Write six 120-note series based on pre-selected intervals.
Write a fairly long composition for four wood-wind instruments, using 48 different forms of a selected series (12 transpositions of each).
Compose a fairly long passage of piano music exclusively using three selected intervals in their horizontal ordering (e.g., 1, 2, 6 or 1, 5, 6; Example 390).
74 Series that determine the sound language
75 Multi-intervallic series
The following method can be used in the present state of development of composition: instead of establishing a series, which is always encumbered with a feature that limits the sound language, we assume that it is not the language that results from the application of the series but, on the contrary, the series itself that derives from a sound language established a priori. Since intervals are more decisive than pitch material
In working on the problem of inner variability, the composer should get to know a peculiar aspect of variation, i.e. parallel variation in two fields,, in the field of pitches and that of intervals. There is a possibility of building series composed, in addition to 12 different 46
notes, of 11 different intervals. Example 391 shows such a possibility in its simplest aspects: the intervals increase or decrease in numerical order. However, there is also a possibility of constructing series comprising all the intervals, but not arranged in numerical order. Such series bear characteristics of two schemes at the same time and so they may arouse the composer's interest thanks to their specific universality. Multiintervallic series (also termed all-intervallic series) constitute the antipodes of microserial schemes, schemes which can be reduced to a serial minimum. Example 392 presents a method of contriving such series. Example 393 supplies a Survey that facilitates orientation of the full material of multi-intervallic series (the complete table is based on the tables published by Herbert Eimert and Eduard Herzog). Example 394 illustrates the application of such a series in composition. Example 395 shows the results obtained from the rearrangement of a multi-intervallic series by the numerical method (1, 12, 2, 11, 3, ...). Attention should be given to the fact that in this way we repeatedly acquire new chordal vertical combinations with continuously changing "harmonic contents".
Example 396 illustrates the possibility of treating an optional numerical set as a series. Naturally, such a method can be applied practically in composition. It is a very simple, not to say primitive method, but may render remarkable services when the material is to be varied and at the same time it need not be formed in a conscious and intentional manner. An intermediate method is also possible; in this instance we choose an intervallic series and — without paying much attention to the strictness of change — we build on it optional sound schemes. These can become the basis for the ordering of the material. It is also possible to arrange pitch material making use of intervallic dispositions. The intervallic dispositions' determine the order of the remaining pitches of the series. Table 398 illustrates the problem of the dependence of pitch orderings on the initial triadic material; in each case the final triadic result is the retrograde inversion of the initial material. The remaining tones are arranged according to the same principle. Triadic material determines the intervallic make-up of the series. Such triadic material is not only decisive for the internal ordering, but also is decisive in terms of the relations between groups of pitches.
Apart from the multi-intervallic series (the material gathered together in the table in Example 393 is useful rather for orientational purposes than for their practical use), the sound model may be approached in another way, by forming a) 24-tone series (quarter-tone material) and b) angularly modified series. The 24-tone series can be based on 23 different intervals. The angularly modified multi-intervallic series constitute a separate problem.
Such broadenings of our conceptions about the series certainly enable us to avoid the heretofore improper treatment of the components of sound language. These new comprehensions of the series create essential deviations from the very idea of ordering (this, for instance, is the case with the series modified angularly). Since the restriction to twelve tones (irrespective of their treatment "thematically", as in Schonberg, or "pointillistically", as in Webern) hinders a composer from thinking freely as regards sound material (for, as we already know, it leads to the "exhaustion" of material too readily); he should reach for such sound arrangements as would relieve him from the continual transposition or alteration of the form of the series, for arrangements "which — as shown in Example 397 — consist of many optional "sub-series", making it possible to work on more widely ranging material than ever before. Such arrangements are termed macroseries.
e Write six 24-tone series (quarter-tone material) and two 36-tone series (one-sixth-tone material). Analyse the results of the angular approach to multi-intervallic
Compose two pieces, one for piano and the other for string quartet based on a 12- and a 24-tone series respectively.
76 Write a macroseries composed of 240 notes, taking care that similar sonic-intervallic situations do not recur too close to each other.
q Further models of series 47
With the preceding material compose a fairly long piece for flute solo, assuming a selected textural model for its basis.
Write 30 different rhythmic and dynamic series, assuming various methods in their composition as the point of departure.
77 Serialization of rhythm and dynamics
The series as a numerical ordering can also be applied to rhythm and dynamics. As regards rhythm we can introduce, above all, simple series which arise by multiplying the smallest value (Example 399). Such series, however, are not particular enough. In addition, there is the possibility of introducing rhythmic values that scarcely differ from each other (Example 400) or that differ greatly (Example 401). It is possible ,to handle groups of very similar rhythmic indications, sach group then being based on a different model of values. So far as dynamics are concerned, the differentiations cannot be as great as those in the field of rhythm, and so they may be restricted to 6 or 8 indications. Increasing differentiation, we can obtain as many as 12 grades (Example 402) and, besides, we can also combine these with internal changes in dynamics where possible, e.g., in vocal parts, in continuously sounding instruments, or by tremolo in instruments in which continuous sounds cannot be obtained, etc. (Example 403). Examples 404—414 illustrate results obtained with different types of serialization of rhythm and dynamics.
The introduction into composition of serialization based on abundant rhythmic and dynamic differentiations enriches the repertory of means in this field to an extent unheard of in the past. In this respect the serialization of these two elements is sensible and of great consequence. The effect of serialization is however often questionable. This is chiefly due to the fact that most serialization is imperceptible to the listener. Nevertheless, this should not blind the composer to the sense of using serialization in rhythm and dynamics — it suffices that he creates effects which he would not obtain in another way. If such effects result, serialization in this field can be used as one of the technological elements of change.
Using rhythmic and dynamic serialization, compose three short pieces: a) a piece based on rhythmic serialization with uniform dynamics, b) a piece based on dynamic serialization with slightly differentiated rhythm and c) a piece based on the full, maximum or optimum, serialization of both rhythm and dynamics (two different series).
78 Serial articulation
As with rhythmic and dynamic materials we can serialize articulation, that is, the means of initiating sounds (in instrumental music, often the physical mode of "attack"). Example 415 shows the method of inventing an articulation series, the use of which in a composition not only contributes to the differentiation of the musical material but, owing to the fact that articulations are at the same time accentuations, virtually punctuates the time; hence the term "serial articulation" is more appropriate than the term suggested by the analogy to other parameters, i.e. "serialization of articulation". Further Examples illustrate the practical application of articulation material in composition.
Articulations cannot be treated apart from dynamics, if for no other reason because some of them are based on sforzato. Composers ocfesionally use articulation independently of dynamics, there being a striking variance in extreme cases with our experience regarding the integration of these two elements (Example 416). The relations between articulation and rhythm present themselves similarly: a number of articulation symbols refer simply to duration, and therefore to a rhythmic factor. Example 417 demonstrates the connections and antinomies between articulation and rhythm. Example . 48
418 expands serial articulations to the limits of the system; here we are more concerned with the results than with the demonstration of the method. Example 419 shows the possibility of making a catalogue of articulations of a higher order according to the properties of the instruments selected. This is intended to produce par excellence articulation effects on them.
Compose two serial pieces based on the same catalogue of components in such a way that they differ as much as possible from each other in that one of them will be non-pointillistic and the other pointillistic par excellence as regards both material and impression.
Write six different articulation series„ taking into consideration different instruments or performing groups.
80 "Oscillatory" and "modulating" serialism
Compose a fairly long piece for chamber orchestra, emphasizing articulation. This element should be serialized much more intensely than the others, e.g„ by increasing the modes of articulation to 16, reducing the rhythmic material to 10 values and the dynamics to 6, etc.
79 Serialization and pointillism
The simultaneous serialization of several elements splits and atomizes the sound material to such an extent, that its material results, and the impression it makes on the listener, make up a music which can best be described as consisting of points rather than of lines. Rests, "which appear either as rhythmic values taken away from the rhythm or as autonomous compositional components, play a very important role in bringing about music made up of points. Examples 420—422 prove that it would be possible to compose with rests. In extreme cases the point of departure would have to be negative material: rests would then, as it were, replace rhythmic values. Examples 423—426 present different results of pointillistic serialization (not all the examples are products of full multiparametric serializa-, tion, yet all of them reveal fundamental characteristics' of serial pointillism).
Full serialism brings with it alarming restrictions: predetermination in many elements at the same time does not allow the composer to enjoy liberties that are necessary in music. The composition seems to be limited to such an extent that no room is left for imagination. This notwithstanding, the result of full serialization is perceived by many listeners in terms of chaos, a disorderly and unorganized matter. In order that it shall not be so, serialism must be developed in certain ways. We choose two out of many possible types of serialism. The first type is an imposed restriction, oscillatory in nature, so-called "oscilatory serialism" (Examples 429 and 430). The second, the "modulating" type of serialism is characterized by the directedness of changes. This permits the statement that not only the matter, but also its organization are animate. This has not yet been taken into consideration (Examples 431 and 432).
Both these types of serialism require some comment. In both of them the method of temporary restriction of material has been adopted, serving as an equilibration of the severity of the pitch discipline. On the one hand, we are still dealing with a fully serialized material; on the other hand, the music is devoid of that not always desirable statistical character.
Make up your own models of these types of serialism in different elements simultaneously or separately (in an integrating and a disintegrating manner).
Analyse the serialization of elements in Examples 427428, writing out catalogues of serial components. 49
same number of serialized components, which appear in constantly varying combinations (such a polyseriaJ programme and its realization are demonstrated in Example 437 and,, in a graphic form, in Example 438; the series of pitches and instrumental timbres as well as rhythmic, dynamic and articulation series are programmed in Example 437; all the possible variants have been exhausted by the rearrangement of the pre-established numerical combinations). This interchangeability, no matter how realized, cannot be grasped. Nonetheless, it may by used to restrict the compositional methods in a particular manner or may be used with the aim of determining the musical material completely (Example 439).
Compose two pieces for small chamber ensembles on the basis of the two types of serialism described above.
81 Modal serialization
A. separate type of serialization is based on modality. Examples 433—436 show the source material (Example 433b: an analysis of the sonic, rhythmic and dynamic series of a composition and the diagrams of the lowest, middle and highest voices) and the final results of modal serialization. Modal serialization need not be associated with linearism; it can also be treated in a pointillistic manner.
Analyse Example 439 very particularly, examining it for the quality of relationships introduced.
Compose two totally organized pieces, one for piano and the other for string quartet (in the string quartet performing methods will have to be taken into account in total serialization).
Modal serialization constitutes a very narrow section of the general serial possibilities, owing to which some regard it as individualization and others as restriction or perhaps even impoverishment. Nevertheless, its application in composition is very instructive and should be practised using elements as various as possible.
83 Problems concerning total serialism
Analyse the modality of Examples 433—436 very closely and study the differences between modal and full serialization.
The problem of mechanical predetermination of music is integrally connected with total serialism. There is only one thing apparent from Examples 440—441: total serialism does not provide any additional possibilities of differentiation, since they are already comprised in the material fixed beforehand. In connection with this, additional corrections, which are in opposition to the schemes resulting from total serialization, are indispensable, e.g., those in the form of "deserialization" of dynamics.
On the basis of your own pattern of modality compose a fairly long piece for a keyboard instrument, using three staves.
82 Total serialization — interchangeability of serialized elements
Compose a short piece for string quartet in two versions, one totally organized and the other corrected (note: the correction should not- impoverish the initial text unduly).
In a musical composition total serialization may be carried out in such a way that each element has the 50
84 Analyse Examples 446—449 thoroughly and carry out reductions of a different nature in them. These reductions should enliven the music (in other words, they cannot be made only for themselves, in a mechanical and indifferent manner).
Technique of deschematization
In serial material it is enough to apply the method of repetition of selected components, a method which is opposed to total change, to turn statistical music into dynamic music, a music alive by reason of the appearance of opposition to modal change (Examples 442—445).
Using the technique for the reduction of those elements which lead to monotony in serialism, write two versions of a fairly long musical passage for a soloistic chamber orchestra, starting from total serialization (the first version will thus be serial and the second version reduced).
Compose a short piece for a solo instrument of your own choice in four versions so that each .successive version shall form part of an increasingly dynamic process, becoming in consequence gradually more opposed to the initial serialism. Find your own methods of deschematization independently of the examples given in this section.
V
85
Transformation of structures into textural formations
Technique of the reduction monotony in serialism
of
elements
inducing
Having at our disposal well-developed techniques for deschematization, we can proceed to the reduction of monotonous pre-determined serialism. (The guiding principle of this book is the constant passage through a sort of sophistication to simplicity. This is why reduction appears only now, towards the end of the discussion on the problems of series and serialization.) Reductions of this type are shown in Examples 446— 449.
The essential problem in this respect is the very method of reducing elements. In order to become well aware of this problem, it is necessary to distinguish reduction from selection: the former consists in decreasing the number of components, whereas the latter is the predetermination of material. In reducing, we make a choice also, but not from the total range of possibilities, only from the present stock of means.
86
The renewal of texture is one of the most important phenomena in new music. Even the most microstructural sound combinations may' become the basis for the renewal of textural forms used so far (Example 450: transformation of structures into formal units). The mere splitting of material into small particles provides textural results which differ in nature from those obtained up till now. Examples 451 and 452 show various textural results obtained from simple elements. Examples 453—458 show their developments. Examples 451 and 452 are based on the principle of homogeneous juxtapositions of material; here texture is formed "mechanically" as a result of the compositional process. It should, however, be realized that texture itself is the main subject of composition (cf. the manner of juxtaposing vertical sound combinations in Example 451 and the complementary nature of the juxtaposition of two parts in Example 452), Examples 453 and 454 demonstrate further developed forms of organizing of a textural result and Examples 455 and 456 show that texture may arise from the juxtaposition of several planes (in Example 456 — what is played by both hands). The last two examples (457—458) present still fuller methods of transformation of structures into 51
textural formations. These examples exhibit a distinct tendency towards the developing of polyphonic texture even when the number of parts is relatively small.
The question arises to what extent the vertical and horizontal distribution of material produces an internally differentiated texture, and when, and to what extent, it produces a homogeneous texture and therefore not the fullest result as regards texture. It seems that we may speak about the problem of transformation of structural forms into texture only when texture is composed deliberately and its renewal has been intended by the composer.
Analyse Examples 453—458 very closely and try the following experiment: on the basis of the five selected examples first make a short simplified version and then go to the opposite extreme, and develop a complex textural form. In other words, texturally try to reduce the material presented by the composer to a minimum (task a) and to expand it to a maximum (task b).
nor the complex built in a circular form arises from existing conventions or habits. Both these textural forms had to be created. Examples 464—465 show compositional action in the sphere of texture based on "semi-conventions" or conventions created ad hoc for the given situation in the concrete composition. The development of this idea is presented in Examples 466—469: those models in which there existed a possibility of an autonomous development of the texture are completed here in various manners. It is possible to compose starting from textural assumptions. This is proved by Example 470, built from a double time system (one of the systems is a programme for tempi, the other, pitch material moulded texturally on deliberately different principles). Examples 471—473 show the different textural concepts formed for the given compositions; the texture of these examples cannot be transposed.
Basing yourself on a selected combination of 24 notes compose samples of 12 various textures (in piano arrangement). . .
Thoroughly analyse Examples 459—473. Find out which sorts of texture are suitable for transposition and which are not. Make up your own programme for the moulding of textures for the following instruments and instrumental ensembles: a) piano, b) harp, c) celesta, d) harpsichord, e) vibraphone, f) 5 wood-wind instruments, g) 6 brass instruments, and h) 8 stringed instruments.
87
88
Study of textures
Series and their textural break-up
Examples 459—473 illustrate the mechanics behind the formation of different textures. Textural differences arise here not only from the manner of disposition and distribution of material in time, but also from an individual * understanding of the problem of texture. In Examples 459—461 the textural effect is moulded consciously; it no longer results simply from fundamental assumptions regarding material, but also from the adoption of a kind of textural convention. Example 462 shows how such conventions can be expanded; its third passage, a little dull in itself, has a texture that appears to be interesting precisely in the light of juxtaposition with the preceding passages. Example 463 proves that texture can be formed outside recognized conventions: neither the fluent glissando
Examples 474—478 illustrate the quasi-textural results of the break-up material over registers. Pitch material, especially that of a series, broken into several registers in itself produces results which may bear the traits of a well-developed texture. This impression is strengthened in Example 474 by the use of the highest and lowest sounds of both instruments and in Example 475 by a crossing of parts, not however permanent, because the effect would then be mechanical, lacking in any importance for our considerations. Example 476 demonstrates the possibility of working with the quasitextural results by maintaining a pitch minimum and Example 477 shows the vertical textural variation attained by the inclusion of more instruments (instrumental timbres). Example 478 presents the result of 52
a textural break-up of a series. The continual repetition of the same intervals (the direct result of using a series and its elementary transformations) would be impossible here and this is why the composer had to resort to the transfer of the principles of composition from material to texture.
of several very simple horizontal textures is a general texture,, about which it may be said that it has been composed in the full sense of the word. Notwithstanding, attention should be given to the moulding of even a monophonic texture. We are here concerned with obtaining as many internal relations as possible within the narrow zone in which the elements co-operate. Most certainly the rhythmic arrangement in Example 479 reduced to uniform values would not represent anything that might be labelled — even in approximation — as a composition. In order to produce a very explicit textural-rhythmic result, one can use an initial disposition involving a precise measuring out of the numbers of concrete rhythmic values and types of rests (Example 484).
The problem arises of the dependence of texture upon serial technique. It is generally claimed, groundlessly, that the series determines music. This however happens only in those cases where the composer concentrates upon the properties of the series. In most successful pieces the composer goes "above" the properties of the series and composes in the field of other elements, taking care that the texture of the composition goes beyond the initial "historical" conventions.
Make up 6 models of rhythmicized series. Study the possibilities for the textural approach in regards to different pitch combinations (specially selected for this purpose).
Write four 36-note sets and compose them into four different semitextural combinations.
Compose a fairly long instrumental piece (flute, vibraphone, piano or string trio), in which horizontal texture will be the chief structural feature of the composition.
89 Series and their rhythmicization (horizontally-conceived texture)
90 Examples 479—481 illustrate possibilities of working with models which bind together series together with ways of rhythmicizing them. In Example 479 we are struck by the assignation to each sound of a rhythmic and a dynamic value. This is the simplest method for combining sounds and rhythm. Example 480: rhythms are bound to sounds in a far more ingenious manner — this is no longer the handling of additive variants (as in Ex. 479), but that of very different proportioned values; Example 481: a different rhythmic value corresponds to almost each pitch, on account of which the horizontal texture undergoes a change, as it were, internally. An exact opposite of this last method can be observed in Examples 482 and 483,, where the repetitions of sounds reduce the horizontal texture to a minimum.
Possibilities of textural melodization horizontal pitch combinations
of
series
or
Examples 485—488 show different ways of presenting the textures of series or horizontal pitch combinations. Example 485 —• classical in its form — demonstrates the most elementary manner of presenting a horizontal pitch succession texturally. The retention of the same rhythms coupled with the restrictions of the structural properties of the series shifts the centre of gravity to the texture itself, and it is the texture that we hear primarily. In Examples 486—487 we are concerned with the different consequences of the horizontal arrangement of textures; in an elementary case (486) the horizontal texture is constantly or mostly monophonic. In Example 487 the appearance of single notes or two-note chords does not result from the scheme but is due to the free treatment of horizontal texture. In
The question of horizontal texture needs a fairly extensive explanation. It often happens that the result 53
other words, the point is that the horizontal texture not be confined to the presentation of a single part. Example 488 shows a number of horizontal combinations. Owing to the textural way linear motion is understood, a way different from that prevailing till now, these horizontal combinations become something more than a common pitch succession (this after all is not yet music).
Arrange four different horizontal combinations, taking into account as many forms of textural melodization as possible. Different methods of textural "thickening" are to be used, for in practice a single part should not be a result of the succession of single notes but it should be freely thickened vertically. This is more important than the mechanical superimposition of several simple lines. Utilizing the information obtained from the analysis of possibilities of the textural melodization of horizontal pitch combinations, compose a fairly long piano piece, which in its fundamental principles however will admit of free (even very intense) vertical thickening (write on one stave, adding, if necessary, an upper or a lower leger-line or both of them at the same time).
the sound or colour technique adopted and, last but not least, from the authentically individual character of the composer's attitude to the possibilities of the textural handling of material in a quartet. In the examples quoted the composers took care, above all, that the four-part texture of the quartet could not be treated as an ordinary transposition of any set of four parts into a string quartet. The following are selected problems connected with the non-mechanical treatment of quartet texture: the application of any number' of parts (489, 490, 497b), the introduction of various sorts of densifications (496, 497a, 497e), the unsettling of proportions between parts (495, 497a, 497h), the change of textures (490, 492, 493, 497g), the relaxation of sound proportions (491, 495, 497b) and lastly the use of different forms of textural presentation of music (typical examples: 494, 497d, 497f, 498). A fairly long variable process of formation of music by changing its texture is extensively shown in Example 496, which displays — despite its.being confined to simple notational forms — a wide range of co-situations assigned to the all-delimitative idea of four constant voices. Compose a string quartet of about 200 bars on the basis of your own textural models.
92
91 Piano texture Examples of four-part textures (string quartet) Examples 489—498 illustrate the possibility of various approaches to the homogeneous four-part texture of the string quartet. As can be seen from the examples, much depends here on the kind of sound technique applied in the string quartet. It cannot be denied however that operations which are very revealing in nature can be performed in this seemingly narrow field. It is worth mentioning that the linearism of music is not binding in the quartet, although we are generally concerned with a constant number of parts.
Here we come to the problem of the source of the differences cited above. They often arise from the historical comprehension of quartet music, often from
Examples 499—514 illustrate possibilities of the varied treatment of texture on one instrument, in our case the piano. In new music the piano affords striking proof of the extent to which the world of scund ideas acquired "directly from the keyboard" is conventional. Most certainly, new piano. music is to be written without regard to the problems of fingering. The examples given show, for the most part, methods for conquering the habit of starting from keyboard notions even if — as in Example 500 — the sound material is associated with the properties of sound-arrangement on the keyboard. The first examples (499—501) are confined to the developed forms of what is still the traditional texture (Example 499 demonstrates extensively how new textural solutions can be built on the basis of the known textural forms; here the 54
rhythms and texture surmount the barrier of the conventional understanding of the instrument). Different textural developments of this type of music are shown in Examples 502 and 503. Examples 504—507 present other ways in which composers tend to overcome conventions,, the existing ones and those handed down by tradition. In these cases the sounds on the keyboard are regarded as sounds chosen independently of any system that might be understood as a system related to the properties of the arrangement of sounds on the keyboard (even the most atonal piano music is restricted to the arrangements subordinated to the "system" of parts on the keyboard, as evinced by Example 508). It happens that a composer arranges sounds in a system approximating the properties of the keyboard ordering: they are then, however, transposed (Example 506: the displacement of the centre from a1 to a-flat 1 would result in the perfect conformity of the musical text with the properties of the keyboard). Example 509 indicates that it is possible to produce both lines and points on the piano and, consequently, they can be introduced as factors that can be composed .texturally. Example 510 shows how to overcome thinking according to the parts, in Example 511 textural problems are focused on dynamics (dynamic scale from 0,0 to 10.0), in Example 512 on the ambiguity, of articulation. The last two examples (513—514) demonstrate two different ways of understanding contemporary piano texture.
larger ensembles. Here attention should be drawn to the fact that the mere scattering of material over some dozen parts does not yet make a well-developed texture (Example 515, more than half the material is reduced to a minimum as material redundant in nature). In order to obtain a fuller picture of the polyphonic texture, we should guarantee to each voice actual autonomy (517a) or distinctness in timbre (517b, in which each part is analytically heard separately despite a large number of rests). Both examples consist of the same notes. Polyphony is often reduced to a common denominator, which is sensible only where this is the composer's actual intention (516). A collage composed from a short piano piece by Schbnberg (518) shows how homogeneous complexes can be read polyphonically. Examples 519—521 illustrate different textural developments in music for small instrumental or vocal ensembles, in which, notwithstanding a small number of parts, the textural polyphony is perceptible and audible (in the last example, 521, the textural polyphony is perceptible and audible because the. parts are not put together in a complementary manner).
Analyse Examples 522—526 with respect to texture, taking the studies on true polyphony as a point of departure.
Compose two short pieces for 10 different solo instruments on the basis of your own textural models.
From the survey above pick out pairs of a) the most similar textures and b) those that are the most diverse. In case b try to exchange textures between the examples.
94 Texture and density
Write a piece for piano solo, taking about 6 mjnutes to perform, and apply at least a dozen different modes of handling textures on this instrument.
Possibilities in the handling of textures in music for larger ensembles
Examples 527—540 illustrate the problems connected with relations between texture and density in the vertical and horizontal aspects. It is clear that the density parameter is readable, above all, when the textural material informs us about the real scale of density from monophony to great complexes of several dozen parts, in which —- and this is important — there cannot be room for repetitions.
Examples 515—522 show, naturally in brief, some possibilities for the handling of textures in music for
The possibility of handling the density parameter after the fashion of other parameters arises in new music.
93
55
If the density of material is too great, the audibility of this parameter becomes markedly diminished, but, in spite of this, density indirectly influences the nature of music being composed, and then it has an active force and can be used as a music-moulding compositional factor. Examples 527 and 528 show the conventional density arising from the habit of treating the sum of parts as an inseparable complex (in string quartet and jazz), Example 529 shows a tendency towards the equipoise of parts (a perfect example of the neutrality of parts). Examples 530 and 531 prove that density can manifest itself not only in vertical structures but also — -additionally or autonomously — in horizontal ones. Examples 532—534 provide material for the observation of the density factor from different view-points, ranging from purely textural problems, as in Example 532, up to the composition of density parameters (533 and 534). Examples 535—536 illustrate the possibilities of handling the density factor as if without regard for problems to texture.
structures. Here we are concerned rather with the intensification of texture itself. Maintained in static form, texture would communicate little, if anything. Example 546 demonstrates the possibility of the elementary addition of parts to obtain a fuller (and also more anonymous) material and so does Example 547. The last example (548) illustrates the possibility of the introduction of collage into composition. Thanks to the collage technique the musical matter passes into a completely different state.
A number of questions arise here, which at least are worth touching on perfunctorily. First, on account of the vertical thickening, the musical matter loses much of its initial substance and becomes something different from what it was originally. Secondly, in,mechanically thickening lines already composed, we perform an act of decomposition on them, i.e., we deprive the music of many of its original relationships, adding some new ones, but not in such a number as might be expected, judging from the very number of procedures. Thirdly (this is related to the previous item), the composer must be aware of the fact that thickening the vertical structure thorough an increase in the quantity of material, he performs an act which is sensible only when such indeed are his intentions. In other words, the thickening of vertical structures by increasing the quantity of material must be applied in full consciousness, and not mechanically.
Analyse closely the influence of the density factor upon the moulding of music in Examples 537—540. Find in which examples the density factor was composed consciously as a factor determining the final sound form of the music.
Basing yourself on your own model,, compose a fairly long musical piece so that the density parameter is fully utilized in it.
Construct a number of models demonstrating thickening of music in its vertical dimension.
95
the
On the basis of your most successful model,, compose a fairly long musical passage for a deliberately reduced group of instruments.
Possibilities of thickening vertical structures through an increase in the quantity of material employed
Examples 541—548 provide us with information about possibilities of thickening the vertical structures by increasing the quantity of material employed. This increase in material may be mechanical and may follow the general guiding principles of composition (Examples 541 and 542). In new music there is a tendency to increase material in order to intensify expression (Examples 543 and 544). Example 545 illustrates other reasons for employing methods of thickening vertical
96 q Dispersal of material
Examples 549—559 demonstrate the so-called dispersal of material. It consists — at least in conception — of 56
the uniform distribution of material in all parts without giving preference to any place in musical space or to any part. Thus, the dispersal of material (Example 549 is typical in this respect) consists of a scheme to preserve a perfect equivalence in all the particles of dispersed material. Such perfect equivalence is however unattainable. Evidence for this exists in composing practice. In composing practice material is automatically doomed to supremacy or to secondary roles. For this reason it is easier to observe the dispersal of material in longer examples, for then the equivalence of material is revealed more fully than in the case of a short section (Example 550, in which there appear" certain hints of musical hierarchy despite the equivalence of material). Examples 551—553 illustrate the results of the dispersal of material arising from various sources: the break-up of the matter into parts and registers (551), the treatment of the eight-part structure as a matrix for dispersal (552), or the treatment of single parts as if the sum-total of parts were important, but not the parts in themselves (553). Dispersal can be used to shape the timbre in a musical process (554 and 555). Example 556 demonstrates putting together musical matter according to the principle of dispersal. Nevertheless this musical matter is treated homogeneously. Examples 557—559 expand what has been said on the subject of dispersal covering a range from chamber ensemble to fairly large ensembles. It will clearly be seen from the examples that the dispersal of material demands — by the mere nature of this phenomenon — that all the instruments be treated in a soloistic manner.
Two questions, emerge here: a) concerning the choice of measures for transforming the optic linearity of musical processes into pulsating matter and b) concerning the anonymity of sound material. The technique under discussion can be used only when the composer is really eager to treat the sound material statistically (however, it should be kept in mind that in execution some of the particles of even the most scattered material come into prominence as more important, more distinct, more audible, etc.).
97 Influence of mechanical composing on texture
In Examples 560—562 music arises from the statistical dispersal of sound material over all registers and from the continual crossing of parts. Generally speaking, these examples form a complement to what has been said about the dispersal of material in space, but here we are concerned more with the textural effects of such treatment of material. The uniformity of sound material particles is clearly manifest in Example 560. The composition's value would not lose anything of its substance if the parts had been interchanged, the best proof of the equivalence of material particles. Example 561 shows two simultaneous forms of dispersal of material: those of tied notes and of short accented notes. Despite this division of musical material into two categories the very idea of dispersal has been maintained. It is important to us that the material disposed mechanically, as it were, influences the shape of the texture, which in itself cannot be reduced to the conventional forms of polyphony. The automatic process of composing has a still greater effect on texture. This is shown in Example 562a and b. Here the texture appears to be a completely automatic result of the procedure of composing in the vertical and horizontal dimensions without taking into consideration the traditional canons of polyphony.
Compose a short passage for string quartet based on the principle of the total crossing of parts and the statistical scattering of material.
98 Combined constructions
Examples 563—564 show a further expansion of texture resulting from the vertical and horizontal combination of musical structures. These examples need no extensive commentary, but must be explained with regard to one point only. In observing the mechanics of arranging
Compose six different short vertical structures based on the technique of dispersal. They should be designed for instrumental ensembles and orchestras that are as different as possible. 57
many layers or musical texts one above another, we readily come to the conviction that the material thus obtained is enriched in a one-sided way. However, this may be the intention of the composer, who, dealing with material that can be superimposed in strata, is justified in laying out the music in this manner even at the cost of the audibility of the original text. In contemporary music this method allows one to achieve a multiformity of musical material which can be "interpreted" freely for a fairly long time. Owing to this, music passes from the category of unequivocal structures into the sphere of ambiguity — a sphere that is highly desirable in many instances.
parts. Such a complex of parts gives rise to a matter which owing to the application of distinct techniques for each particular complex may contain — despite the variety of its particles —• something homogeneous (typical example —• 565). In the group technique what is initially multivocal becomes univocal (Example 566). Examples 567 and 568 display specific forms of the reduction of instrumental groups to several or even single instruments. Examples 569 and 570 show the full textural effects arising from an application of group technique.
The question arises as to the distinctness of a process formed in this way. However, it will be seen from most of the examples above that even where there is considerable vertical concentration, music may be characterized by a distinctness of a higher order and perceptibility not in details but in its general organic whole.
It is characteristic that the method itself seems onesided, but its results are diverse and consequently more versatile than1 the results of a more extensively ordered activity. This is so because in musical substance increased repeatedly by additions of material there appear some processes which have not been known till now. Thanks to their attractiveness these prove useful, being furthermore capable of practical assimilation. The method of combined constructions should not be regarded as a technical innovation, but as a direct consequence of the evolution of music from homophony to polyphony or, more stricly, in this situation from "monotextuality" to "polytextuality".
Compose a short musical passage on the basis of group technique.
100 Texture of large forms
Using the principle of combined constructions compose a passage of music, taking some dozen seconds in performance, with three different kinds of textural disposition.
1
In the composition of large forms textural reductions are required (Examples 571—575). Such simplifications may be connected with distinctness and need not arise at all from the arrangement of the material in the elementary units. In each of the examples given, we < are concerned with material composed in a different manner but always arranged so as to suggest that it is a part of a larger whole. Here the texture is not restricted to stereotypes but goes beyond them, finding its own new solution for each selected sound situation. Large forms, if they are to be cultivated any longer, demand a non-uniform treatment of texture. Thus the composition stops being monolithic (which is of minor importance). Instead it becomes polymorphous in its textural complexity and, at the same time, uninterpretable in a single definite manner. This fact in itself is interesting from the view-point of composing practice. It is clear that where stylistic stereotypes come
Textural results of the application of group technique
Examples 565—570 show that a specific expansion of texture in the vertical dimension can also be attained by superimposition in strata, not only now of single sounds or lines, but also of whole groups. This technique may be called the group technique. It consists in the setting together by the composer of several parts (more than ten if required) to form a texturally unequivocal whole in spite of differences between individual 58
into play (572), the large form treated in the way presented is an illusion. The example showing stylistic stereotyping is contrasted with Example 571 in which each part of the large form, established by the composer beforehand, is based on periodically varying material. Examples 573—575, which illustrate the results of preset large formal constructions, differ from the other two simple textures in large forms. Here the texture is not confined to periodical changes but flows from the interpenetration of different methods of expansion of sound material in musical space.
e Analyse the examples above, giving special attention to the impressional effect of the material so composed.
Using your own model, compose a fairly long piece based on the specially selected material of sounds (at least 12 different textural variants are to be included in the piece).
VI 101 True composition of music
Not all music — nor all new music — is truly c o m p o s e d . By composition we mean structuring compositional information in such a way that its outcome is richer than that which is written down. Therefore music must comprise a number of internal relations which not only enrich the work but also lead to its interpretation, the realization of which departs from the actual notation. All the relations occurring in music have a semantic value. They mean something, whereas mere notation, the mere notational image, does not mean much. A very essential feature of composition is its complexity. This complexity need not express itself at all in the number of means accumulated — this would be too simple. Compositional complexity is attained when we create a field in music capable of sustaining the most various possible interrelations. Such relations form a sort of open system of
musical dynamics, and the more numerous they are in a composition the more confidently we may speak about vitality in the music. The question to be asked here is: when is music composed and when is it not, i.e. when is it only written? This problem is not very easy to solve, but most certainly much here depends upon that semantic intensity, upon how much we want to say. It has been found that the value of information does not depend upon its amount but upon the richness of its internal relations. It has already been seen from the first rhythmical exercises in this manual that the intensity of change in music is conditioned by the way we comprehend it. The composition in the full sense of the word should comprise as many relations as possible with the fewest means required for this purpose (this is why in this book we keep chiefly to forms for a few instruments or small chamber orchestra, leaving the possibility of "multiplication" of means for large forms. This, we surmise, does not increase the stock of information but only leads to its further compositional stratification). In music there must exist the possibility of several or even many interpretations (by interpretation we mean the mode of reception and understanding of music, characteristic of individual listeners). If a music may be interpreted quite unequivocally, it deviates considerably from our ideal of composition. Thus in order to write good music, one should not compose in one dimension but in many dimensions simultaneously. For this purpose another composition and perhaps still more may be built within the same compositional framework. This is done because the unequivocal notation of music presents the compositional idea in a purely external manner. Such composition on composed material may (but need not) guarantee this desirable richness of relations. What it looks like in practice, we shall see in the course of analysis of Example 576. Taking as your basis the models in which the method of Example 576 is developed, assemble the musical material in a number of versions in which larger and larger numbers of relations present themselves (relations as well as material should be complemented, since only then can music be made many times richer). Utilizing the idea of composition on composed material as your starting-point, write a musical passage of about 59
80 bars for string quartet in three versions: a) an ordinary initial version, b) a version of great virtuosity in the executive sense and c) a version enriched to a maximum in respect of composition.
102 Precomposition
The whole process of composing may be preceded by preparatory work. Such work proceeds in us when we intend to write a new composition and, in the best instances, even when we have no such intention, our thoughts merely going round and round the problems of musical possibilities. Considered from the view-point of psychology of creation, this preparatory work constitutes a kind of constant inclination to composition. This inclination can sometimes be acquired in a practical way, when we work at music without any special concretion of its compositional appearance. We can simply conjecture extensively on the possibilities of music in our imagination without casting them in the form of a designed composition. We may have musical material at our disposal before we know what service it will be to us (most of the models in this book consist of material of this sort). Apart from this, there also exists the possibility of tangible preparatory work preceding composition, and this sort of work is here referred to as precomposition. In practice its aim is progress from the zero point to a certain concretion. Precomposition was unnecessary in old music,, for there were (albeit very generally outlined) some b a s e s for composition (principles of polyphony, harmony, etc.). In contemporary music, where the mere possibility of various musical relations constitutes the compositional basis, it is worth attempting the working-out of methods for the control of material before embarking on composition proper. The composer can produce control models (either his own or some in more general use) on which he can compose music. Series, numerical combinations, geometrical proportions, order of timbres, etc. are such models; for instance, the instruments (timbre), pitch material for each instrument (chosen models of the chromatic universe — cf., Example 279), and rhythmic material in 15 versions (in the first version without rests) identical for the whole set have been decided in Example 577 in advance.
The range of possibilities that may be employed within the framework of a chosen model is an extremely important factor here. If we establish that any sequence of twelve different notes is our model, such a sequence can most certainly be treated arbitrarily in composition in the vertical dimension, in the horizontal, etc. If however, we confine ourselves to a closed divisible series, then the methods of treatment available will be limited to variants of models already well known to us hence to a very narrow range of similar processes. Nevertheless, this relationship should not be treated one-sidedly, for we know (e.g., from Webern's Opus 30) that a considerable restriction in a single field (in this case in the field of pitches) c o m p e l s the composer to extend compositional controls in other fields. This serves music very well. Thus the nature of precomposition is not only restrictive here but also positively predetermining, and it makes the composer direct his activity to other fields of music (in order to compose in t h e m ! ) , or, in some measure, automatically induces him to proper composition (for writing a series out in time is not yet composing).
Analyse closely Examples 578—584 and examine that material which was precomposed in them. Here our chief aim is to reconstruct the sound material in the general direction of its initial form (most of the examples demonstrate that such an initial form need not be a series).
Make four precompositional models: a) model of pitches, b) model of intervals, c) model of colour order and d) model of rhythms. Construct a composition for a small orchestra of solo instruments on them. Ensure that true composition takes place in musical aspects other than those of thej given models.
103 Composition of time Precomposition forms scarcely one link in the musical chain. Instead of precomposition we may employ 60
spontaneous activity (though precomposition may occasionally be spontaneous activity) which included as an important component in creativity may cause a shift in the centre of gravity towards play in the imagination. Spontaneous activity directed horizontally, i.e., activity related above all to the time flow (composing along time), is called the c o m p o s i t i o n of t i m e . In conceiving a composition, we can try to hear it not in its sounding but in time. Example 585 shows disposition of time (handled in a version deliberately set vertically so that even the treatment of time shall not be conventional). In place of the conventional adding-up of timeparticles into a larger whole or the division of a larger passage into small particles there appears here the idea of seemingly "dividing" silence by points of various accentual value. As can easily be 'seen, regularity of the proportions between sections is casual here and all schemes that lend themselves to an accord with a comprehensive principle are schemes which we impose (ex post facto) upon the text and which in themselves are dependent only on the spontaneous control of time. Example 586 illustrates a more traditional, but perhaps a clearer manner of controlling time. A number of motives, each composed differently, appear in a slow tempo. By the very fact of the motives having various accentual values, t i m e is here deprived of both measure and that form of ordering that arises from our conventional approach to it. In other words, it is actually created, c o m p o s e d . Examples 587—589 offer different developments of .the above statements.
are the more variously moulded horizontally the longer the time they are given). Examples 592—595 display other ways of getting rid of time orderings which suggest themselves incessantly: the first way is based on movable time proportions and the other one — expressed in different tempi — breaks up the time of the composition without annihilating its own autonomous time structures.
Example 596 is the beginning of a composition and Example 597 the ending. Analyse both examples and find how far they suggest the initial and final control of time and to what extent they determine music or are determined by it.
Compose 12 initial and 12 final passages so that they shall allow us to surmise, in the first case, the continuation of the time disposition and, in the second case, what may have appeared before the closing passage. In both cases the conjectural disposition of material is to be introduced in an exceptional way: it should be imagined that uniform starting-up of variable parameters and relations is the ideal for this music. Compose . all these passage for 5—8 parts (vocal or instrumental). After a few minutes' pause add to all the 24 passages short passages "from the middle", seeing that they contain as many contrasts as possible with regard to time dispositions (these passages should not be dissociated from the type of texture, modes of disposition of density, etc. characteristic of the previously written passages).
In new music we are still concerned with the composition of time. Generally speaking, we know that we can impose controls upon time and that, on the other hand, we can draw impulses from it for compositional activity. It is certain that composers who really compose t i m e always keep in mind possibility of action a g a i n s t the time controls imposed by the metre. Let us look attentively at Example 590: in all certainty, the play between the expectation of musical events and the ensuing events themselves is as obvious as possible from the view-point of its time function. The longer we expect an event, the greater seems to be the intensity of its appearance. Example 590 shows the elementary handling of action resulting from the expectation of an event, whereas Example 591 illustrates the disciplining of such a treatment into a new canon (densely composed quarter-tone music is contrasted by the composer with single notes which
104 Abstract and concrete Obviously, musical abstraction does not exist. In music each thing thought of as an abstraction undergoes a concretion the very moment it has been written down. Within traditional conventions of composition, notation is frequently substituted for composition; one composes not only with the help of notation but often simply thanks to it. In new music the composer must tear himself away from this convention and conse61
quently from the notation. To this end he must give less attention to the writing-down of music, its notation, and more to the formation of the idea of what is to be said, believing that in the case of successful concretion this idea will materialize readily and firmly. Let us have a look at Example 598. Its idea goes beyond conventional sonic thinking and enters the sphere of a peculiar sort of musical vision for which the composer finds appropriate signs in notation. If we compared the written record of the composition with its graphic representation,, we would understand readily that the composer had a twofold notion of the composition, an abstract idea of music and a concrete conception in the form of notation. The next examples (599—602) demonstrate the direct link between the idea and its counterparts in the written record, between the abstract and the concrete. Most certainly, the musical shorthand sometimes applied here allowed the composer to participate himself in the direct realization of the idea, which in such cases seemingly identified itself with the concrete form of the music.
Analyse closely Examples 603—611 for the independence of the music from the idea lying beyond the notation. Treat the material of Examples 612—614 as conventional and add a few further bars at your own ("notational") discretion.
Write several motives containing the characteristics of an abstract idea. Check them for possibilities of concretion.
105 Aesthetic problems
Aesthetic problems have never been considered in combination with compositional technique. Nevertheless, they are problems that penetrate deep into the very essence of composition. In deciding on anything in composition, we make decisions concerning aesthetics. This is an immanent property of composition. The mere musical material, the sound, is an aesthetic fabric. It contains a message concerning the sphere of beauty. We have no precise data about aesthetic criteria, but we have a certain opinion formed in the maturing of our aesthetic sense on what truly has aesthetic value. The question arises whether the composer is to assume aesthetics as his p o i n t of d e p a r t u r e . Is he to be prompted by it in composing? The development of music, the development of musical idiom tells us that the answer is negative. Beauty is subject to wear and tear just as novelty is; moreover, perceived by most and subject to imitation, it becomes common property and ceases to arouse admiration. This is probably why composers willingly reach for new aesthetic media which mean little, if anything, to the general public. Composing then is an action "beyond good and evil" in the aesthetic sphere. Thus, aesthetics cannot be a point of departure for the composer,, he must not estimate his action from the view-point of aesthetic criteria, those existing till now are no criteria at all and the new ones are terra incognita, one of the secrets so numerous in art. Anyone engaged in creative activity in the field of art knows that many artistic elements undergo a specific ennoblement: what is regarded hardly possible today may come into demand
The problem of the transformation from the abstract to the concrete is not a primary problem in composition, but in many cases it constitutes a point of departure for an evaluation of the techniques of composing, for we still cannot resist the impression that there must be an idea that underlies music, that music cannot emerge from the spontaneous action of mere w r i t i n g , from the c o n v e n t i o n of n o t a t i o n , which is apt to happen nowadays (there exists the p o s s i b i l i t y of writing music e x c l u s i v e l y based on the belief, plausible in a sense, that everything written down is music). Especially in serial music and immediately post-serial music, writing with such spontaneous automatism creates, as if by its very nature, full-fledged creations (within their own realm) which possess all the characteristics of musical completeness: Example 603 — polarization of serial methods, 604—607 —• free activity in which only the idea of serialism is emphasized, 608—611 — "playing" at vertical and horizontal composition without the motivation of a compositional idea. The method of "automatic" writing cannot be treated on a par with that of transformation of an abstract idea into the concrete. The difference consists in the fact that the action arising from notation is much easier, less creative and, practically, open to everyone acquainted with the general rules of the notation of new music. 62
in the artistic sphere tomorrow. To compose therefore means to act independently of aesthetic considerations, yet also to act precisely in their interest, on behalf of their truths, which will become verifiable later. However, problems connected with the aesthetics of material alone will always arrest composers' attention. Concrete material, electronic material, new instruments, a new treatment of the voice, the introduction of new media — they are all matters for dispute. Even the seemingly most serious creators hesitate to adopt new techniques, always, they claim, for aesthetic reasons. Now, let us look at a few examples of new music: 608—611. Sure enough, music expressed in t h i s manner may seem to be too individual for other composers to be willing to adopt and unhesitatingly make use of its techniques. Even the mere possibility of adapting somebody else's achievements for one's own needs presents an aesthetic problem. The contemporary composer will not hesitate to write music similar to the first two examples which are still marked by some conventionality, but he will show definite inhibitions as regards the last examples. However, the progress of aesthetic thought consists precisely in overcoming these primitive inhibitions. And if modern music has not as yet developed to such an extent that we are satisfied, this in a considerable measure is because of these aesthetic inhibitions, quite unjustified where the development of art is at stake. Most certainly, the contemporary composer who rejects, e.g., electronic media, simply because they do not suit him for aesthetic reasons, ruins his chances of acting in the field of aesthetics (in our times this issue is deepened by reciprocal impulses that occur in connection with composition in different domains!).
There are no rules for composing in new music. In general those rules for composing about which we know come not so much from compositional practice as from the fact that at critical moments models of old music were often used as examples to demonstrate compositional possibilities. Whereas in the past possibilities were demonstrated with the help of earlier examples, now, in the epoch of flourishing sciences we find it much easier in many fields of music to become acquainted immediately with the possibilities themselves rather than with practical indications that might be treated as rules. Hence the comparative lack of rules for composing and their individual treatment (what might toe a rule in the eyes of one composer need not be recognized as such by another). The possibilities of new music then are based not on a system but on direct action. At the present stage of development of musical material and its relationships, the principle of change, already well known in its various aspects, may be acknowledged to be a fundamental canon. It may, naturally, concern very various elements, ranging from the basic material itself to the methods of composition of time.
Examine Examples 615—621 for application of the canons of change. Find in which examples the canon of change is of compositional importance and in which their composers apply variation in the composition of time (here we are concerned mainly with variation in those fields to which composers have not as yet devoted their special attention).
107
e Analyse the foregoing examples thoughtfully. Try to find a) which examples come close to your aesthetics and b) for what reasons the other examples are aesthetically remote from you. Investigate to see if these reasons are associated with the technique of music, its notation, individuality, etc., etc. Find the conditions under which you could turn to the achievements presented in these examples.
Counterindications and prohibitions
The theory of composition, which usually trails behind composition by several decades, moulded not only the formal-technical fundamentals of music but also its rules for many years. Sets of rules and prohibitions, expressing authoritatively what was allowed and what forbidden, were handed down in theory of composition and transferred to the field of practice. The development of music, especially in recent years, has shown clearly how much music owes to those who were able
106 Canons of composing 63
to evade prescriptions and prohibitions, to those who vidually for each particular configuration — this is managed to place music (a music formed according to why we have recourse to so many different aesthetics its autonomous laws emerging only in the course of in this book). composition) above the ever-changing canons. Traditional rules (canons and prohibitions) arise rather from historical data than from direct aesthetic estimation Here we are concerned with the problem of the weight (i.e. observation of the process alone, independent of of counterindications and prohibitions, whether and to what is seemingly known about music). Musical what extent they can be introduced as binding in new practice — in our case compositional work only — music. So far it is known that they are valid only always overcame all sorts of rules and bans, even temporarily and that quite certainly not all of them those which seemed to be the most steadfast. If a man may claim to be steadfast. It is worth emphasizing that cnanges his views and principles in the course of time they result chiefly from diagnosis of the present state as art develops (and this he must do, otherwise he of composition and knowledge of the subject of comaccomplishes nothing), then it is true to an even position. greater extent that art as a whole must undergo changes. Bans are always anachronistic and faultlessness, which seemingly results from their observance, does Analyse Examples 622—629 from the view-points not prove to be as perfect in art as might be supposed. discussed above, giving attention, above all, to faults Faultlessness of this sort is merely common prig- resulting from the disregard of the following fundagishness and will not prevent the composer from mental facts: 1. Contemporary music ought to remain committing far more grievous errors resulting from a product of the composer's aesthetic attitude. 2. Even his inability to imagine art as free, unconstrained the most modern means become conventionalized at play of the imagination rather than the fruits of con- a rate we do not suspect in contemporary art. 3. vention. Rules and prohibitions are conventional: the Although creative consciousness is not of much fallacies of one epoch may and often do become the advantage to the composers of today (the myth that rules of another epoch. Canons and prohibitions estab- there are composers fully conscious of creative action lished in one epoch (or derived from it), then retaining is groundless), much, even very much, can be said validity in the next — what a misunderstanding! The about the composition from the technical point of view destructive effect of such prohibitions is obvious. They after it has been written. Write several compositions, may be of some instructive, not fully aesthetic, purposely demonstrating all the contemporary faults importance, but only in the periods in which they mentioned above. Try to find h o w we can counteract are formed. In new music too, we can distinguish them and how extensive the changes must be to make several such bans (although without any claim to that material acceptable compositionally. permanence). They enlighten us splendidly on the nature of musical composition today. They are by way of example: 1. Avoidance of repetitions (because a repetition is sensible only when it aims to preserve Compose a piece for string quartet (taking about 3 continuity; one need not emphasize that the composer's minutes to perform), entirely eliminating the faults aesthetic taste may be a sufficient criterion in this discussed above. Find — critically — why the mere respect). 2. Avoidance of progression, especially the elimination of faults does not suffice to produce a fully clearly audible regular progression of material. 3. artistic work. Using the same material, freely reAvoidance of full complementarity (the composer should compose the music without thinking constantly about make efforts to attain ever new textural co-situations, correctness within the terms under discussion. Now, textural arrangements in which notes would mean establish exactly what constitutes the value of composisomething more than merely their own ordering). 4. tion which in this respect is spontaneous. Avoidance of the conjecturability of the process (music that we can guess in advance, that might be — even in part — foreseen, is inadmissible). These bans — 108 allowable at present — do not indicate a mode of proper composing (in short, nothing like that exists at all; the propriety of composition is revealed indi- Choice of techniques, antinomies 64
The choice of techniques is a problem in' itself. Till recently composers gave much time to it. Today we know that the choice of techniques is, so to say, automatically connected with the individuality of the composer, that what is more the composer can afford the luxury of taking no notice of this problem, knowing . that each decision is a choice. It is enough to analyse Examples 630—633 from this point of view. In each case we are concerned not only with an individual treatment of music but also with a decision as to the choice of techniques.' Antinomies,, a deliberate play with decisions, constitute a separate problem related to the choice of techniques. Their result is music that cannot be boiled down to decisions and choice despite the fact that the composers, in their own way, make themselves clear. Both examples (634 and 635) show antinomies between the decision concerning the notation of music and its effect. Playing with antinomies is one of the most interesting phenomena in new music.
Both the choice of techniques and antinomies arising from the deliberate opposition to conventions (among these we must number the composers' own habits, in which — whatever may be said about them — they should never take a pride) are problems that demand everybody's genuine consideration. In this matter it is difficult to impose any principles on the composer.
tions before he is able to discipline himself fully. Discipline, exactness, restrictions — they are all important, especially when they are being rejected, when they c a n be rejected. From this section onwards, our thoughts will be directed chiefly to those regions of activity that are based on freedom and independence. If till now we have always had to admit some restrictions as the basis of composing, now, being familiar with the possibilities of music, we can begin thinking of free composition' composition which is not encumbered with the thought, always present hitherto, that one thing should flow from another or that one thing should pass into another. In short we can begin thinking of discontinuous composition. It consists in imposing no restrictions on ourselves. Thus, we do not fix time, instrumentation, texture or any sort of continuity. We base ourselves on the statement, which must by now be capable of bearing fruit at this stage of composition, that music may owe its unity to the very fact that it is composed by one person (it is clear that a piece of music written by many composers would be an ideal of discontinuous music par excellence]). Discontinuous composition is fully illustrated in Example 636, in which beside the initial idea some information is given about the discontinuity within the idea itself.
In Examples 637 and 638 note which elements bear characteristics of discontinuity irrespective of whether the composition examined has an open or "defined" form.
Construct a table fully illustrating your own idea of a composition from the view-point of discontinuous composing. In the form of notes to the table, add several results obtained from the adoption of such an idea.
Examine to -what extent it is possible to speak about the choice of techniques in your past musical production and, in addition, in what measure playing with antinomies appeared in it. Analyse particularly closely the passages of music which, when developed, might form a further link in the evolution of musical ideas.
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109
Automization of composition
Discontinuous composition In contemporary composing the automization of composition forms a separate section. Some of the questions which make up this problem are already known to us; we got to know them in connection with the experiments involving strict (tabular) serialism.
Strict discipline has been a sort of foundation for creative activity for a long time. A composer cannot deal-freely with his material and rise above all restric65
Consequently only a few complementary remarks will be given here. The adoption of a method imposed on material by a system unrelated to it is possible in music. Example 639 teaches us about the effects of a nearly automatic modelling of music using a table of random figures on a table of chords constructed for this particular purpose (version for vibraphone). Adoption of such a method results in the inversion of the precompositional order: the series appears as a r e s u l t of the arrangement of two-note chords instead of these last being a result (or choice) of the control contained in the series. Examples 640—642 illustrate the transposition of non-material ideas into concrete musical material (computer music).
Automization of composition needs a more detailed explanation. A composition produced by automatic acting and, in practice, by the open programming of music seems to be very remote from what we Customarily think of as the essence of music, remote, above all, from the commitment of the composer to his musical work. This is not the case, however. In order to become aware of the true significance of music composed automatically, it should be recalled that a large number of artistic works arise from open action, action in which each compositional component is "exposed" to fortuity, to an appearance without any close motivation. And yet there is no regularity in art although, in some cases, regularity is imposed on it. Whatever we might think of music, it will never be something planned and ordered beforehand, since then we should be concerned with soulless acting, stripped of any of the charms of surprise. The automatic composing process allows as many types of. action as are outlined in this book. It involves "learning from material", becoming more familiar with the potentialities of music than ever before. Experiments in this field are of great cognitive importance and this very fact demonstrates the benefits arising from their application.
Compose a fairly long piece of music basing yourself upon mechanical modelling (uncorrected) on separately constructed tables.
Ill q Aleatorism
In the previous section exactness was shown to be the most essential property of compositional procedure. Its extreme opposite is fortuity. It is however very hard to achieve perfect fortuity (in disciplines that deal with mathematical material one must use special tables of random numbers — Example 643; a true random sequence is unheard of). Music involving the interference of chance in the r e a l i z a t i o n of a composition is defined as aleatory. Aleatorism (Lat. alea—dice; fig. chance, hazard) is not a technique in the strict sense of the word, it is only a method of handling musical material. Examples 644—654 present a survey of problems connected with aleatorism in its very various aspects. Aleatorism allows observation of the function of the variation factor in music. It may concern different elements and techniques: linear motion structures (644), asynchronous temporal process (645), interchangeability of particles within a general form (646), formal freedom of a process (647), temporal approximation (648), approximation in numerous elements (649), underdetermination of succession, attained by means of individual and independent musical actions (650), indefiniteness of the musical text (651), openness in the occurrence of parts in the context (652), proportionment of time (653) and openness of the form treated as a sum of particles (654).
Here I must explain one of the basic misunderstandings that have slipped into new composition: aleatorism i s not improvisation since the latter implies the constancy of a model (melodic or harmonic or more rarely rhythmic), whereas in aleatorism we are concerned with countering structuralism, with the "destructuring" of music. Neither does aleatorism consist in the free interchanging of parts and passages, for this does not at all change the essence of music, which as regards material always remains the same music. The most important feature of aleatorism is the fact that the whole is designed in outline and the details are governed by chance. It should be added that aleatorism must not be regarded as the renunciation of the composer's own ingenuity. Nor should it be censured on the grounds that the composer is reduced to the embarrassing position of being a coauthor of music who has resigned some of his functions in favour of chance. Composing, as far as art is concerned, is admittedly a, very strenuous activity, and the outline of the composition in which we are interest66
ed very often becomes transformed during its moulding into a work which can be related only with difficulty to the composer's original conception. The more the composer occupies himself with the details of the musical material, the less attention he can give to the composition as a whole. Aleatorism — the coding of chosen elements in a shortened manner — affords the opportunity of a better comprehension of the form than ever before and allows the composer to concentrate on the most important factors, which are most often very precisely established or — as has already been said — designed in general outlines but not in details. To leave everything to chance —• as Cage sometimes does — is somewhat risky and too individualistic a method to be repeated and recommended. Compose 6 short musical pieces in which aleatorism is marked by diverse action within different elements. The instrumentation of these compositions: from instrumental trio to large vocal-instrumental ensemble.
112 Composing of co-situations
Examples 655—668 demonstrate various realizations of the elementary principle of equipoise between the vertical and the horizontal structure (classic example' 656).
What is important is the general effect achieved through the co-situation of instruments presented. There is here" a shift of emphasis from material to the architecture of the whole. One can also compose with whole blocks (typical example: 657). These are separated from the whole process by their specific internal structure (Example 660 shows that they can be composed quasiseparately). There is also the possibility of introducing one. general co-situational denominator (Examples 663— 664). Naturally pitch co-situations can be created artificially by an increase in the quantity of material (a method already known to us; Examples 665 and 668), by a graphic representation of relations between parts (666), by an arrangement of vertical configurations according to individual rules (667), an by a reduction of a co-situation to a dynamic factor formed on the basis of proportional relationships between the parts (655). Examine Examples 658—661 and find which of them might be turned into graphic representations (Examples 658 and 659 show the direct conversion of a' musical "specimen" into graphic images). Examples 662—663 illustrate the interdependence of notation and cosituational representation. These examples should be analysed from the view-point of the potential they contain for further complications. It is obvious that a further enrichment would at the same time constitute an impoverishment as regards co-situation. Examine the mechanism of the co-situations in Examples 664— 668, determining exactly t h a t w h i c h is decisive in so far as the. textural effect of the co-situations created.
Examples 655—668 naturally do not cover all co-situational possibilities. These are as numerous in practice as are the possibilities for distinct compositional ideas (of course, neither conventional conceptions nor those based on someone else's models are included). It will be seen from these examples that the composing of co-situations is not confined to the problems of texture. It involves composing in all possible parameters, these having now however lost individual significance. In other words, one does not compose any longer with pitch or rhythm now, but in terms of larger material conceptions against which the elementary parameters appear as material of inferior rank. Let us see Example 655: here neither pitches nor time proportions nor, in the end, the order of the entries of notes is important.
Taking Examples 657—659 as your point of departure, compose a serial (quasi-serial) piece of music using a personal graphic model and a graphic composition (quasi-graphic) using a serial model — naturally a different one. Both compositions are to be for piano.
113 Multihiotivic work The principle of 'thematic (or motivic) unity is not observed by composers in new music and, what is 67
more, this unity seems to be downright undesirable. It is increasingly replaced by multimotivic composition. This resembles fortuity since for its appearance it is necessary that the composer should be familiar with the possibilities arising from' multimotivic presentations of music. Examples 669-612 demonstrate the simplest forms of multimotivic technique and Examples 673—682 show it in various compositional aspects.
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114 Break-up of the model
Permutations, transpositions, serial transformations — all these methods employed in the animation of homogeneous models fail as regards the modern methods of breaking-up material (which follows the pattern established by the splitting of the atom). The most reliable method of splitting an established model is its angular reading, owing to which interrelated pitch and duration changes take place. Example 683a — two-note cell; 683b — three-note group showing an initial temporal symmetry; 683c — similar but temporally asymmetrical group; 683d —• symmetrical four-note group; 683e — similar but asymmetrical group; 683f — six-note group showing large intervals and temporal uniformity; 683g — temporally non-uniform eight-note group. Examples 684—687 illustrate different ways of breaking-up the model: by levelling the pitches with regard to their significance and the angular treatment of the parameter of "speed" in the first three examples and by introducing a graphic point of departure for the arrangement of homogeneous material in the last one.
This technique needs detailed explanation. All new music is, as a rule, multimotivic. This is not the case as regards practice: in most cases musical material, however varied, becomes similar and homogeneous during the progress of a work in defiance of the composer's intentions. In order to prevent this the composer must mould each particle of music — each "motive" —• according to its own individual principles. Example 669 illustrates this activity in an elementary fashion and Example 670 presents music with motives that have become similar,, even though different structural principles lie at the basis of each of them (the fact that parts of the musical process seem to be similar is due to our perception rather than to the composer's activities). Example 671 demonstrates motivic isolation very clearly, but only that which proceeds horizontally. Finally in Example 672 the multimotivic technique consists in the formation of each particle, even a single note, in a different manner. In subsequent examples we The examples presented in this section present posare concerned with some better-developed forms of sibilities which go beyond current ideas on composing. multimotivic composing. It is on these that the com- The first examples (683a-g) deal with variation practice, poser focuses his attention in most cases (typical ex- which is in no way related to the various hitherto amples: 673 and 674; in Example 675 the multimotivic • existing manners of transforming pitch-rhythm monature exists only in parts., but it can be relatively tives. Comparing more and more well-developed easily isolated). Example 676 shows the multimotivic models based on the same structural relationship (structechnique in four individual processes and Examples ture in its abstract sense), we pass to a completely dif677—682 present it in several more aspects: 677 — ferent world of sound ideas. Musical matter remains multimotivic technique in notation; 678 — dispersal of the same structurally. What changes is the point of separate pitches among four associated groups; 679— view from which we look at it and it is this very 680 — separate motives for different instruments, change of point of view that may contribute to the allowing for the specific nature of their timbres and greatest changes in the field with which we are contechnical limitations within the confines of certain cerned, while the break-up of existing schemes, the special situations; 681 — several dozen small motives decomposition of conventions,, presents itself as the which "fnake up" a musical whole. central item in general problems of composing.
Applying the multimotivic technique, compose a piece of music for a large symphonic orchestra treated in a soloistic manner (take as a textural model Example 682).
Compose a fairly long piece for flute using several models in their uniform and non-uniform variants and the angular technique for reading the models (Examples 683a-g). 68
115 Multidimensional composition
i If we keep to one musical dimension,, we create music that is, so well-ordered as on account of this very fact, impoverished. New music provides *us with the possibility of applying the spatial parameter. Different methods of treating music spatially may be employed. They are: the introduction of "topophony" (Example 688 — instruments "reshuffled" according to the plan given in the score), the location .of sound sources in a specific way (Example 689 —• instrumentalists sitting in a semicircle) and the stereophonic presentation of material (in electronic music —• cf., Example 676). It should be added that the phenomenon of self-interpretation of music often occurs in multidimensional compositions. It consists in the music, broken up in space, revealing its material to us in a new form (interpretation), proper to i t s e l f , very much like music transformed by means of a ring modulator during its execution (Example 690). The examples presented suggest that multidimensional composition serves to widen thinking within traditional categories. So far the opinion has been held that music can be either made up of fine elements or — assuming a larger number of parameters as the point of departure — treated in such a way that the whole accumulation of material shall "divide" into fine particles. In postpointillistic techniques this gave rise to many methods which furthermore readily underwent conventionalization. Composing in many dimensions, i.e., handling material in terms of its topophonic and locational relationships, we gain a wider view over m u s i c a l m a t e r i a l i t s e l f . This — it should be mentioned -— ought not to be reduced to a minimum, a process evident in some practices in this field. The potentialities of multidimensional music are enormous and require further compositional work in new fields (modern technology will presumably make further developments of this trend in music possible in the near future).
c Write two short compositions showing topophonic and stereophonic characteristics in their multidimensional qualities (e.g. orchestral music and a design for electronic music).
116 Ambiguous music
Form, in the sense of an architectural design, a construction, does not exist in new music. Naturally, each work has a form, but, thus conceived?' it is only the result of the co-ordination of compositional factors. In this new situation t h | form is not an aim, the composer cannot and does not want to foresee the process prescriptively (as before). On the contrary, he willingly surrenders himself to the charm of free development in music, without determining the composition temporally or architecturally. In order to obtain ambiguity of form (and consequently ambiguity of music), different, accurately established fragments must be put together in> such a manner that, having their place in . the notation, they should not have a fixed place in the development of music. The simplest method of treating music in this way is the disposition of several fragments (perhaps ten or more), the performing of which is left to the discretion of the performer (a simple example: 691). Examples of various forms of ambiguous music: 692—700.
There are no separate techniques for ambiguous music. Here we are more concerned with showing musical ideas that allow for the open treatment of material. The openness of material may involve the free disposition of its particles (as in the elementary examples of this series) and it may also involve a large number of parameters simultaneously (typical examples: 695 and 700). This makes the musical matter still more anonymous and the final musical effect still more enigmatic. From all appearances, the result will not seem serious or concrete enough, for (everybody will say) music ought to be composed of concrete rather than fluid material. It must however be stated that there is already quite a lot of music composed in a concrete manner; on the other hand, we have little information about what happens to musical material when it is given a larger (or improbably large — Example 699) margin of freedom. No doubt activity in the field of ambiguous music contributes to the development of the composer's consciousness, perhaps just because in this case the composer' receives information from controls formed by himself.
Compose two pieces on the principle of ambiguity for one and several instruments, respectively.
117 Multitechnical canons as models
Between the extremes of strictness and freedom we can find models containing both these properties. A typical model of this sort is the multitechnical canon (Example 701).
Multitechnical canons do not cover all the problems of polyphonic composition, but they make a very good example of free and at the same time well-disciplined action. In our example the musical figure which makes up the frequently repeated canonic model is free, whereas the vertical-horizontal handling of the canon is entirely and perfectly disciplined (note that a nearly identical statistical vertical structure appears every fourth section; this is naturally seen more clearly in the passage where a full 36-part vertical complex occurs).
From the example given choose two vertical structures from a place where the material is most dense. Compare them with one another, paying attention to the differences in value in those cases where the same horizontal form occurs at different pitch levels, etc.
closed in a single scheme if other similar schemes are possible and, what is more, if some of them can be, or are, even better than those emerging from our always in some way conditioned decision. -Examples of polyversional music: 702—705. .
Polyversional music in the first place serves to widen the range of information. The closing of a composition within a definite scheme does not fulfil the conditions that we impose on modern music, for then music becomes organized one-sidedly. This occurs to the disadvantage of the composer, especially so .when he could afford to realize many different ideas (furthermore, this is unattainable in practice, since it is difficult to imagine that a composer would like to exclude potentialities inherent in presentation, performance, etc., completely from his work). Composing music in various versions, we are able to penetrate the domains which in the composer's earliest consciousness pass for the most fluid ones. Polyversional music is of greater importance to the composer than it is to its listeners. This however does not lower it in value.
Compose a fragment of a string quartet in 6 different versions, constantly keeping a certain layer of music as an invariable scheme.
119 Composing musical actions
Polyversional music
Music, its course, can be imagined as action in time (Examples 706 and 707; more developed forms: ^OS). Here we compose "along" the time without embarking on decisions that involve its filling-up. The best way of presenting such musical actions is to compose using the musical graphic method (using among other means specially selected musical shorthand writing: Examples 709—711). Examples 712—714 illustrate the method for a graphic representation of music realizable with different material. Thus we gain the constant possibility of renewing substance.
The idea of polyversional music stems from the fact that music itself demands openness, that it cannot be
The composition of musical action carries us over to a realm of action independent of the elementary
Starting from a catalogue of selected means (made precompositionally), compose several different many-part (at least 8-part) multitechnical canons.
118
70
methods of setting music together from particles. This is not the case now: the composer forms something like a catalogue of means which he puts together either as a succession (Examples 706, 707, 708), or more independently of time (a typical example: 711). This means a departure from concretion and an approach to a realm of action unrelated to any order (Examples 713—714 constitute perhaps the most developed model of such composition). Compose a fairly long piece of music in the form of a programme of musical action, leaving (thanks to open graphic representation) a wide margin for filling it with various material.
120 Final remarks
The task of the creative composer is to study the potentialities of music, to detect relations that may occur in its material and, lastly, to produce aesthetic and sound results that have never existed before. This book does not claim to have exhausted the problems inherent in the potentialities of music. This is beyond one person's power. The extent of the possibilities of music is immense and cannot be embraced in one glance. For this reason, having completed this book, the author (apart from the hope that he will be well understood and that what he has to communicate on composition will be helpful to the reader) also entertains the hope that the laborious study of compositional potentialities in music initiated by him will be undertaken by other writers, encouraged by new prospects in this respect. Contemporary conventions are narrow and dull, the new possibilities enormous. One should reach for them, keeping in mind that true art arises from anxiety, from searching.
alphabetical index of examples tne numerals .in parentheses indicate example numbers, e.g., (1) refers to Example 1
A b s i l J e a n Toccata p o u r p i a n o 414 (622d) A m y G i l b e r t Diaphonies p o u r double ensemble de douze i n s t r u m e n t s (Editions H e u g e l & Cie, P a r i s 1965) 99 (140) — Inventions p o u r flute, piano, celesta, h a r p e , v i b r a p h o n e , m a r i m b a (Editions H e u g e l & Cie, P a r i s 1965) 364 (533) A r r i g o G i r o l a m o Quarta occasione p e r c o r o d i 7 voci e 5 s t r u m e n t i ( E d i t o r e A l d o B r u z z i c h e l l i , F i r e n z e 1965) 229 (346) B a r b e r S a m u e l Pieces for p i a n o , N o 3 414 (622a) B a r r a q u e J e a n Sequence p o u r v o i x , b a t t e r i e et d i v e r s i n s t r u m e n t s . T e x t e s e x t r a i t s de „Ecce h o m o " s u i v i des Poesies de F r e d e r i c Nietzsche (Editore Aldo Bruzzichelli, F i r e n z e 1956) 66 ,(61), 84 (107), 98 (137), 110 (164), 128 (199), 167 (256), 357 (520), 373 (551), 415 (624) — Sonate p o u r piano (Editore Aldo Bruzzichelli, Firenze 1953) 83 (105), 102 (146), 330 (462), 443 (671) ' B a r t 6 k B61a Pod gotym niebem (Szabadban), 5 u t w o r 6 w na f o r t e p i a n 349 (501) B e c k e r G u n t h e r stabil-instabil fiir g r o s s e s O r c h e s t e r ( M u s i k v e r l a g H a n s G e r i g , K o l n 1966) 377 (559), 436 (657) B e r g A l b a n Lyrische Suite fiir S t r e i c h q u a r t e t t ( U n i v e r s a l E d i t i o n , W i e n 1927) 43 (23), 63 (55), 158 (229, 232), 166 (255), 171 (260), 172 (262), 227 (342), 232 (354), 247 (380), 329 (457), 342 (489), 344 (493) — Streichquartett o p . 3 ( U n i v e r s a l E d i t i o n , Wien) 360 (527) B e r i o L u c i a n o Circles fiir e i n e F r a u e n s t i m m e , H a r f e u n d 2 S c h l a g z e u g s p i e l e r . T e x t v o n E. E? C u m m i n g s a u s „ P o e m s 1923—1954" ( U n i v e r s a l E d i t i o n , L o n d o n 1961) 73 (79), 154 (219), 211 (309), 304 (418), 341 (486), 359 (525), 409 (609), 418 (630), 444 (674), 466 (706) — Passaggio. M e s s a i n s c e n a di L u c i a n o B e r i o e di E d o a r d o S a n g u i n e t i p e r s o p r a n o , d u e cori e s t r u m e n t i ( U n i v e r s a l E d i t i o n , M i l a n o 1963) 448 (682) — Sequenza V f o r t r o m b o n e solo ( U n i v e r s a l E d i t i o n , L o n d o n 1968) 238 (365) — Sincronie for s t r i n g q u a r t e t ( U n i v e r s a l E d i t i o n , L o n d o n 1964) 72 (76), 232 (353), 345 (496) — Tempi concertati fiir F l o t e , Violine, z w e i K l a v i e r e u n d a n d e r e I n s t r u m e n t e ( U n i v e r s a l E d i t i o n , W i e n 1960) 64 (58), 71, (74), 111 (165), 116 (172), 127 (195), 133 (207), 159 (234), 164 (247), 167 (257), 206 (298), 307 (424), 328 (453), 331 (464), 337 (480), 350 (507), 376 (557), 382 (567), 402 (590), 408 (607), 446 (678) Biel M i c h a e l v o n Quartett fiir S t r e i c h e r ( U n i v e r s a l Edition? L o n d o n 1965) 422 (637) B o o n e C h a r l e s Parallels for v i o l i n a n d p i a n o ( K o m p . , S a n F r a n c i s c o 1964) 69 (69) B o u l e z P i e r r e Don (Pli selon pli. I) p o u r o r c h e s t r e ( U n i v e r s a l E d i t i o n , L o n d o n 1967) 237 (362), 326 (445), 384 (570), 433 (652) — Bclar p o u r 15 i n s t r u m e n t s ( U n i v e r s a l E d i t i o n , L o n d o n 1965) 62 (53) — Improvisation sur Mallarme (Pli selon pli. II), I — „Le v i e r g e , le v i v a c e et le b e l a u j o u r d ' h u i " p o u r s o p r a n o , h a r p e , v i b r a p h o n e , cloches e t 4 p e r c u s s i o n s ( U n i v e r s a l E d i t i o n , L o n d o n 1958) 214 (316)
— Le rnarteau sans maitre p o u r v o i x d ' a l t o et six i n s t r u m e n t s , d ' a p r e s d e s t e x t e s d e R e n e . C h a r (Universal E d i t i o n , L o n d o n 1954) 53 (37), 94 (131), 111 (166), 212 (311), 303 <413), 356 (519), 412 (618), 442 (669, 670) — L e soleil des eaux p o u r s o p r a n o , t e n o r et b a s s e solos, c h o e u r m i x t e et o r c h e s t r e . D e u x p o e m e s d e R e n e C h a r ( E d i t i o n s H e u g e l & Cie. P a r i s 1959) 132 (205), 332 (467), 361 (529), 363 (531), 365 (536), 371 (547), 437 (660), 439 (663) — Le visage nuptial p o u r s o p r a n o , c o n t r a l t o solos, c h o e u r d e f e m m e s et o r c h e s t r e . C i n q p o e m e s d e R e n e C h a r ( E d i t i o n s H e u g e l & Cie, P a r i s 1959) 85 (110) — Sonate II p o u r p i a n o (Editions H e u g e l & Cie, P a r i s 1950) 82 (100), 84 (106), 86 (111), 161 (240), 173 (263), 174 (266), 177 (276), 251 (385), 336 (475), 337 (478) — Structures I p o u r 2 p i a n o s a 4 m a i n s ( U n i v e r s a l Edition, L o n d o n 1955) 54 (41), 68 (66), 93 (129), 108 (158), 122 (187), 123 (188), 250—251 (384), 298 (405), 300 (409), 304 (416, 417), 321 (441), 351 (509), 373 (550), 407 (603) B r a u n P e t e r M i c h a e l 2 Klavierstucke (Thesis/Medium) (Mus i k v e r l a g H a n s G e r i g , K o l n 1968) 72 (78) B r i t t e n B e n j a m i n Holiday Diary f o r p i a n o 414 (622e) B u c z k o w n a B a r b a r a Anekumena. K o n c e r t n a 89 i n s t r u m e n t o w ( K o m p . , K r a k o w 1974) 447 (670) B u s s o t t i S y l v a n o Five Piano Pieces for David Tudor ( U n i v e r s a l E d i t i o n , L o n d o n 1959) 459 (695) — La passion selon Sade. M y s t e r e d e c h a m b r e a v e c T a b l e a u x v i v a n t s , precede de Solo, avec u n couple Rara (dolce) et s u i v i d ' u n e a u t r e P h r a s e a t r o i s p e r voci, s t r u m e n t i e n a r r a t o r e . T e s t o d i L o u i s e L a b e (G. R i cordi & C. S. p . 'A., M i l a n o 1966) 226 (339), 367 (539), 374 t (554), 409 (610), 459 (694) — Memoria con voci e o r c h e s t r e , r a p p r e s e n t a t o in c i n q u e s c e n e : l a — Memoria Marcello Elisei, l b — Per un manifesto antifascista: „Geographie Francaise", He — • Siciliano, H d — Alia bandiera rossa, H e — „La partition ne pent se faire que dans la violence" (Editore A l d o B r u z z i c h e l l i , F i r e n z e 1965) 387 (575), 465 (704), 466 (707), 467 (709) — „mit einem gewissen sprechenderi Ausdruck" fiir K a m m e r o r c h e s t e r ( H e r m a n n M o e c k V e r l a g , Celle 1966) 209 (304), 237 (363), 433 (651), 441 (667), 442 (668), 445 (677) — Sette fogli. Nr 1: Couple p o u r flute et p i a n o ( U n i v e r s a l ' E d i t i o n , L o n d o n 1963) 461 (698) C a g e J o h n Fontana Mix, Aria for a n y v o i c e (C. F . P e t e r s . C o r p o r a t i o n , N e w Y o r k ) 459 (696) — M u s i c of Changes f o r p i a n o , I I (C. F . P e t e r s C o r p o r a t i o n , N e w Y o r k 1961) 89 (118) C a r d e w C o r n e l i u s February Pieces for p i a n o ( H i n r i c h s e n E d i t i o n L t d . , L o n d o n 1962) 464 (703) — Two Books of Study for Pianist ( H i n r i c h s e n E d i t i o n Ltd., L o n d o n 1966) 87 (114), 153 (216) C a s t i g l i o n i Niccolo Alef. K o m p o s i t i o n fiir O b o e (Ars Viva V e r l a g , G m b H , M a i n z 1967) 83 (102) — Gymel p e r f l a u t o e p i a n o f o r t e (Edizioni S u v i n i Zerboni, M i l a n o 1960) 23 (17), 45 (27), 55 (42)
72
— Iriizio di movimenti per pianoforte (Edizioni Suvini Zerboni, Milano 1958) 11 (2), 307 (425) — Movimento continuato per pianoforte e 11 strumenti (Edizioni Suvini Zerboni, Milano 1959) 78 <93), 103 (149), 105 (151), 219 (326), 245 (374), 321 (440), 354 (516), 363 (532) Chou Wen-chung Cursive for flute and piano (C. F. Peters Corporation, New York 1965) 45 (26), 328 (452), 330 (460), 336 (474) — Three Folk Songs for harp and flute (C. F. Peters Corpora-' tion, New York 1950) 12 (3) Clementi Aldo Composizione n. 1 per pianoforte (Edizioni Suvini Zerboni, Milano 1958) 87 (113), 308 (427), 398 (581) — Ideogrammi n. 2: Composizione per flauto e 17 strumenti (Edizioni Suvini Zerboni, Milano 1960) 397 (579), 401 (587), 403 (593), 406 (600), 410 (613) — Reticolo: 11 per undici esecutori (Edizioni Suvini Zerboni, Milano 1968) 422 (638) — Sette scene per orchestra da camera da „Collage", azione musicale in un tempo su materiale visivo di Achille Perilli (Edizioni Suvini Zerboni, Milano 1961) 66 (62), 69 (67), 103 (147), 123 (189), 133 (206), 302 (411), 306 (421), 333 (468), 337 (481), 378 (561), 412 (620) — Triplum. Composizione per flauto, oboe e clarinetto (Edizioni Suvini Zerboni, Milano 1961) 83 (103) Copland Aajon The Cat and the Mouse for piano 414 (622g) Cowell Henry Dixon Tiger for piano (Associated Music Publishers Inc., New York) 338 (482) . .
— Sequences fur Violine und Orchester in vier Gruppen (Universal Edition, London 1959) 104 (150) — Les symphonies de timbres (Universal Edition, London 1958) 95 (132), 358 (522), 375 (555) Hiller Lejaren & Baker R. A. Computer Cantata (Edition Presser, Bryn Mawr 1963) 378 (562) Hiller L. & Baker R. A. Electronic-Study No. 4 (Edition Presser, Bryn Mawr 1963) 426 (641) Hiller L. & Isaacson Leonard Iliac Suite for string quartet. Experimental Music, Experiment No. 3 (Edition Presser, Bryn Mawr 1957) 426 (640) Honegger Arthur Prelude pour piano 414 (622c) Huber Klaus Moteti cantiones fiir Streichquartett (Komp., 1963) 88 (116), 163 (245), 343 (492), 344 (495), 444 (675)
Devoid Natko Structures transparentes fiir Harfe (Musikverlag Hans Gerig, Koln 1967) 407 (606) Donatoni Franco Movimento per clavicembalo, pianoforte e 9 strumenti (Edizioni Suvini Zerboni, Milano 1959) 83 (104), 108 (159), 1.10 (163), 329 (456), 338 (483), 341 (487), 415 (625) Durko Zsolt Psicogramma per pianoforte solo (Editio, Musica, Budapest 1966) 221 (329)
Kagel Mauricio Anagrama fiir vier Gesangsoli, Sprechchor und Kammerensemble (Univarsal Edition, London 1965) 92 (127), 224 (336), 439 (662) — Heterophonie fiir Orchester (Henry Litolff's V e r l a g / C . F. Peters, Frankfurt a. Main 1961) 225 (338) — Sexteto de cuerdas fiir 2 Violinen, 2 Violen, 2 Violoncelli (Universal Edition, London 1957) 102 (145), 103 (148), 116 (171), 120 (184), 124 (191), 161 (237), 196 (284), 230 (348), 307 (426), 321 (439), 328 (454), 364 (534), 404 (596), 412 (619), 418 (631), 437 (659) — Sonant (1960/...) fiir Gitarre, Harfe, Kontrabass und Fellinstrumente (Henry Litolff's Verlag / C. F. Peters, Frankfurt a. Main 1964) 155 (221), 210 (308), 358 (523) — Transicion II fiir Klavier, Schlagzeug und zwei Tonbander (Universal Edition, London 1963) 399 (584) Kayn Roland Signals per orchestra (Edizioni Suvini Zerboni, Milano 1967) 441 (666) Koering Rene Combat T3N fiir Klavier und Orchester (Verlag Ahn & Simrock, Berlin/Wiesbaden 1962) 78 (94), 91 (124), 162 (244), 208 (302), 334 (470), 400 (586) Kopelent Marek Snehah. Komposition fiir Soprano solo, Jazz Altistin (uber Tonband) und Kammerensemble (Edizio Supraphon, Praha / Hans Gerig, Koln 1968) 154 (218) — Streichquartett No. 4 {Musikverlag Hans Gerig, Koln 1970) 416 (626)
Ives Charles The Unanswered Question for orchestra (Southern Music Publishers Co., New York 1953) 109 (161) Jolas Betsy Mots. 7 pieces pour 5 voix solistes et 8 instruments (Editions Heugel & Cie, Paris 1969) 57 (46), 175 (270) — Quatuor II pour soprano colorature, violon, alto et violoncelle (Editions Heugel & Cie, Paris 1969) 407 (605), 411 (615) — Tranche pour harpe seule (Editions Heugel & Cie, Paris 1968) 333 (469) Jongen Joseph •Sarabande pour piano op. 58 414 (622b)
Eloy Jean-Claude Equivalences pour 18 instrumentistes (Editions Heugel & Cie, Paris 1965) 417 (629) Evangelisti Franco Aleatorio per quartetto d'archi (Edition Tones, Darmstadt 1964) 429 (646) Feldman Morton Intervals for bass-baritone voice, v'cello, trombone, vibraphone, percussion (C. F. Peters Corporation, New York 1962) 428 (645), 464 (702) Foss Lukas Echoi for four soloists (clarinet, cello, percussion and piano) (Verlage Carl Fischer, Inc., New York/ B. Schott's Sonne, Mainz 1964) 225 (337), 430 (648), 433 (653) Guyonnet Jacques Polyphonie I pour flute en sol et pianO (Studio A.R.T., Genewa / Universal Edition, Zurich 1963) 52 (36), 54 (40), 70 (73) — Polyphonie II pour deux pianos (Universal Edition, Zurich 1968) 65 (59)
Lampart Zb'igniew Kwartet smyczkowy (Komp., Krak6w 1974) 347 (498) Ligeti Gyorgy Apparitions fiir Orchester (Universal Edition. Wien 1964) 460 (697) — Atmospheres fiir grosses Orchester ohne Schlagzeug • (Universal Edition, Wien 1963) 213 (313), 366 (538), 370 (545)
Haubenstock-Ramati Roman Interpolation. Mobile pour flute (1, 2 et 3) (Universal Edition, Wien 1959) 430 (647) — Jeux 6. Mobile fiir sechs Schlagzeuger (Universal Edition, Wien 1965) 431 (649) — Petite musique de. nuit. Mobile fiir Orchester (Universal Edition, London 1959) 382 (568) 73
— Aventures fur drei Sanger und sieben Instrumentalisten (Henry Litolff's Verlag / C. F. Peters, Frankfurt a. Main 1964) 81 (98), 97 (136), 205 (295), 209 (305), 210 (306), 224 (335), 238 (366), 334 (471), 409 (611), 411 (616) — Konzert fur Violoncello und Orchester (Henry Litolff's Verlag / C. F. Peters, Frankfurt a. Main 1969) 80 (96), 362 (530) — Lux aeterna for 16-part chorus (C. F. Peters, Frankfurt a. Main 1966) 218 (324) — Ramifications for string orchestra or 12 solo strings (B. Schott's Sonne, Mainz 1970) 90 (121) Logothetis Anestis Agglomeration fur Solovioline mit Oder ohne Streicherbegleitung (Universal Edition, Wien 1964) 461 (699) — Mdandros fur Orchester in variabler Besetzung, bis zu 50 Spielern (Universal Edition, Wien 1963) 462 (700) Louvier Alain Etudes pour Agresseurs pour piano, Etude XIII pour 8 agresseurs (Alphonse Leduc, Editions Musicales, Paris 1869) 420 (633) Maderna Bruno Quartetto per archi in due tempi (Edizioni Suvini Zerboni, Milano 1956) 344 (494) Mayuzumi Toshiro Metamusic for piano, violin, saxophone and conductor (C. F. Peters Corporation, New York 1964) 238 (364) — Prelude for string quartet (C. F. Peters Corporation, New York 1964) 217 (320), 343 (491) Mefano Paul Interferences pour 12 musiciens (pour piano, cor et ensemble de chambre) (Editions Heugel & Cie, Paris 1969) 73 (80), 128 (197), 221 (330), 407 (6U4) — Lignes pour voix de basse noble et ensemble de chambre (Editions Heugel & Cie, Paris 1969) 359 (526) Messiaen Olivier CanteyodjayA pour piano (Universal Edition, London 1953) 85 (108), 310 (433) — II de feu II pour piano (Editions Durand & Cie, Editeurs Proprietaires, Paris 1950) 312 (435) — Oiseaux exotiques pour piano solo et petit orchestre (Universal Edition, London 1959) 75 (85), 116 (173), 119 (179), 158 (231), 330 (459), 348 (499), 369 (543), 411 (617), 415 (623) — Vingt regards sur I'Enfant Jesus pour piano (Editions Durand & Cie, Editeurs Proprietaires, Paris 1947) 312 (434, 436), 349 (502, 503) Miroglio Francis Reseaux pour harpe et orchestre (Universal Edition, London 1966) 212 (312) Moran Robert Four Visions for flute, harp and string quartet (Universal Edition, London 1964) 457 (692) Nilsson Bo Ein irrender Sohn fur Altsjimme, Altflote und Orchester. Textfragment von Gosta Oswald (Universal Edition, London 1959) 216 (318), 368 (542), 408 (608), 417 (628) — Quantitaten fur Klavier (Universal Edition, London 1958) 352 (511) Nono Luigi Cantiones a Guiomar fur Sopran solo, 6 stimmigen Frauenchor, 2 Gitarren, Viola, Violoncello, Kontrabass, Schlagzeug und Celesta (Ars Viva Verlag, GmbH, Mainz 1963) 327 (449) —. Con di Didone aus „Le terra promessa" von Giuseppe Ungaretti fur gemischten Chor und Schlagzeug (Ars Viva Verlag, GmbH, Mainz 1959) 162 (242), 218 (323), 331 (465), 358 (521), 376 (558), 397 (580), 419 (632) — II canto sospeso nach Abschiedsbriefen zum Tode ver-
— — — —
urteilter Widerstandskampfer fur Sopran-, Alt- und Tenor-Solo, gemischten Chor und Orchester (Ars Viva Verlag, GmbH, Mainz 1956) 118 (178), 124 (190), 134 (208), 230 (349), 299 (408), 303 (414), 306 (420), 330 (461), 359 (524), 436 (656) La terra e lo compagna. Canti di Cesare Pavese fur Sopran- und Tenor-Solo, Chor und Instrumente (Ars Viva Verlag, GmbH, Mainz 1959) 308 (428) Polifonica-Monodia-Ritmica per 6 strumenti e batteria (Ars Viva Verlag, GmbH, Mainz 1951) 53 (39), 91 (126), 131 (204), 157 (228) Sard dolce tacere. Canto per 8 soli da „La terra a la morte" di Cesare Pavese (Ars Viva Verlag, GmbH, Mainz 1960) 374 (552) Varianti. Musica per violino solo, archi e legni (Ars Viva Verlag, GmbH, Mainz 1957) 226 (340), .301 (410), 401 (588)
Oliveros Pauline Sound Patterns fiir gemischten Chor (Edition Tonos, Darmstadt) 398 (582) Petrassi Goffredo Trio per violino, viola e violoncello (Edizioni Suvini Zerboni, Milano 1960) 92 (128), 117 (176) Pousseur Henri Exercices pour piano {Impromptu et variations II) (Edizioni Suvini Zerboni, Milano) 69 (68), 166 (253), 353 (514) — Madrigal 3 pour clarinette, violon, violoncelle, piano et percussion (Universal Edition, London 1966) 403 (594) — Mobile pour deux pianos (Edizioni Suvini Zerboni, Milano 1961) 368 (541) — Symphonies a quinze solistes (Universal Edition, London 1961) 59 (48), 89 (119), 90 (122), 95 (133), 162 (241), 302 (412), 306 (422), 364 (535), 375 (556), 437 (658), 448 (681) Rands Bernard Action for Six (percussion, percussion, viola, flute, harp and v'cello) (Universal Edition, London 1965) 458 (693) Reynolds Roger The Emperor of Ice Cream for 8 voices, piano, percussion and double bass (C. F. Peters Corporation, New York 1963) 468 (710) Rieti Vittorio Due studi per pianoforte 414 (622f) Schaffer Boguslaw Artykulacje na fortepian (Polskie Wydawnictwo Muzyczne, Krak6w 1960) 153 (217) — Collage and Form for eight jazzmen and orchestra (PWM, Krak6w 1965) 55 (43), 109 (162), 122 (186), 360 (528), 369 (544), 372 (548), 385 (572), 404 (595) — Concerto per sei e tre na zmienny instrument solowy i 3 orkiestry (PWM, Krak6w 1863) 156 (226), 228 (345), - 231 (351), 236 (361), 336 (476) — Course ,J" na zespol jazzowy i filharmoniczny (PWM, Krak6w 1964) 119 (181), 205 (296), 219 (325) — Equivalenze sonore per 20 esecutori (PWM, Krakow 1962) 51 (33), 52 (35), 56—57 (45), 70 (71), 74 (82), 76 (87, 88), 79 (95), 91 (123), 99 (139), 117 (175), 125 (192), 130 (203), 207 (299) — ..extreme" fiir 10 Instrumente (Verlag Ahn & Simrock. Berlin/Wiesbaden 1962) 203 (292), 401 (589) — Free Form I for five instruments (Komp., Krak6w 1972) 470 (713) — 4HI1P fiir Klavier fur vier Hande (Verlag Ahn & Simrock, Berlin/Wiesbaden 1966) 70 (72), 108 (157), 126 (194), 327 (446), 413 (621)
74
— Imago viusicae f u r Violine solo m i t i n t e r p o l i e r e n d e r I n s t r u m e n t e n b e g l e i t u n g (Verlag A h n & S i m r o c k , B e r l i n / / W i e s b a d e n 1963)' 62 (54), 71 (75), 126 (193), 233 (356), 236 (360), 453 (686) — Kody n a orkiestre. k a m e r a l n a . ( K o m p . , K r a k 6 w 1961) 204 (293) — Kompozycja n a f o r t e p i a n ( P W M , K r a k o w 1960) 283 (394) — Kompozycja swobodna n a f o r t e p i a n ( P W M , K r a k o w 1960) 342 (488) — Koncert skrzypcowy ( P W M , K r a k o w 1965) 76 (86), 230 (350), 335 (472), 387 (574), 405 (599) — Konfiguracje n a f o r t e p i a n ( P W M , K r a k 6 w 1960) 351 (510) — Kontury n a f o r t e p i a n ( P W M , K r a k 6 w 1960) 400 (585) — Model I n a f o r t e p i a n ( P W M , K r a k o w 1960) 47—48 (29) — Model II n a f o r t e p i a n ( P W M , K r a k 6 w 1960) 177 (275) — Modell III f u r K l a v i e r ( V e r l a g A h n & S i m r o c k , B e r l i n / / W i e s b a d e n 1963) 223 (332), 309 (429), 352 (512) — Monosonata p e r 24 a r c h i ( P W M , K r a k 6 w 1960) 63 (56), 198 (289), 235 (359), 331 (463) — Montaggio p e r sei e s e c u t o r i ( P W M , K r a k 6 w 1962) 177 (274), 371 (546), 440 (665) — Music for Ml n a w i b r a f o n , glos, 6 r e c y t a t o r 6 w , zespol jazzowy i orkiestre. ( P W M , K r a k o w 1968) 422 (636) — Musica ipsa n a orkiestre. n i s k i c h i n s t r u m e n t 6 w ( P W M , K r a k o w 1965) 416 (627), 435 (655), 443 (672), 455 (689) — Non-stop n a f o r t e p i a n ( P W M , K r a k o w 1960) 468 (711) — Open M u s i c for a n y i n s t r u m e n t or v o i c e ( K o m p . , K r a k 6 w 1975) 471 (714) — Permutationen f u r 10 I n s t r u m e n t * ( V e r l a g A h n & S i m rock, B e r l i n / W i e s b a d e n 1964) 101 (143), 134—135 (209), 211 (310) — Quattro movimenti p e r pianoforte e orchestra (PWM, K r a k 6 w 1960) 43 (22), 46 (28), 49 (30), 58 (47), 83 (101), 93 (130), 117 (174), 118 (177), 120 (183), 172 (261), 196 (285), 309 (432) — S'alto n a s a k s o f o n a l t o w y i solistyczna. orkiestre. k a m e ralna. ( P W M , K r a k 6 w 1965) 155 (222), 207 (300, 301), 219 (327), 223 (333), 229 (347), 428 (644), 446 (679) — Scultura. Mala syrnfonia ( P W M , K r a k 6 w 1967) 67 (64), 121 (185), 129 (201), 206 (297), 227 (341), 233 (357), 239 (367), 305 (419), 386 (573), 432 (650), 463 (701) — Sinfonie in 9 T e i l e n ( V e r l a g A h n "& S i m r o c k , B e r l i n / . / W i e s b a d e n 1973) 469 (712) — Streichquartett (Verlag A h n & Simrock, Berlin/Wiesbaden 1966) 12 (4), 72 (77), 74 (81), 77 (90), 128 (200), 154 (220), 155 (223), 160 (236), 210 (307), 224 (334), 346 ( 4 9 7 V 402 (591), 406 (601), 453 (685) — Studium poUekspresyjne na fortepian (PWM, KrakoW 1960) 444 (673) • — Studium poliformalne n a f o r t e p i a n ( P W M , K r a k o w 1960) 456 (691) — S t u d i u m poliwersjonalne na fortepian (PWM, K r a k o w 1960) 197 (287) — Studium w diagramie n a f o r t e p i a n ( P W M , K r a k 6 w 1960) . 199 (290), 200 (291) — Syrnfonia elektroniczna ( P W M , K r a k o w 1968) 80 (97), 379 (563), 445 (676) — Tertium datur. T r a k t a t k o m p o z y t o r s k i n a k l a w e s y n i ins t r u m e n t y ( P W M , K r a k o w 1962) 465 (705), 467 (708) — Topofonieo n a 40 i n s t r u m e n t 6 w ( P W M , K r a k o w 1962) 160 (235), 215 (317), 335 (473), 380 (564), 454 (688) — 8 utworow n a f o r t e p i a n ( P W M , K r a k o w 1960) 44 (25), 50 (32), 91 (125), 193 (280), 410 (612)
— 2 utwory n a s k r z y p c e i f o r t e p i a n ( P W M , K r a k o w 1965) 240 (369), 434 (654) — 4 utwory n a t r i o s m y c z k o w e ( P W M , K r a k o w 1963) 77 (89), 120 (182), 217 (321), 227 (344), 232 (352), 309 (430), 327 (448), 453 (684) S c h n e b e l D i e t e r Glossolalie fur S p r e c h s t i m m e n u n d I n s t r u m e n t ? ( K o m p . , B a d H o m b u r g ) 398 (583) S c h o n b e r g A r n o l d 3 Klavierstiicke o p . 11 ( U n i v e r s a l E d i t i o n , W i e n 1910) 156 (224), 157 (227) 158 (230), 165 (250, 252), 227 (343), 349 (500), 351 (508) — 6 kleine Klavierstiicke o p . 19 ( U n i v e r s a l E d i t i o n , W i e n 1913) 130 (202), 165 (251), 174 (265), 247 (381), 356 (518) — Phantasy for v i o l i n w i t h p i a n o a c c o m p a n i m e n t o p . 47 (C. F . P e t e r s C o r p o r a t i o n ; N e w Y o r k 1952) 64 (57) S t o c k h a u s e n K a r l h c i n z Nr. y Kreuzspiel f u r Oboe, Bassklarinette, K l a v i e r und Schlagzeug (Universal Edition, L o n d o n 1960) 43 (24), 49 (31), 51 (34), 61 (52), 69 (70), 101 (144) — Nr. 1 Kontra-Punkte ftir O r c h e s t e r ( U n i v e r s a l Edition, L o n d o n 1953) 53 (38), 89 (120), 98 (138), 107 (154), 159 (233), 214 (315), 297 (404), 298 (406), 365 (537) — Nr. 2 Klavierstiick II ( U n i v e r s a l E d i t i o n , L o n d o n 1954) 74 (84), 85 (109), 128 (198), 174 (267), 403 (592) — Nr. 2 Klavierstiick II ( U n i v e r s a l E d i t i o n . L o n d o n 1954) 148 (213), 161 (238) —; Nr. 2 Klavierstiick III ( U n i v e r s a l E d i t i o n , L o n d o n 1954) 298 (407) — Nr. 2 Klavierstiick IV ( U n i v e r s a l E d i t i o n , L o n d o n 1954) 107 (156) — Nr. 3 Elektronische Studien. Studie II ( U n i v e r s a l Edition, L o n d o n 1956) 241—242 (370), 453 (687) — Nr. 4 Klavierstiick IX ( U n i v e r s a l E d i t i o n , L o n d o n 1967) 166 (254) -r- Nr. 4 Klavierstiick X ( U n i v e r s a l E d i t i o n , L o n d o n 1967) 352 (513) — Nr. 5 Zeitmasse f u r fiinf H o l z b l a s e r ( U n i v e r s a l E d i t i o n , L o n d o n 1957) 65 (60), 68 (65), 86 (112), 88 (115), 97 (135), 107 (155), 112 (168), 148 (214), 196 (286), 217 (319), 218 (322), 246 (378), 337 (479), 373 (549), 374 (553), 381 (566), 404 (597), 405 (598), 421 (635) — Nr. 6 Gruppen fur drei Orchester (Universal Edition, L o n d o n 1963) 127 (196), 325 (443), 327 (447), 332 (466), 381 (565), 383 (569), 438 (661) — Nr. 9 Zyklus fur einen Schlagzeuger (Universal Edition, L o n d o n 1961) 406 (602), 420 (634) — Nrt. 16 | Mixtur ftir O r c h e s t e r , S i n u s g e n e r a t o r e n u n d R i n g m o d u l a t o r e n ( U n i v e r s a l E d i t i o n , W i e n 1968) 208 (303), 239 (368), 243 (371), 385 (571), 456 (690) S t r a w i n s k i I g o r L e s a c r e du printemps. T a b l e a u x de la r u s s i e p a i e n n e e n d e u x p a r t i e s (Edition R u s s e d e M u s i q u e , 1921 / Boosey & H a w k e s M u s i c P u b l i s h e r s Ltd., L o n d o n ) 67 (63) W e b e r n A n t o n 6 Bagatellen f u r S t r e i c h q u a r t e t t o p . 9 (Univ e r s a l E d i t i o n , W i e n 1924) 164 (249), 342 (490) — Konzert fur Fldte, Oboe, Klarinette, Horn, Trompete, P o s a u n e , Geige, B r a t s c h e u n d K l a v i e r op. 24 ( U n i v e r s a l E d i t i o n , W i e n 1948) 11 (1), 77 (91), 171 (259), 253 (387, 388), 254 (389), 336 (477), 341 (485) —• Quartett fur G e i g e , K l a r i n e t t e , T e n o r s a x o p h o n u n d K l a - v i e r op. 22 ( U n i v e r s a l E d i t i o n , W i e n 1932) 78 (92), 307 (423), 377 (560) — 5 Sdtze fur S t r e i c h q u a r t e t t op. 5 (Universal Edition W i e n 1922) 396 (578), 410 (614) 75
— Streichtrio op. 20 (Universal Edition, Wien 1925) 100 (142), 106 (153), 173 (264), 246 (377), 329 (455) — 5 Stiicke fiir Orchester op. 10 (Universal Edition, Wien 1923) 214 (314), 329 (458), 354 (515) — Variationen fiir Klavier op. 27 (Universal Edition, Wien 1937) 350 (504, 505, 506) ' — Variationen fiir Orchester op. 30 (Universal Edition, Wien 1956) 252 (386) Welin Karl-Erik No 3 • 1961 per 9 strumenti (Verlag Ahn & Simrock, Paris/Wiesbaden 1961) 220 (328), 328 (451) Wolff Christian Suite I for prepared piano (C. F. Peters
Corporation, New York 1963) 96 (134), 108 (160), 162 (243) 175 (271), 222 (331), 247 (379) Xenakls Yannis Achorripsis fiir 21 Instrumente (Bote & Bock Verlag, Berlin 1958) 100 (141), 112 (167), 135 (210), 232 (355), 325 (444) — Pithoprakta fur Orchester von 50 Instrumenten (Boosey & Hawkes Music Publishers Ltd., London 1957) 234 (358), 427 (642), 440 (664) — ST/10-1, 080262 for 10 instruments (Boosey & Hawkes Music Publishers Ltd., London 1967) 367 (540)
