Algorithmic Composition Using Max MSP

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Max MSP Musings

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2006 International Workshop on Computer Music and Audio Technology

THE APPLICATIONS OF SIEVE THEORY IN ALGORITHMIC COMPOSITION USING MAX/MSP AND BASIC Duarte, Jose*, Hsiao, Shu-Chin**, Huang, Huan g, Chih-Fang***, and Winsor, Phil****

Music Institute of National Chiao Tung University 1001 Ta Hsueh Road, Hsin Chu, Taiwan 300, ROC * [email protected] [email protected],, **[email protected] **[email protected],, *** [email protected] [email protected],, **** [email protected]

ABSTRACT

The following paper compares tools used at the Music Institute of National Chiao Tung University to generate Sieves based on Xenakis Theory. Also reveals the importance of continuous research in the area of algorithmic composition. The comparison between BASIC language and MAX (cycling 74) will show how the development of the research and teaching techniques of the institute. Also at the end remarks the necessity of the use of new platforms using a different approach like the case of athenaCL developed at the New York University.

1. INTRODUCTION

Since 1989 Music Institute of National Chiao Tung University has been developing applications and methodology to compose music algorithmically. In this paper we will discuss di scuss the Sieve Si eve Theory and two examples of its application utilizing MAX and BASIC. The importance of this comparison is part of an effort to define the direction of the Algorithmic composition education in the Institute and part of an evaluation of the software applications available. The use of Sieve Theory represent a very important exercise in algorithmic composition at a very basic level, allowing the user to start dealing with mathematical

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2. BASIC APPLICATIONS IN ALGORITHMIC COMPOSITION

BASIC is a programming language ideal for first level Algorithmic composition courses. It provides a friendly environment to work with, and resources of information are all spread out in libraries and in the Internet. As a composition tool, it is also useful in the generation of Sieves. Xenakis even used BASIC to compile the first Sieve generator. BASIC is applied to deal with musical concepts like pitch classes, transposition, inversions, rhythmic values and so on. For more information see Winsor’s Automated Music Composition [1], where many topics can be found like examples of programs dealing from simple transposition of pitch classes to the generation of Fibonacci series and fractal patterns.

3. XENAKIS SIEVE THEORY

Proposed originally in 1964, During Xenakis staying at Berlin from the fall of 1963 to the spring of 1964. During this time, he developed Sieve Theory further [2]. Sieves output numerical sequences that can be translated to musical and sound events such as pitches, time points, dynamics, densities, degrees of order, local timbres, etc. [3]. In the search of symmetry in musical figures, Xenakis

A tutorial on MaxMSP

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Magazines might want, and inversely, to retrieve from a given series of events or objects in space or time the symmetries that constitute the series. We shall call these series “Sieves” Documents

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Max MSP Musings

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[3]. Sheet Music

6, 8, 10…}. The next table will show more examples of the operands: MRC1 {0, 1, 2, 3} {0, 1, 2, 3} {0, 1, 2, 3}

AND OR NOT

MRC2 {-2,0, 2,4} {-2,0, 2,4} {-2,0, 2,4}

RESULT {-2,0,1,2,3,4 } {0,2} {-2, 1, 3}

The operand “Or” will display all the values that both sets have in common. In the case of {0, 1, 2, 3}OR {-2,0, 2,4}={0,2} On the other side, operand “Not” will output the values that both sets do not have in common: {0, 1, 2, 3}NOT{-2,0, 2,4}={-2, 1, 3} The generation of Sieves allows the composer to create musical pieces based on new rules and also represents a great tool for developers to program automated composition software. FIGURE 1: Mycenae Alpha(UPIC Graphic/Computer) composing By Xenakis

Sieve is analogous to scale in music, and Xenakis makes emphasis that it is not a mode. The idea of this theory is to generate scales (if we are dealing with pitch), generate rhythmic patterns (if we are working with rhythm) and so on. Sieves are composed by a sequence of integers (in the case of scales) and the interval between each value. This interval is called the modulo. A Sieve can be defined as MRC, in which RC stands for the residual class, or the starting point of the scale and M will be the modulo. To be more detailed RC is where the pitch class begins, RC= 0 starts from C, then RC=1 will start from C#, etc. The modulo determines the constant interval between the elements of the class. For example, RC=0 and M=1 or 1 0 = {…-2, -1, 0, 1, 2, 3, 4, 5…} will output a Chromatic scale starting from C like this: C, C#, D, D#, E, F, F# and so on. For modulo 2, Whole-tone scale is generated: 2 0= C, D, E, F#, G#, A#… (Or 20= {0, 2, 4, 6, 8, …} Other combinations are possible. We only need to follow these restrictions: modulus can be any positive integer greater than 0 (M>0); RC, for a given modulus M, can be any integer between 0 and M-1 (0
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4. APPLICATIONS OF SIEVE THEORY

Going back to BASIC, an example to generate music scales will be shown, as well for MAX examples of patches for scales and rhythmic patterns. Different software is available to generate sounds from BASIC programs one example is Music Sculptor (Winsor & Kuo-Lung Chang). To accomplish this task Sculptor will out a MIDI file and provide a music score. But first let see the code to generate a Sieves for different known scales:

FIGURE 2: QBASIC Interface


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Max MSP Musings

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THEN PRINT P$(X);" "; ELSE 2050 2045 PRINT #1, NOTEON;X;VELOCITY; ARTDUR;CHANNEL Documents 2046 NOTEON=NOTEON+DURATION 2050 NEXT X Sheet Music 2060 RETURN Previous example shows how to calculate the Major Scale Sieve. Line 2040 can be read as “if x mod 3 is not equal to 2 and X mod 4 is equal to 0, or if X mod 3 is not equal to 1 and X mod 4 is equal to 1, or if X mod 3 is equal to 2 and X mod 4 is equal to 2, or if X mod 3 is not equal to 0 and X mod 4 is equal to 3 then X passes the test.”[1] Then the execution of the program will show the major scale: Enter number of background scale elements: 12 Enter scale type: (1=major, 2=harm. Minor, 3=pentatonic) ? 1 C1 D1 E1 F1 G1 A1 B1

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FIGURE 4: Music Sculptor (Phil Winsor & Kuo-Lung Chang) Interface.

Regarding Max software (Cycling 74), there are several ways to implement a Sieve analysis. The Max predefined objects allow users in different ways to produce several sequences. In Figure 5 we can visualize one example to generate sieves using Max Objects. The real time capabilities of this platform permit the user to modify the parameters of the modulo and the residual class

Now, after the generation of any Sieve (in this case the Sieve corresponding to a Major Scale) we can transport the file to Music Sculptor. See Figure 2 and then if needed save a MIDI file to display a music Score, to be imported by Music Sculptor as shown in Figure 3. Figure 4 shows that the program generated pitch data, saved as “pitch.dat”, can be loaded from Music Sculptor, to compose the music piece automatically by the sieve algorithm. Many other sieves can be generated using the same procedure; there are many combinations yet to be discovered.

FIGURE 5: Sieve Implementation Using MAXMSP

while playing the sequence. In addition, predefined presets may change several parameters at the same time. On the other side, different variables can be added to form part of the patch, for example: Metro and Random objects, influencing the sound event by changing the distance between the “noteon” and “noteoff” or by modifying the order of the attacks respectively. Max, apart of being a great tool to design patches, it


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serial music based on the sieve theory using the MAX internal objects, as shown in Figure 7.

more about this implementation see Xenakis, Formalized Music [3]. Another more recent application is the one developed by Christopher Ariza (Graduate School of Arts and Sciences, New York University), which is an objectoriented model and Python implementation [5]. This model is executed using a bigger platform called “athenaCL”, which is an open-source, interactive command-line environment for algorithmic composition in Csound and MIDI [5]. The work of Ariza will represent a great deal of new and easier ways to deal with Sieve theory and other Algorithmic composition areas. For more information see athenaCL User’s guide. [7]

FIGURE 6: Twelve Tone Matrix for Sieve Theory Serial Music Composition Using M AX /MSP 6 . REFERENCES

[1] Winsor, Phil, “Automated music composition”, University of North Texas. 1989. [2] Barthel-Calvet, A. S., “Chronologie.” In F. B. Mache, ed. Portrait(s) de Iannis Xenakis. Paris: Bibliotheque Nationale de France, pp. 133–142, 2001.

FIGURE 7: Sieve Theory for Twelve Tone Serial Music Composition Using M AX /MSP

[3]

Xenakis, Iannis, “Formalized Music Pendragon revised revision, 1990.

[4]

Solomos, M., “Xenakis’ Early Works: From ‘Bartokian Project' to 'Abstraction'," Contemporary Music Review 21(2-3): pp. 21-34.’, 2002.

[5]

Ariza, Christopher. The Xenakis Sieve as Object: A New Model and a Complete Implementation. New York University. Computer Music Journal.

[6]

Joseph N. Straus, “Introduction to Post-Tonal Theory”, Prentice-Hall International UK Limited, pp. 118-146, 1990.

5. CONCLUSION

After showing two examples of Sieve Applications a wider panorama appeared. The ways of experimentation in the topic vary in time, and others remain because of their success. This is the example of BASIC language, which provides ways to implement many musical-based concepts; in this case the Sieve Theory can be studied and analyzed. On the other side, Max software (Cycling 74), shows a different perspective. The comparison of different set of sieves is done thanks to its capabilities of real time parameter settings. In other words, this characteristic

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Tutorial”,

[7] Ariza, Christopher, “AthenaCL User Guide”, Second Edition, Version 1.4.3.

Algorithmic Composition Using Max MSP

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