tion Acoustique/Musique in Paris, is available within the now more widely used computer-music systems Max/ MSP and Open-Music. OMAX uses AI-based machine-learning techniques to parse incoming musical data from human musicians, then the results of analysis to generate new material in an improvisatory context. 2

slippery chicken. In my own case, work on the specialized algorithmic composition program slippery chicken13 is ongoing since 2000. Written in Common Lisp and its object-oriented extension, the Common Lisp Object System, it is mainly deterministic but also has stochastic elements. It has been used to create musical structure for pieces since its inception and is now at the stage where it can generate, in a single pass, complete musical scores for traditional instruments or with the same data write sound files using samplesp or MIDI file realiza-tions of the instrumental score.q The project’s main aim is to facilitate a melding of electronic and instrumental sound worlds, not just at the sonic but at the structural level. Hence certain processes common in one medium (such as audio slicing and looping) are transferred to another (such as the slicing up of notated musical phrases and instigation of sub-phrase loops). Also offered are techniques for innovative combination of rhythmic and pitch data, which is, in my opinion, one of the most difficult aspects of making convincing musical algorithms.

Lindenmayer systems. Like writing a paper, composing music, especially with computer-based algorithms, is most often an iterative process. Material is first set down in raw form, only to be edited, developed, and reworked over several passes before the final refined form is achieved. For the composer, stochastic procedures, if not simply to be used to generate material to be reworked by hand or in some other fashion, represent particular problems. If an alteration of the algo-

Figure 6. Fibonacci-based transition from material 0 to material 1. note the first appearance of 1 is at position 13, with the next eight positions after that, the next again five positions after that, and so on; all these numbers are so-called Fibonacci numbers.

0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1
1 1 1 1 1 1

Figure 7. Extract beginning bar 293 of the author’s Tramontana for viola and computer.

Figure 8. Foreground melodic pattern (scale steps) of Désordre. 26

Right hand (white notes), 26 notes, 14 bars Phrase a: 0 0 1 0 2 1-1 Phrase a’: - 1 -1 2 1 3 2 -2 Phrase b: 2 2 4 3 5 4-1 0 3 2 6 5

Left hand (black notes), 33 notes, 18 bars Phrase a: 0 0 1 0 2 2 0 Phrase a’: 1 1 2 1-2- 2-1 Phrase b: 1 1 2 2 0-1-4-3 0-1 3 2 1-1 0-3-2- 3 -5

rithm is deemed necessary, no matter
how small, then rerunning the proce-
dure is essential. But rerunning will
generate a different set of randomly
controlled results, perhaps now lack-
ing some characteristics the compos-
er deemed musically significant after
the first pass.r
Deterministic procedures can be
more apposite. For instance, Linden-
mayer Systemss (henceforth L-Systems)
whose simplicity and elegance yet re-
p Samples are usually short digital sound files
of individual or arbitrary number of notes/
sonic events.

r This is a simplistic description. Most stochastic procedures involve encapsulation of various tendencies over arbitrarily large data sets, the random details of which are insignificant compared to the structure of the whole. Still, some details may take on more musical importance than intended, and losing them may detrimentally affect the composition. The composer could avoid such problems by using a random number generator with fixed and stored seed, guaranteeing the pseudo-random numbers are generated in the same order each time the process is restarted. Better still would be to modify the algorithm to take these salient, though originally unforeseen features, into account.

s Named for biologist Aristid Lindenmayer (1925–1989) who developed this system (or formal language, based on grammars by Noam Chomsky33) that can model various natural-growth processes (such as those of plants).

sulting self-similarity make them ideal for composition. Take a simple example, where a set of rules is defined and associates a key with a result of two further keys that in turn form indices for an arbitrary number of iterations of key substitution (see Figure 3).

Given a starting seed for the lookup and substitution procedure (or rewriting, as it is more generally known), an infinite number of results can be generated (see Figure 4).

Self-similarity is clear when larger result sets are produced; see Figure 5, noting the repetitions of sequences (such as 2 1 1 3 and 2 3 2 3). These numbers can be applied to any musical parameter or material, including pitch, rhythm, dynamic, phrase, and harmony. Seen musically, the results of such simple L-Systems tend toward stasis in that only results that are part of the original rules are returned, and all results are present throughout the returned sequence. However, the result is dependent on the rules defined: subtle manipulations of more com-plex/numerous rules can result in musically interesting developments. For instance, composers have used more finessed L-Systems—where the result