designs and space exploration, and several films.” 16 It premiered at the University of Illinois, Urbana-Champaign, in 1969. Summarizing perspicaciously an essential difference between traditional and computer-assisted composition, Cage said in an interview during the composition of HPSCHD, “Formerly, when one worked alone, at a given point a decision was made, and one went in one direction rather than another; whereas, in the case of working with another person and with computer facilities, the need to work as though decisions were scarce—as though you had to limit yourself to one idea—is no longer pressing. It’s a change from the influences of scarcity or economy to the influences of abundance and— I’d be willing to say—waste.” 3

Stochastic versus deterministic procedures. A basic historical division in the world of algorithmic composition is between indeterminate and determinate models, or those that use stochas-tic/random procedures (such as Markov chains) and those where results are fixed by the algorithms and remain unchanged no matter how often the algorithms are run. Examples of the latter are cellular automata (though they can be deterministic or stochastic34); Lindenmayer Systems (see the section on the deterministic versus stochastic debate in this context); Charles Ames’s constrained search algorithms for selecting material properties against a series of constraints1; and the compositions of David Cope that use his Experiments in Musical Intelligence system. 10 The latter is based on the con-

Figure 3. Simple L-System rules.

1 → 2 3

2 → 1 3

3 → 2 1

Figure 4. Step-by-step generation of results from simple L-System rules and a seed.

seed: 2
1 3
2 3 | 2 1
1 3 | 2 1 | 1 3 | 2 3
2 3 | 2 1 | 1 3 | 2 3 | 2 3 | 2 1 | 1 3 | 2 1

Algorithmic
composition is often
viewed as a sideline
in contemporary
musical activity,
as opposed to a
logical application
and incorporation
of compositional
technique into
the digital domain.

cept of “recombinacy,” where new music is created from existing works, thus allowing the recreation of music in the style of various classical composers, to the shock and delight of many.

Xenakis. Known primarily for his instrumental compositions but also as an engineer and architect, Iannis Xenakis was a pioneer of algorithmic composition and computer music. Using language typical of the sci-fi age, he wrote, “With the aid of electronic computers, the composer becomes a sort of pilot: he presses buttons, introduces coordinates, and supervises the controls of a cosmic vessel sailing in the space of sound, across sonic constellations and galaxies that he could formerly glimpse only in a distant dream.” 40

Xenakis’s approach, which led to the Stochastic Music Programme (henceforth SMP) and radically new pieces (such as Pithoprakta, 1956), used formulae originally developed by scientists to explain the behavior of gas particles (Maxwell’s and Boltzmann’s Kinetic Theory of Gases). 31 He saw his stochastic compositions as clouds of sound, with individual notesj as the analogue of gas particles. The choice and distribution of notes was determined by procedures involving random choice, probability tables weighing the occurrence of specific events against those of others. Xenakis created several works with SMP, often more than one with the output of a single computer batch process,k probably due to limited access to the IBM 7090 he used. His Eonta (1963–1964) for two trumpets, three tenor trombones, and piano was composed with SMP. The program was applied in particular to the creation of the massively complex opening piano solo.

Like another algorithmic composition and computer-music pioneer, Gottfried Michael Koenig (1926–), Xenakis had no compunction adapting the output of his algorithms as he saw fit. Regarding Atrées (1962), Xenakis’s biographer Nouritza Matossian claims Xenakis used “75% computer material, j Notes are a combination of pitch and duration, rather than just pitch.