A term used in music on the basis of its use in probability theory, where it applies to a system producing ‘a sequence of symbols (which may… be letters or musical notes, say, rather than words) according to certain probabilities’ (Weaver, p.267). The term (from Gk. stochos: ‘goal’) means in modern parlance ‘random’. A stochastic process operates on a family of random variables which is indexed by another set of variables with compatible probability of distribution. A stochastic process particularly appropriate to music is the Markov process. In this the probabilities at any one point depend on the occurrences of events so far; the process thus contains a high degree of uncertainty in its initial stages, an increasing certainty as events unfold, and a high degree of determinacy in its closing stages.
The principal user of stochastic processes in musical composition has been Iannis Xenakis, who uses them to determine such elements as durations, speeds and ‘intervals of intensity, pitch, etc.’ (1963, p.13), particularly when he is composing with ‘clouds’ or ‘galaxies’ of sounds in which very large numbers of events are present. The idea of the stochastic process also appears in the musical application of Information theory, and forms an important part of the aesthetic theory of Leonard B. Meyer, who sees music as a Markov process or chain.
See also Analysis, §II, 5.
W. Weaver: ‘Recent Contributions to the Mathematical Theory of Communication’, Etc.: a Review of General Semantics, x (1953), 261
I. Xenakis: Musiques formelles (Paris, 1963, 2/1981; Eng. trans., 1971, enlarged 2/1992)
L.B. Meyer: Music, the Arts, and Ideas: Patterns and Predictions in Twentieth-Century Culture (Chicago, 1967, 2/1994)
K. Jones: ‘Compositional Applications of Stochastic Processes’, Computer Music Journal, v/2 (1981), 45–61; repr. in The Music Machine, ed. C. Roads (Cambridge, MA, 1989), 381–98
I. Xenakis: ‘More through Stochastic Music’, Computer Music Conference: Montreal 1991, 517–18