Stochastic music controls broad statistical properties of a piece rather than specifying individual events exactly

In stochastic composition (pioneered by Iannis Xenakis from the 1950s), probability distributions govern the selection of musical events. Rather than producing random music in a pejorative sense, the composer controls distribution parameters: choosing which notes are more likely, how dense events are, what spread of duration is used. Distributions can be uniform, Gaussian, beta, or any function. A key insight: stochastic methods do not lose compositional control but shift it to a higher level of abstraction, defining character through statistical shape. The cumulative distribution function maps a uniform random number in [0,1] to the desired distribution. Stochastic music is related to information theory: equal-probability distributions maximise entropy while heavily biased ones reduce it.

Examples

Xenakis’ Metastasis (1954) used statistical mechanics to shape cloud textures. The beta distribution allows asymmetric probability shapes between 0 and 1. Pink noise (1/f) is often cited as a good model for musical event statistics.

Assessment

Describe how to use a cumulative distribution function to sample from a custom probability distribution. Why does a uniform probability distribution produce the maximum entropy sequence?