T is for Stochastic Art

| May 4, 2014

When studying music composition, I became very interested in the integration of chance into composition. Several composers in the 20th Century integrated chance into their process. These techniques are usually referred to as “stochastic”.

Stochastic comes from the Greek word στόχος, which means “aim”… In probability theory, a purely stochastic system is one whose state is non-deterministic (i.e., “random”) so that the subsequent state of the system is determined probabilistically. Any system or process that must be analyzed using probability theory is stochastic at least in part.

Some artists use technology to apply more control to their work, while others use technology to give up control, introducing elements of randomness into their work.

Why would you let a computer make decisions for you? And why, in particular, would you let it make those decisions randomly?
Iannis Xenakis used stochastic methods (“chance operations”) to compose some of his music. Xenakis used chance as a way to “suspend time”, thinking that time is not a fixed entity.

“Chance music is naturally associated with a relinquishing of compositional control. Paradoxically, Xenakis argued that in certain cases chance operations could represent a composer’s intentions more closely than any other compositional process.” (Tako Oda. Iannis Xenakis and John Cage: Two Sides of a Tossed Coin)

In one of his more notable stochastic pieces, Metastasies, Xenakis uses chance operations and indeterminacy to mimic molecular behaviors. His composition process was… unorthodox. In this visualization of the piece, a video artist uses the frequency spectrum to represent the composition of the piece.

Metastasis or Metastaseis (“dialectic transformations”), is an orchestral work by Iannis Xenakis, a Greek composer-architect and a major figure in the postwar development of musical modernism worldwide. He is particularly remembered for the pioneering use of stochastic mathematical techniques in his compositions, including probability (Maxwell-Boltzmann kinetic theory of gases, aleatory distribution of points on a plane, minimal constraints, Gaussian distribution, Markov chains), game theory, group theory, Boolean algebra and Brownian motion.

Metastasis was inspired by Einstein’s view of time (a function of matter & energy) and structured on mathematical ideas by Xenakis’s colleague Le Corbusier. The 1st and 3rd movements don’t have a melodic theme to hold them together, but rather depend on the strength of this conceptualization of time. The 2nd movement does have some sort of melodic element. A fragment of a 12-tone row is used, with durations based on the Fibonacci sequence (1,1,2,3,5,8,13,21,34…)

The preliminary sketch for Metastasis was in graphic notation looking more like a blueprint than a musical score, showing graphs of mass motion and glissandi like structural beams of the piece, with sound frequencies on one axis and time on the other. In this video I tried to display this by presenting the frequency spectrum (0-20.000Hz) of the piece and how Xenakis actually “drew” music.

While Xenakis’ process seems fascinatingly complex and erudite, I’m not sure the ‘expressiveness’ of the results register with me as anything other than cerebral.

How else can we bring chance into the creative process in meaningful ways that further the expressive impact of a work of art?