Theory of Groups: In Search of a Method to Analyse Group Structures in the Music of Xenakis

Abstract

The use of abstract groups marked an important change in Xenakis' compositional processes. Whereas "stochastic music" relies on indeterminism, group structures organize predetermined elements according to a specific order. Xenakis has used these structures in many works. However, he has given very little information on how to analyze them apart from in Nomos Alpha.1 Because of this, most articles on this subject confine themselves to that particular work. The purpose of this paper is to present an analytical tool that permits us to identify certain processes related to the theory of groups, and consequently enables us to widen the study of group structures in Xenakis' music. A complete overview of the mathematical aspect of groups falls outside the scope of this article.