Theory of groups

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 Xenakis also gives some details there about group structures in Nomos Gamma. Because of this, most articles on this subject confine themselves to that particular work. 2 However, references to group structures in Psappha can be found in Flint (1993). 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. 3 A more details presentation of group structures can be found in Xenakis (1992), Vriend (1981), and Delio (1980)

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• Xenakis’ Sieve Theory

  Open Access•Jos&eacute L Besada•Music Theory Online•2022

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• Metabolae, arborescences and the reconstruction of time in Iannis Xenakis'Psappha

  Ellen Rennie Flint•Contemporary Music Review•1993

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