Formal aspects of Iannis Xenakis' "Symbolic music": A computer-aided exploration of compositional processes

We present computer models of two works for solo instrument by Iannis Xenakis: Herma for piano (1962) and Nomos Alpha for cello (1965). Both works were described by the composer (in his book Formalized Music) as examples of "symbolic music." Xenakis' detailed description of formal aspects in his compositional process makes it possible to implement computer models that recreate essential elements of the final scores. For our implementations, we use OPEN-Music, a visual programming language based on Common-Lisp/CLOS developed at Ircam. Based on the experiences gathered from developing and exploring these computer models, we discuss the theoretical concepts used by Xenakis in his creative process. Further, we examine how the algebraic organization of Nomos Alpha can be considered as an abstraction of the set-theoretical one used in Herma. We finally suggest to extend Xenakis' outside-of-time/in-time dichotomy by means of a third conceptual category: the "logical time.".