Xenakis’s Analytical Tools : The Theory of Sieves

Benoît Gibson (Universidade de Évora/Escola Superior de Música de Lisboa, Portugal)

Iannis Xenakis was among the first modern composers to foresee the need for a broader approach to music, one that would not limit itself to musical tradition. His efforts to break the barriers between music and other areas of knowledge opened up new compositional paths. Xenakis sought the theoretical basis that lies behind his musical ideas and used mathematics to understand and formulate them. By carrying out his research on a general level, he put forth a formalization of music.

Xenakis did not develop his theoretical ideas only as a means of creating new sonic entities, but also as a means of understanding music in broader or more abstract terms. He explained how stochastic music embraces serial music as a particular instance, how the traditional transformations of a melodic pattern are related to group theory, how sieves theory can retrieve the symmetries from any given series of events or objects in space or time, etc.

This presentation discusses the extent of Xenakis's program of analyzing sieves. Relying on the difference between symmetrical and asymmetrical sieves, it proposes to adapt Xenakis's method in order to reduce the number of points necessary to disclose the sieves' periodicities. Analyses of scales elaborated by Xenakis as well as by other composers are given as examples.

Benoît Gibson studied viola, analysis and music theory at the Music Conservatory of Montreal in Canada.  He completed his Doctorate at the Ecole des hautes études en sciences socials (Paris).  Member of the Research Center of Aesthetics and Sociology of Music (Lisbon), he is presently teaching at the University of Evora as well as at the Superior Music School of Lisbon.