FORMALIZATION AND INTUITION IN ANALOGIQUE A ET B (with some remarks on the historical-mathematical sources of Xenakis)1

Analogique A et B (for 9 string instruments and tape, 1958-59) is considered one of Xenakis ’ most thoroughly formalized compositions. Two chapters of Musiques Formelles are dedicated to theoretical and technical issues behind it, mostly dealt with by Xenakis using mathematical notations and other formalisms. However, in this paper I argue that a very rich exchange took place, in the composition of this music, between formalization and more intuitive insight. The paper first overviews the mathematical sources of Xenakis ’ efforts in the late 1950s, and then illustrates details of the “mechanism ” (formalized compositional process) by which he created Analogique A (the instrumental layer of Analogique A et B). The composer pursued a generative process that would function as the analogon of a stochastic process, the latter consisting in what Xenakis called sound clouds. A close look at the procedures he implemented to that aim, shows that (1) a binary logics informs both the “mechanism ” and the final musical results, and (2) the composer actually created a discrete, digital representation of the stochastic process he had in mind. The paper discusses the dialectic between formalized and intuitive choices, including Xenakis ’ final decision to paste together the two separate manifestations of the same design, the instrumental (Analogique A) and the electronic (Analogique B). «Le nombre n’a donc pas éliminé l’inconscient. Mais quel est son rapport au sens, et