How can communication occur between architecture, music, and mathematics? This presentation responds to this question taking as a starting point the use of the “Modulor” system of proportion in the composition and the notation of Iannis Xenakis’s Metastasis, who was at once a composer, architect, and mathematician and collaborated with Le Corbusier for the architectural composition of the Philips Pavilion at the 1958 World’s Fair in Brussels. Specific attention will be paid to the relationship between Xenakis’s understanding of music as thought’s materialisation and Deleuze and Guattari’s conception of art gesture as a passage of material into sensation. Xenakis’s conception of sound is spatial. For the notation of Metastasis he used graphs of glissandi, which look like ruled surfaces or hyperbolic paraboloids, described by him as “ruled surfaces of sound.” They look like the structural components he designed for the Philips Pavilion.
Xenakis’s compositional approach is based on a relationship between music and architecture that goes beyond the metaphoric. In the composition of Metastasis the role of architecture was direct and fundamental by virtue of the Modulor, which found an application in the very essence of the musical development. Xenakis was interested in the Modulor because it is at once a geometric and an additive series. Metastasis seeks equivalence between a geometric series and an additive series. In Formalized Music: Thought and Mathematics in Composition Xenakis mentions, “It is not so much the inevitable use of mathematics that characterizes the attitude of these experiments as the overriding need to consider sound and music as a vast potential reservoir in which knowledge of the laws of thought and the structured creations of thought may find a completely new medium of materialization.”
Xenakis, Deleuze, and Guattari share the intention to associate art gesture with the zones of indetermination. Xenakis’s evaluation of musical composition is based on “the quantity of intelligence carried by the sounds” and “to make music means to express human intelligence by sonic means.” He underscores that “action, reflection, and self- transformation by the sounds themselves—is the path to follow.” He believes that “when … mathematical thought serves music . . . it should amalgamate dialectically with intuition.” He understands the composition of music as “a fixing in sound of imagined virtualities,” dividing musical construction into two categories: a first that pertains to time and a second that is independent of temporal becomingness. The latter includes “durations and constructions (relations and operations) that refer to elements (points, distances, functions) that belong to and that can be expressed on the time axis. The temporal is then reserved to the instantaneous creation.”Deleuze underscores that in the case of Boulez’s musical composition “number has not disappeared, but has become independent of metric or chronometric relations.” My presentation examines how this freeing of the compositional process from “metric or chronometric relations” to which Deleuze refers can be related to Xenakis’s outside-time mode of composition, described by Xenakis. Deleuze intends to grasp the process of “making sound the medium which renders time sensible, the Numbers of time perceptible, to organize material in order to capture the forces of time and render it sonorous”. He associates this kind of compositional process with Messiaen’s project and understands Boulez’s stance as a continuation of such a procedure “in new conditions (in particular, serial ones).” For Xenakis, the power of musical composition resides in the expression of intelligence through sonic means, while, for Deleuze, the deterritorialising forces of musical composition are inextricably linked to the “functions of temporalization that are exerted on sonorous material that the musician captures and renders sensible the forces of time” (Deleuze, “Boulez, Proust and Time: ‘Occupying without Counting’”). Deleuze and Guattari’s understanding of arts as an invention of material embodiment of the virtual is very close to Xenakis’s understanding of music as thought’s materialisation. Pivotal for shedding light on how arts invent “possibilities of life” is the thought that “the arts operate within the domain of sensation, which is that of the continuous passage of the virtual into the actual” and that, during the creative process of art making, “invention of possible worlds proceeds through embodiment” (Ronald Bogue, “The Art of the Possible”). My objective here is to reflect on the marriage between architecture, music, and mathematics, and on the potentialities of the zones of indeterminacy that emerge when these three domains of experience are thought together.