Mathematics, Architecture, and the Works of Iannis Xenakis
It is undeniable that Iannis Xenakis made use of many different mathematical theories such as the golden section, the Fibinacci series, and stochastic laws, in his music. In this essay, I will show the reader how extensively these principles governed much of his compositional process. I will also present the reader with examples where these different principles and theories are evident in his music.
Xenakis was hired at the studio of Le Corbusier in 1947. While under the tutelage of Le Corbusier, Xenakis composed during his free time, and took lessons from many different composers. For Xenakis, none of these composers would let him compose in the manner which he felt the most comfortable. This was the case until he was encouraged by Le Corbusier to study with Olivier Messiaen. Messiaen was unlike his previous teachers, he “advised him not to take conventional theory lessons but to continue to bring in his expert knowledge of architecture and mathematics.” There are three notable factors that contribute to the initial incorporation of numerical proportions within the compositions of Iannis Xenakis: he was already familiar with the Golden Section from his studies of Greek architecture; the encouragement he received from Messiaen to further pursue his incorporation of mathematics and architecture into music, and the many references to music made by Le Corbusier with his Modulor. The Golden Section and the Fibonacci series appear multiple times throughout the compositions of Xenakis. This paper will only discuss three specific instances: Le Sacrifice, Psappha, and Metastasis.
The first principle that I will discuss is the Golden Section. The Golden Section ...
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...vent occurs k times per unit of measurement”. The Poisson distribution is a frequently used formula in works by Xenakis.
Yet another group of probability laws are used to characterize glissandi. The characteristic of an acoustic glissando uses “the speed (df/dt) of a continuous movement and the distribution of speed follows another law of probability, Gussian Law.” This is further explained in the following figure
Figure 7: Acoustic characteristic of a glissando, Speed
f: frequency, t: time, speed=df/dt
All of these probability laws were utilized by Xenakis in Metastasis. I will now show the correlation of the mathematical version and the musically notated version of the glissadi in Metastasis. Figure 8 is the first page of the score to Metstasis, and Figure 9 is a graphic score of bars 309-314 of Metastasis.
Figure 8: Metastasis
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