Mathematics, architecture and works of Iannis . In this essay I will show the reader the extent to which 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 Le Corbusier's studio in 1947. Under Le Corbusier's tutelage, Xenakis composed in his spare time and took lessons from many different composers. For Xenakis, none of these composers would let him compose in the way he felt most comfortable. This was the case until he was encouraged by Le Corbusier to study with Olivier Messiaen. Messiaen was different from his previous teachers: he “advised him not to follow conventional theoretical courses but to continue to bring his in-depth knowledge of architecture and mathematics”. There are three notable factors that contribute to the initial incorporation of numerical proportions in Iannis Xenakis's compositions: he was already familiar with the golden ratio from his studies of Greek architecture; the encouragement he received from Messiaen to pursue his integration of mathematics and architecture into music, and the many references to music made by Le Corbusier with his Modulor. The golden ratio and the Fibonacci series appear several times in Xenakis's compositions. This article will only discuss three specific instances: The Sacrifice, Psappha, and Metastasis. The first principle I will discuss is the golden ratio. The golden ratio...... middle of paper ...... venting occurs k times per unit of measurement.” The Poisson distribution is a formula frequently used in the works of Xenakis. Another group of probability laws is used to characterize the glissandi. The characteristic of an acoustic glissando uses "the speed (df/dt) of a continuous movement and the distribution of the speed follows another law of probability, Guss's law". This is explained in more detail in the following figure: Figure 7: Acoustic characteristics of a glissando, Speedef: frequency, t: time, speed=df/dtAll these probability laws were used by Xenakis in Metastasis. I will now show the correlation between the mathematical version and the musically notated version of the glissadi in Metastasis. Figure 8 is the first page of the Metstasis score, and Figure 9 is a graphical score of bars 309 to 314 of Metastasis. Figure 8: Metastasis