Thesis (MMus (Music))--University of Stellenbosch, 2009. / The relationship between music and mathematics has been subjected to debate for centuries. There are two schools of thought with the one viewpoint holding that the relationship between mathematics, which is conceived as an abstract and cold discipline, compared to music, which is rich with emotion, must be very limited. Arguments for this view draws, for example, on recent research which indicates that musical talent is not inherently linked to mathematical capability. On the other pole of the debate is the belief that although music and mathematics contribute to different parts of society, there is a very important inter-relationship between the two fields. Of great interest to the latter is the Greek composer Iannis Xenakis whose musical aesthetics incorporates this philosophy. As composer, Xenakis used mathematical theories as basis for his musical works. He not only incorporated well known mathematical principles such as the Golden Section into his compositions but went further and, for instance, utilized Boolean Algebra, Probability theory and Stochastic processes in his music. His composition method based on these mathematical principles became known under the term Stochastic music and forms the focus of this thesis. The research project concentrates on the early part of Xenakis’ life in order to provide insight into the development of his composition methods. The mathematical principles at the centre of his stochastic compositions receive specific rationalisation. In doing so, the most significant probability distributions (Linear, Exponential, Poisson and Normal distribution) are defined in terms of their properties and Xenakis’ use of them. The application of these distributions is considered by looking at the early works Metastaseis (in which Xenakis confronted most of his musical problems and which formed the basis for his musical style) and Achorripsis (where he fully developed their implementation). An in-depth examination of the construction of Achorripsis is performed while scrutinizing Xenakis’ calculations. Specific attention is drawn to alterations and adjustments made to the calculations. His implementation of them into the final score is furthermore examined and it is shown where he deviated between the calculations and score. The thesis concludes by considering the extent and significance of the adjustments made by the composer in the name of artistic freedom.