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This thesis is divided in three parts, the first two of which are theoretical and the third analytical. Part I is an investigation of lannis Xenakis's general theory of composition, the theory of outside-time musical structures. This theory appears in many of Xenakis's writings, sometimes quite idiosyncratically. The aim of this part is to reveal the function of the non-temporal in Xenakis's musical structures, by means of a historical approach through his writings. This exploration serves to unveil certain aspects discussed more thoroughly through a deconstructive approach. The deconstructive is demonstrated in the classification of musical structures and aims partly at showing the nature of Time in Xenakis's theory. Part II is preoccupied with Xenakis's Sieve Theory. In the earlier writings on Sieve Theory he presented a slightly different approach than in the later, where he also provided an analytical algorithm that he developed gradually from the mid1980s until 1990. The rationale of this algorithm and the pitch-sieves of 1980-1993 guides Part III, which is preoccupied with a methodology of sieve analysis, its application, and an exploration of the employment of sieves in some of Xenakis's compositions of the 1980s. When possible, the analysis takes in consideration the pre-compositional sketches, available at the Archives Xenakis, Bibliotheque Nationale de France. The sketches reveal aspects of the application of Sieve Theory, not included in Xenakis's theoretical writings. As with the application of other theories, Xenakis progressed to less formalised processes. However, this does not mean that Sieve Theory ceased to inform the process of scale-construction. As the conclusion of this dissertation indicates, he employed Sieve Theory in order to achieve structures that conform to his general aesthetic principles that relate to various degrees of symmetry and periodicity.
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