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Iannis Xenakis and Sieve Theory an Analysis of the Late Music (1984-1993)

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Iannis Xenakis and Sieve Theory an Analysis of the Late Music (1984-1993) Iannis Xenakis and Sieve Theory An Analysis of the Late Music (1984-1993) A Dissertation Presented in Fulfilmentof the Requirements forthe Degree of Doctor of Philosophy Goldsmiths College, University of London by Dimitrios Exarchos Volume 1 of 2: Text Dissertation Supervisor: Dr Craig Ayrey November 2007 2 Abstract Iannis Xenakis and Sieve Theory An Analysis of the Late Music (1984-1993) Dimitrios Exarchos 2007 This thesis is divided in three parts, the firsttwo of which are theoretical and the third analytical. Part I is an investigation oflannis 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 classificationof 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 differentapproach than in the later, where he also provided an analytical algorithm that he developed gradually from the mid 1980s 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. 3 As with the application of other theories, Xenakis progressed to less formalised processes. However, this does not mean that Sieve Theory ceased to informthe process of scale-construction. As the conclusion of this dissertation indicates, he employed Sieve Theory in order to achieve structures that conformto his general aesthetic principles, that relate to various degrees of symmetry and periodicity. 4 Contents Acknowledgements 8 .......................................................................................... Abbreviations 9 .................................................................................................. Introduction 10 .................................................................................................. PART I 1 Outside-Time Structures 20 .............................................................................. 1.1 Literature 20 ...................................................................................................... 1.2 Overview 21 ........................................................................................................ 1.3 Symbolic Logic ('Symbolic Music'- 1963) 23 .................................................. 1.4 Two Natures ('La de la de la 28 voie recherche et question' -1965) ............... 1.5 Tomographies Over Time ('Towards Metamusic' 31 a -1965) ....................... 1.6 `Towards Philosophy Music' (1966) 33 a of ...................................................... 1.7 Ontological/Dialectical ('Une 34 note' -1968) .................................................. 1.8 Arts/Sciences: Alloys (1976) 36 ........................................................................... 2 Outside-Time Structures Writing 38 as ............................................................ 2.1 The Third Term 38 ............................................................................................ 2.2 The Critique Serialism 40 of .............................................................................. 2.2.1 General Harmony 40 ......................................................................................... 2.2.2 Magma 42 ........................................................................................................... 2.3 The Temporal Outside-Time 44 as .................................................................... 2.4 Outside-Time Supplement 46 as ........................................................................ 2.5 Symmetry 47 ...................................................................................................... 2.5.1 Series 47 .............................................................................................................. 2.5.2 Non-Retrogradable Rhythms 50 ....................................................................... 2.6 Spacing 51 .......................................................................................................... PART II 3 Sieve Theory 54 .............................................. .................................................... 3.1 The Sieve Eratosthenes 54 of ......................... .................................................... 3.2 Logical Operations 57 .................................... .................................................... 3.2.1 Union 57 ......................................................... .................................................... 3.2.2 Intersection 58 ................................................ .................................................... 3.2.3 Complementation 59 ...................................... .................................................... 3.3 Transcription 60 ............................................. .................................................... 3.3.1 Transcription 61 of unions ............................ .................................................... 3.3.2 Transcription intersections 62 of ....................................................................... 3.4 Types Sieves 63 of .......................................... .................................................... 3.4.1 Symmetry 64 .................................................. .................................................... 5 3.4.1.1 Symmetric Sieves 65 .......................................................................................... 3.4.1.1.1 Symmetric Sieves Even Number Intervals 66 with of ...................................... 3.4.1.1.2 Symmetric Sieves Odd Number Intervals 68 with of ........................................ 3.4.1.2 Asymmetric Sieves 70 ........................................................................................ 3.4.2 Periodicity 71 ..................................................................................................... 3.4.2.1 Prime Sieves 71 .................................................................................................. 3.4.2.2 Composite Asymmetric Sieves 72 ...................................................................... 3.5 Metabolae Sieves (Transformations) 74 of ........................................................ 3.5.1 Residues 74 ......................................................................................................... 3.5.1.1 Inversion 74 ........................................................................................................ 3.5.1.2 Cyclic Transposition 76 ..................................................................................... 3.5.1.3 Variables 79 ........................................................................................................ 3.5.2 Moduli 80 ........................................................................................................... 3.5.3 Unit 81 ................................................................................................................ 4 Sieve Theory Primes 82 and .............................................................................. 4.1 Canonical Form 82 ............................................................................................. 4.2 Limitations 86 .................................................................................................... 4.3 Types Formulae 86 of ........................................................................................ 4.3.1 Decomposed Formula 86 ................................................................................... 4.3.2 Simplified Formula 88 ....................................................................................... 4.4 Program: Generation Points 91 of .................................................................... 4.5 Sieve Theory Sieves 94 and ................................................................................ 4.6 Symmetries/Periodicities 95 ............................................................................... PART III 5 Methodology 101 ................................................................................................ Inner Periodicities Formulae Redundancy 101 5.1 and ......................................... Inner-Periodic Simplified Formula 104 5.2 Construction of the ........................... Analytical Algorithm: Early Stage 107 5.3 ............................................................. 5.4 The Condition Inner Periodicity 110 of ............................................................ 5.5 Inner-Periodic Analysis 112 .............................................................................. 5.6 Interlocking Periodicities 116 ............................................................................ Analytical Algorithm: Final
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