From Xenakis' Sieves to Emotional Mathematics

This essay traces a thirty-year engagement with Iannis Xenakis’ sieve theory and its eventual transformation into a practical, lyrical compositional language. Drawing on interval- constraint principles suggested by Brian Ferneyhough, it describes how Xenakis’ sieves— structures that determine pitch availability rather than voice-leading behaviour—were adapted into a single rule-set governing melody, counterpoint, and harmony within a non- octavating pitch universe. The result is a generative mechanism in which horizontal and vertical dimensions are unified. The essay then examines how this mechanism operates in the author’s 2025 piece Emotional Mathematics and introduces a complementary technique, ‘snap- to-diatonic contour mapping’, whereby sieve-derived material is quantised onto a chosen diatonic collection. The article presents the full constraint matrix alongside score examples and audio, demonstrating how such methods allow non-tonal pitch structures to inhabit diatonic surfaces without compromising their underlying logic.