From Xenakis' Sieves to Emotional Mathematics
Year: 2025
Type: article
Abstract: 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.
Author: Hannan, Geoffrey Martin Francis
Language: English
Subfield: Music
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7111305239
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