A Notation-Free Approach to Encoding Commatic Drifts in Just Intonation

Abstract

Musics in just intonation pose a wide number of challenges to encoding but perhaps none more imposing than their potential to freely drift through rational pitch space by minute intervals. Though such commatic drifts—whether Pythagorean, syntonic, septimal, or otherwise—are all too often framed as ‘problems’ inherent to rational tuning systems, the study of musics in which they are used as a compositional resource motivates a methodology that can sensibly account for them. This paper accordingly presents a pragmatic approach to encoding commatic drifts in just intonation deliberately divorced from any particular notation system and instead based on tracking changes both to and relative to (not necessarily sounded) ‘1/1’ reference fundamentals. Notably, this approach helps facilitate understandings of commatic drifts that can be obscured by compromises inherent to notation systems

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