Towards Experimental Nanosound Using Almost Disjoint Set Theory

TL;DR

This paper explores the application of almost disjoint set theory to digital audio composition, demonstrating that intersecting sound gestures results in lower complexity, which has implications for nanosound and self-organization in music.

Contribution

It validates the use of fractal set theory in audio frequency sets and shows how intersection operations produce almost disjoint sound gestures, linking set theory with musical complexity.

Findings

Intersection of sound gestures shows lower complexity than union.

Sound gestures' intersection behaves as an almost disjoint set.

Results connect set theory with musical self-organization.

Abstract

Music composition using digital audio sequence editors is increasingly performed in a visual workspace where sound complexes are built from discrete sound objects, called gestures that are arranged in time and space to generate a continuous composition. The visual workspace, common to most industry standard audio loop sequencing software, is premised on the arrangement of gestures defined with geometric shape properties. Here, one aspect of fractal set theory was validated using audio-frequency sets to evaluate self-affine scaling behavior when new sound complexes are built through union and intersection operations on discrete musical gestures. Results showed that intersection of two sets revealed lower complexity compared with the union operator, meaning that the intersection of two sound gestures is an almost disjoint set, and in accord with formal logic. These results are also discussed with reference to fuzzy sets, cellular automata, nanotechnology and self-organization to further explore the link between sequenced notation and complexity.