Undecidability Results and Their Relevance in Modern Music Making

TL;DR

This paper explores how undecidability, a concept from computational theory, applies to modern music creation, affecting digital tools, harmony, and compositional constraints, with implications for practitioners and theorists alike.

Contribution

It demonstrates the relevance of undecidability in various aspects of music technology and composition, providing theoretical proofs and practical insights.

Findings

Ableton's Turing completeness implies undecidable processes.

Undecidability of sound effects satisfiability impacts sound design.

Constraints on polymeters and harmony are undecidable.

Abstract

This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that undecidability, a principle traditionally associated with theoretical computer science, extends its relevance to the music industry. The study adopts a multidimensional approach, focusing on five key areas: (1) the Turing completeness of Ableton, a widely used digital audio workstation, (2) the undecidability of satisfiability in sound creation utilizing an array of effects, (3) the undecidability of constraints on polymeters in musical compositions, (4) the undecidability of satisfiability in just intonation harmony constraints, and (5) the undecidability of "new ordering systems". In addition to providing theoretical proof for these assertions, the paper elucidates the practical relevance of these concepts for practitioners outside the field of theoretical computer science. The ultimate aim is to foster a new understanding of undecidability in music, highlighting its broader applicability and potential to influence contemporary computer-assisted (and traditional) music making.