Geometry of Music Perception

TL;DR

This paper develops a geometric model of music perception combining neuroscientific and acoustic data, representing chords as a stratified space with Riemannian manifolds, enabling rigorous analysis of psychoacoustic phenomena.

Contribution

It introduces a novel geometric framework for music perception, modeling the space of chords as a Whitney stratified space with compatible metrics for psychoacoustic analysis.

Findings

Chord space is a Whitney stratified space with Riemannian manifolds.

The model provides a geodesic distance compatible with voice-leading.

Framework facilitates analysis of roughness and harmonicity.

Abstract

Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown to be a Whitney stratified space. Each stratum is a Riemannian manifold which naturally yields a geodesic distance across strata. The resulting metric is compatible with voice-leading satisfying the triangle inequality. The geometric model allows for rigorous studies of psychoacoustic quantities like roughness and harmonicity as height functions. In order to show how to use the geometric framework in psychoacoustic studies, concepts for the perception of chord resolutions are introduced and analyzed.