Geometry of Music Perception

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 such as 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.

Music through Curve Insights

“…In [7], a measure for determining the similarity between two melodies with multiple-note change has been discussed based on pitch distance, the effects of primacy, and two-note changes. In [8], a geometric model of psychoacoustics has been defined to express roughness and harmonicity with the help of a height function.…”