Geometry of Music Perception

Abstract

Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent differential-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 stratifold, whose Riemannian metric naturally yields a geodesic distance function compatible with voiceleading satisfying the triangle inequality even between chords with a different number of chord tones. The stratifold model allows for rigorous studies of psychoacoustic quantities like roughness and harmonicity as height functions. Lastly, concepts for the perceptive strength of chord resolutions are introduced and analyzed based on the differential-geometric framework.