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
voice-leading 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 perception of chord resolutions are
introduced and analyzed based on the differential-geometric framework. This
research shows how to use the differential-geometric framework in
psychoacoustic studies.
