Geometry of Music Perception

Benjamin Himpel ()
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Benjamin Himpel: Department of Computer Science, Reutlingen University, 72762 Reutlingen, Germany

Mathematics, 2022, vol. 10, issue 24, 1-34

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.

Keywords: music psychology; music theory; Riemanian geometry; Whitney stratification; music perception; voice leading; dissonance; transitional harmony; chord progression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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