Geometry of music perception
- 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.
| Author of HS Reutlingen | Himpel, Benjamin |
|---|---|
| URN: | urn:nbn:de:bsz:rt2-opus4-39881 |
| DOI: | https://doi.org/10.3390/math10244793 |
| ISSN: | 2227-7390 |
| Erschienen in: | Mathematics |
| Publisher: | MDPI |
| Place of publication: | Basel |
| Document Type: | Journal article |
| Language: | English |
| Publication year: | 2022 |
| Tag: | Riemanian geometry; Whitney stratification; chord progression; dissonance; music perception; music psychology; music theory; transitional harmony; voice leading |
| Volume: | 10 |
| Issue: | 24 |
| Page Number: | 34 |
| First Page: | 1 |
| Last Page: | 34 |
| Article Number: | 4793 |
| DDC classes: | 510 Mathematik |
| Open access?: | Ja |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
