Musical scales: an empirical ground for number theory?
- Date
- Jun 19, 2024
- Time
- 3:00 PM - 4:00 PM
- Speaker
- Alexandre Guillet
- Affiliation
- MPI-PKS
- Language
- en
- Main Topic
- Physik
- Other Topics
- Physik
- Description
- The antique problem of musical harmony, finding tunings and scales based on the commensurability of sound waves, has been approached by Helmholtz in terms of a dissonance curve in the frequency domain. This model is here recast in an elementary form related to number theory and statistical mechanics. The biophysics pioneer's idea meets Riemann's zeta function along the imaginary direction as a model of harmonic timbre and Minkowski's question mark function as a mean field description of harmony in the high temperature limit. The spectrum of the resulting fractal curve predicts the quasi-period of widely used musical scales, from the pentatonic division of the octave to microtonal ones, thus constituing a natural —or at least mathemusical— common ground underlying the endless design of musical scales across genres and cultures.
Last modified: Jun 19, 2024, 7:40:11 AM
Location
Max-Planck-Institut für Physik komplexer SystemeNöthnitzer Straße3801187Dresden
- Phone
- + 49 (0)351 871 0
- MPI-PKS
- Homepage
- http://www.mpipks-dresden.mpg.de
Organizer
Max-Planck-Institut für Physik komplexer SystemeNöthnitzer Straße3801187Dresden
- Phone
- + 49 (0)351 871 0
- MPI-PKS
- Homepage
- http://www.mpipks-dresden.mpg.de
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