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BP: Fachverband Biologische Physik

BP 22: Statistical Physics of Biological Systems II (joint session DY/BP)

BP 22.5: Vortrag

Mittwoch, 11. März 2026, 16:15–16:30, ZEU/0114

Elementary spectrum for the dissonance curve: from biophysics to number theory of musical harmony — •Alexandre Guillet — Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

Musical harmony, as the ancient problem of 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 a thermodynamical formalism for musical intervals and frequency ratios. The idea of the pioneer of biophysics connects with Riemann's zeta function along the critical line, and Minkowski's question mark measure. The former models rational relationships resulting from the acoustics of a harmonic timbre, while the latter models the probability distribution of the neurocognitive effort to assess the commensurability of frequency pairs. The spectrum of the resulting fractal curve predicts the quasi-periods of widely used musical scales, from the pentatonic division of the octave to microtonal ones, thus constituting a biophysical and mathemusical common ground to harmony across musical genres and cultures.

Keywords: musical scales; dissonance curve; arithmetic gas; commensurability; number theory