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Musical pitch quantization as an eigenvalue problem

  • How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz.

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Metadaten
Author: Peter Beim Graben, Maria Mannone
DOI:https://doi.org/10.1080/17459737.2020.1763488
ISSN:1745-9745
Title of the source (English):Journal of Mathematics and Music
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2020
First Page:1
Last Page:18
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Kommunikationstechnik
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