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Musical pitch quantization as an eigenvalue problem

 
: Graben, Peter beim; Mannone, Maria

:

Journal of mathematics & music (2020), Online First
ISSN: 1745-9737
ISSN: 1745-9745
Englisch
Zeitschriftenaufsatz
Fraunhofer IKTS ()
circle of fifths; transposition symmetry; scales; quantum cognition; discrete; cyclic groups; continuum

Abstract
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.

: http://publica.fraunhofer.de/dokumente/N-593132.html