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  4. Musical pitch quantization as an eigenvalue problem
 
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2020
Journal Article
Title

Musical pitch quantization as an eigenvalue problem

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.
Author(s)
Graben, Peter beim
Fraunhofer-Institut für Keramische Technologien und Systeme IKTS  
Mannone, Maria
University of Palermo
Journal
Journal of mathematics & music  
Open Access
DOI
10.1080/17459737.2020.1763488
Additional full text version
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Language
English
Fraunhofer-Institut für Keramische Technologien und Systeme IKTS  
Keyword(s)
  • circle of fifths

  • transposition symmetry

  • scales

  • quantum cognition

  • discrete

  • cyclic groups

  • continuum

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