6533b85ffe1ef96bd12c1afe

RESEARCH PRODUCT

Musical pitch quantization as an eigenvalue problem

Peter Beim GrabenMaria Mannone

subject

Circle of fifthscircle of fifthsscalesCyclic groupcontinuumcyclic groupsquantum cognition050105 experimental psychology060404 musicSchrödinger equationsymbols.namesaketransposition symmetrycircle of fifths; continuum; cyclic groups; discrete; quantum cognition; scales; transposition symmetry0501 psychology and cognitive sciencesQuantum cognitionEigenvalues and eigenvectorsMathematicsSettore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniSettore INF/01 - InformaticaQuantization (music)Applied Mathematics05 social sciencesMathematical analysis06 humanities and the artsSettore MAT/04 - Matematiche ComplementariSettore MAT/02 - AlgebraComputational Mathematicscircle of fifths continuum cyclic groups discrete quantum cognition scales transposition symmetryComputer Science::SoundModeling and SimulationFrequency domainsymbolsdiscrete0604 artsMusicPitch (Music)

description

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.

yearjournalcountryeditionlanguage
2020-01-01
https://publica.fraunhofer.de/handle/publica/263060