@misc{BeimGrabenMannone, author = {Beim Graben, Peter and Mannone, Maria}, title = {Musical pitch quantization as an eigenvalue problem}, series = {Journal of Mathematics and Music}, journal = {Journal of Mathematics and Music}, issn = {1745-9745}, doi = {10.1080/17459737.2020.1763488}, pages = {1 -- 18}, 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 Schr{\"o}dinger 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.}, language = {en} }