Quantum approaches to music cognition

TL;DR

This paper explores how quantum cognition models, inspired by physical quantum theory, can better explain tonal attraction phenomena in music psychology, integrating symmetry principles and wave functions.

Contribution

It introduces quantum models based on symmetry principles to explain tonal attraction, extending quantum cognition beyond probability to include musical structure.

Findings

Quantum models replicate and improve predictions of tonal attraction.

Symmetry principles like octave equivalence and transposition are fundamental.

Wave function descriptions effectively model static and dynamic musical phenomena.

Abstract

Quantum cognition emerged as an important discipline of mathematical psychology during the last two decades. Using abstract analogies between mental phenomena and the formal framework of physical quantum theory, quantum cognition demonstrated its ability to resolve several puzzles from cognitive psychology. Until now, quantum cognition essentially exploited ideas from projective (Hilbert space) geometry, such as quantum probability or quantum similarity. However, many powerful tools provided by physical quantum theory, e.g., symmetry groups have not been utilized in the field of quantum cognition research sofar. Inspired by seminal work by Guerino Mazzola on the symmetries of tonal music, our study aims at elucidating and reconciling static and dynamic tonal attraction phenomena in music psychology within the quantum cognition framework. Based on the fundamental principles of octave equivalence, fifth similarity and transposition symmetry of tonal music that are reflected by the structure of the circle of fifths, we develop different wave function descriptions over this underlying tonal space. We present quantum models for static and dynamic tonal attraction and compare them with traditional computational models in musicology. Our approach replicates and also improves predictions based on symbolic models of music perception.