Quantum approaches to music cognition Peter beim Grabena,∗, Reinhard Blutnerb aBrandenburgische Technische Universit¨at Cottbus – Senftenberg, Institute of Electronics and Information Technology, Department of Communications Engineering, Cottbus, Germany bEmeritus Universiteit van Amsterdam, ILLC, Amsterdam, Netherlands Abstract Quantum cognition emerged as an important discipline of mathematical psy- chology 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 quan- tum similarity. However, many powerful tools provided by physical quantum theory, e.g., symmetry groups have not been utilized in the field of quan- tum cognition research sofar. Inspired by seminal work by Guerino Mazzola on the symmetries of tonal music, our study aims at elucidating and recon- ciling static and dynamic tonal attraction phenomena in music psychology arXiv:1712.07417v4 [q-bio.NC] 18 Jan 2019 within the quantum cognition framework. Based on the fundamental prin- ciples of octave equivalence, fifth similarity and transposition symmetry of tonal music that are reflected by the structure of the circle of fifths, we de- velop 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 ∗Corresponding author Email address:
[email protected] (Peter beim Graben) Preprint submitted to Journal of Mathematical Psychology January 21, 2019 approach replicates and also improves predictions based on symbolic models of music perception.