  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.
