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, such as symmetry groups and their representation theories, particularly local gauge symmetries and their connection to physical forces, have not been utilized in the field of quantum cognition research sofar. This is somewhat astonishing as "mental forces" or "mental energies" appear as important metaphorical concepts in cognitive science. One particular example is music psychology, where static or dynamic tonal attraction phenomena are computationally often modeled in terms of metaphorical forces. Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies . 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.
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.
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such as symmetry groups and their representation theories, particularly local gauge symmetries and their connection to physical forces,
e.g., symmetry groups
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This is somewhat astonishing as "mental forces" or "mental energies" appear as important metaphorical concepts in cognitive science. One particular example is music psychology, where static or dynamic tonal attraction phenomena are computationally often modeled in terms of metaphorical forces.
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connection between musical forces and symmetries in
symmetries of
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musical forces in the framework of quantum cognition
static and dynamic tonal attraction phenomena in music psychology within the quantum cognition framework
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principles of octave equivalence, fifth similarity and
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, as
that are
A
structure of the
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, governed by a Schr\"odinger equation containing different interaction energies