@inproceedings{BeimGrabenBlutner, author = {Beim Graben, Peter and Blutner, Reinhard}, title = {Toward a gauge theory of musical forces}, series = {Quantum Interaction, 10th International Conference, QI 2016, San Francisco, CA, USA, July 20-22, 2016}, booktitle = {Quantum Interaction, 10th International Conference, QI 2016, San Francisco, CA, USA, July 20-22, 2016}, editor = {Barros, Jose Acacio de and Coecke, Bob and Pothos, Emmanuel}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-52289-0}, doi = {10.1007/978-3-319-52289-0_8}, pages = {99 -- 111}, abstract = {How well does a given pitch fit into a tonal scale or key, being either a major or minor key? This question addresses the well-known phenomenon of tonal attraction in music psychology. Metaphorically, tonal attraction is often described in terms of attracting and repelling forces that are exerted upon a probe tone of a scale. In modern physics, forces are related to gauge fields expressing fundamental symmetries of a theory. In this study we address the intriguing relationship between musical symmetries and gauge forces in the framework of quantum cognition.}, language = {en} } @misc{BlutnerBeimGraben, author = {Blutner, Reinhard and Beim Graben, Peter}, title = {Gauge models of musical forces}, series = {Journal of Mathematics and Music}, volume = {15}, journal = {Journal of Mathematics and Music}, number = {1}, issn = {1745-9745}, doi = {10.1080/17459737.2020.1716404}, pages = {17 -- 36}, abstract = {Metaphors involving motion and forces are a source of inspiration for understanding tonal music and tonal harmonies since ancient times. Starting with the rise of quantum cognition, the modern interactional conception of forces as developed in gauge theory has recently entered the field of theoretical musicology. We develop a gauge model of tonal attraction based on SU(2) symmetry. This model comprises two earlier attempts, the phase model grounded on U(1) gauge symmetry, and the spatial deformation model derived from SO(2) gauge symmetry. In the neutral, force-free case both submodels agree and generate the same predictions as a simple qubit approach. However, there are several differences in the force-driven case. It is claimed that the deformation model gives a proper description of static tonal attraction. The full model combines the deformation model with the phase model through SU(2) gauge symmetry and unifies static and dynamic tonal attraction.}, language = {en} } @misc{BeimGrabenBlutner, author = {Beim Graben, Peter and Blutner, Reinhard}, title = {Quantum approaches to music cognition}, series = {Journal of Mathematical Psychology}, volume = {91}, journal = {Journal of Mathematical Psychology}, issn = {0022-2496}, doi = {10.1016/j.jmp.2019.03.002}, pages = {38 -- 50}, 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.}, language = {en} }