Gauge models of musical forces. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Blutner, Reinhard; beim Graben, Peter
• Is Part Of: Journal of mathematics and music. Volume 15:Issue 1(2021)
• Page Start: 17
• Page End: 36
• Publication Date: 2021-01-02
• Subjects: Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2020.1716404
• Languages: English
• ISSNs: 1745-9737

Abstract

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.