Gauge models of musical forces
作者：
Reinhard Blutner*;Peter beim Graben
通讯作者：
Reinhard Blutner
作者机构：
Universiteit van Amsterdam, ILLC, Amsterdam, Netherlands
Department of Communications Engineering, Brandenburgische Technische Universität Cottbus-Senftenberg, Institute of Electronics and Information Technology, Cottbus, Germany
通讯机构：
Universiteit van Amsterdam, ILLC, Amsterdam, Netherlands
语种：
英文
期刊：
Journal of Mathematics and Music
ISSN：
1745-9737
年：
2021
卷：
15
期：
1
页码：
17-36
摘要：
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 ...
