Gauge symmetries of musical and visual forces

After reviewing the physicalistic or metaphorical accounts to musical and visual forces by Arnheim and Larson, respectively, which were inspired by the basic tenets of gestalt psychology, I present a novel, naturalistic, mathematical framework, based on symmetry principles and gauge theory. In music...

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Bibliographic Details
Published in:Journal of mathematics and the arts 2023-10, Vol.17 (3-4), p.347-382
Main Author: beim Graben, Peter
Format: Article
Language:English
Subjects:
Deformation
force
gauge invariance
Gauge theory
Geometry
Lie groups
Music
quantum cognition
Riemannian geometry
Symmetry
vision
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Summary:After reviewing the physicalistic or metaphorical accounts to musical and visual forces by Arnheim and Larson, respectively, which were inspired by the basic tenets of gestalt psychology, I present a novel, naturalistic, mathematical framework, based on symmetry principles and gauge theory. In musicology, this approach has already been applied to the phenomenon of tonal attraction, leading to a deformation of the circle of fifths. The underlying gauge symmetry turns out as the SO(2) Lie group of a musical quantum model. Here, I present an alternative description in terms of Riemannian geometry. Its essential constraint of invariance of the infinitesimal line element leads to a deformation of the circle of fifths into a heart of fifths. In vision, the same approach is applied to Fraser's twisted cord illusion where concentric circles are deformed to squircle objects by means of an optical gauge field induced through a checkerboard background.
ISSN:1751-3472
1751-3480
DOI:10.1080/17513472.2023.2281895