Abstract
The “colored Cube Dance” is an extension of Douthett’s and Steinbach’s Cube Dance graph, related to a monoid of binary relations defined on the set of major, minor, and augmented triads. This contribution explores the automorphism group of this monoid action, as a way to transform chord progressions. We show that this automorphism group is of order 7776 and is isomorphic to \(({\mathbb {Z}_3}^4 \rtimes D_8) \rtimes (D_6 \times \mathbb {Z}_2)\). The size and complexity of this group makes it unwieldy: we therefore provide an interactive tool via a web interface based on common HTML/Javascript frameworks for students, musicians, and composers to explore these automorphisms, showing the potential of these technologies for math/music outreach activities.
A. Popoff—Independent Researcher.
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Popoff, A., Guichaoua, C., Andreatta, M. (2022). An Interactive Tool for Composing (with) Automorphisms in the Colored Cube Dance. In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_4
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DOI: https://doi.org/10.1007/978-3-031-07015-0_4
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