An Interactive Tool for Composing (with) Automorphisms in the Colored Cube Dance - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2022

An Interactive Tool for Composing (with) Automorphisms in the Colored Cube Dance

Résumé

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 (Z 3 4 D 8) (D 6 × 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.
Fichier principal
Vignette du fichier
Popoff_et_al_MCM2022.pdf (356.37 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03872875 , version 1 (22-02-2023)

Identifiants

Citer

Alexandre Popoff, Corentin Guichaoua, Moreno Andreatta. An Interactive Tool for Composing (with) Automorphisms in the Colored Cube Dance. Mariana Montiel; Octavio A. Agustín-Aquino; Francisco Gómez; Jeremy Kastine; Emilio Lluis-Puebla; Brent Milam. Mathematics and Computation in Music. 8th International Conference, MCM 2022, Atlanta, GA, USA, June 21–24, 2022, Proceedings, 13267, Springer International Publishing, pp.41-47, 2022, Lecture Notes in Computer Science, 978-3-031-07014-3. ⟨10.1007/978-3-031-07015-0_4⟩. ⟨hal-03872875⟩
51 Consultations
171 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More