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Symbolic dynamical scales: modes, orbitals, and transversals

Symbolic dynamical scales: modes, orbitals, and transversals We study classes of musical scales obtained from shift spaces in symbolic dynamics through the first symbol rule, which yields scales in any n-TET tuning system. The modes are thought as elements of orbit equivalence classes of cyclic shift actions on languages, and we study their orbitals and transversals. We present explicit formulations of the generating functions that allow us to deduce the orbital and transversal dimensions of classes of musical scales generated by vertex shifts, for all n, in particular for the 12-TET tuning system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematics and Music Taylor & Francis

Symbolic dynamical scales: modes, orbitals, and transversals

Journal of Mathematics and Music , Volume 17 (1): 19 – Jan 2, 2023
19 pages

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References (50)

Publisher
Taylor & Francis
Copyright
© 2021 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1745-9745
eISSN
1745-9737
DOI
10.1080/17459737.2021.1953169
Publisher site
See Article on Publisher Site

Abstract

We study classes of musical scales obtained from shift spaces in symbolic dynamics through the first symbol rule, which yields scales in any n-TET tuning system. The modes are thought as elements of orbit equivalence classes of cyclic shift actions on languages, and we study their orbitals and transversals. We present explicit formulations of the generating functions that allow us to deduce the orbital and transversal dimensions of classes of musical scales generated by vertex shifts, for all n, in particular for the 12-TET tuning system.

Journal

Journal of Mathematics and MusicTaylor & Francis

Published: Jan 2, 2023

Keywords: symbolic dynamics; scales; classification; analytic combinatorics; generating functions; 37B10; 05A15; 00A65

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