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Symbolic dynamical scales: modes, orbitals, and transversals

2020/09/06 by Ricardo Gómez Aíza, Aíza, Ricardo Gómez · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #00A65 #05A15 #37B10 #Cellular Automata and Applications #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2009.02669

openalex publication_date 2020/09/06 · openalex created_date 2020/09/11 · openalex updated_date 2026/07/28

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.

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