Symbolic dynamical scales: modes, orbitals, and transversals

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2020-09-06 DOI:10.1080/17459737.2021.1953169

Ricardo Gómez Aíza

引用次数: 1

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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符号动力尺度:模式、轨道和横向

我们研究了符号动力学中从移位空间中得到的音阶类，通过第一符号规则，它产生了任何n-TET调谐系统的音阶。这些模态被认为是语言上循环移位作用的轨道等价类的元素，我们研究了它们的轨道和截线。我们提出了生成函数的显式公式，使我们能够推导出由顶点移位生成的音乐音阶类的轨道和横向维度，对于所有n，特别是对于12-TET调谐系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematics and Music 数学-数学跨学科应用

CiteScore

1.90

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematics and Music aims to advance the use of mathematical modelling and computation in music theory. The Journal focuses on mathematical approaches to musical structures and processes, including mathematical investigations into music-theoretic or compositional issues as well as mathematically motivated analyses of musical works or performances. In consideration of the deep unsolved ontological and epistemological questions concerning knowledge about music, the Journal is open to a broad array of methodologies and topics, particularly those outside of established research fields such as acoustics, sound engineering, auditory perception, linguistics etc.