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Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift

Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift We address the broad idea of using mathematical models to inform music theory and composition by implementing them directly in the process of music creation. The mathematical model we will use is the Thue–Morse dynamical system. We briefly survey previously published works that were similarly motivated, and then discuss a new piece of music we composed, inspired by this symbolic dynamical system. In the course of our analysis, we also present an alternative proof of the well-know fact that the Thue–Morse subshift has topological entropy zero that motivated us to think of the map between binary sequences and musical scales as “binary keyboards.” Indeed, the binary representation allows to study musical scales through mathematical properties of the sequences that define them; here we present the set of standard Thue–Morse scales and compare them with other well-known musical scales. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition" Taylor & Francis

Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift

Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift


Abstract

We address the broad idea of using mathematical models to inform music theory and composition by implementing them directly in the process of music creation. The mathematical model we will use is the Thue–Morse dynamical system. We briefly survey previously published works that were similarly motivated, and then discuss a new piece of music we composed, inspired by this symbolic dynamical system. In the course of our analysis, we also present an alternative proof of the well-know fact that the Thue–Morse subshift has topological entropy zero that motivated us to think of the map between binary sequences and musical scales as “binary keyboards.” Indeed, the binary representation allows to study musical scales through mathematical properties of the sequences that define them; here we present the set of standard Thue–Morse scales and compare them with other well-known musical scales.

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References (29)

Publisher
Taylor & Francis
Copyright
© 2020 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1745-9745
eISSN
1745-9737
DOI
10.1080/17459737.2020.1732490
Publisher site
See Article on Publisher Site

Abstract

We address the broad idea of using mathematical models to inform music theory and composition by implementing them directly in the process of music creation. The mathematical model we will use is the Thue–Morse dynamical system. We briefly survey previously published works that were similarly motivated, and then discuss a new piece of music we composed, inspired by this symbolic dynamical system. In the course of our analysis, we also present an alternative proof of the well-know fact that the Thue–Morse subshift has topological entropy zero that motivated us to think of the map between binary sequences and musical scales as “binary keyboards.” Indeed, the binary representation allows to study musical scales through mathematical properties of the sequences that define them; here we present the set of standard Thue–Morse scales and compare them with other well-known musical scales.

Journal

"Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition"Taylor & Francis

Published: Sep 2, 2021

Keywords: substitution dynamics; symbolic dynamics; musical composition; musical scales; binary keyboards; Thue–Morse sequence; Thue–Morse dynamical system; 37B10; 00A65; 05A05; applied computing

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