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Journal of Mathematics and Music
Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance
Volume 5, 2011 - Issue 3
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Original Articles

An algebra for periodic rhythms and scales

Emmanuel Amiot Department of Electrical and Computer Engineering, University of Wisconsin, 1415 Engineering Drive, Madison, WI, 53706, USACorrespondence[email protected]
&
William A. Sethares Department of Electrical and Computer Engineering, University of Wisconsin, 1415 Engineering Drive, Madison, WI, 53706, USA
Pages 149-169 | Received 25 Oct 2009, Accepted 25 Oct 2011, Published online: 14 Dec 2011

Citations (22)

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Read on this site (10)

Song An, Alyse Hachey, Daniel Tillman, Danielle Divis & Bryn Birdwell. (2023) Larger versus Luckier: preservice teachers’ exploration of probabilistic reasoning through an aleatoric music activity. International Journal of Mathematical Education in Science and Technology 54:3, pages 325-350.
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Ricardo Gómez Aíza. (2023) Symbolic dynamical scales: modes, orbitals, and transversals. Journal of Mathematics and Music 17:1, pages 46-64.
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Jason Yust, Christopher William White & Leigh VanHandel. (2022) Rhythm, mathematics, and Godfried Toussaint. Journal of Mathematics and Music 16:2, pages 133-137.
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Emmanuel Amiot. (2021) Entropy of Fourier coefficients of periodic musical objects. Journal of Mathematics and Music 15:3, pages 235-246.
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Ricardo Gómez & Luis Nasser. (2021) Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift. Journal of Mathematics and Music 15:3, pages 247-266.
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Emmanuel Amiot. (2017) The discrete Fourier transform of distributions. Journal of Mathematics and Music 11:2-3, pages 76-100.
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Andrew J. Milne, David Bulger & Steffen A. Herff. (2017) Exploring the space of perfectly balanced rhythms and scales. Journal of Mathematics and Music 11:2-3, pages 101-133.
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Gilberto Bernardes, Diogo Cocharro, Marcelo Caetano, Carlos Guedes & Matthew E.P. Davies. (2016) A multi-level tonal interval space for modelling pitch relatedness and musical consonance. Journal of New Music Research 45:4, pages 281-294.
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Jeremy Kastine & Mariana Montiel. (2016) The S-canon and the multi-S-canon: an introduction. Journal of Mathematics and Music 10:3, pages 211-225.
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Marco Castrillón López & Manuel Domínguez Romero. (2016) LR property of non-well-formed scales. Journal of Mathematics and Music 10:1, pages 18-35.
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Articles from other publishers (12)

Güngör Gündüz. (2023) Entropy, energy, and instability in music. Physica A: Statistical Mechanics and its Applications 609, pages 128365.
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Jason Yust. (2021) Steve Reich’s Signature Rhythm and an Introduction to Rhythmic Qualities. Music Theory Spectrum 43:1, pages 74-90.
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María Navarro-Cáceres, Marcelo Caetano, Gilberto Bernardes, Mercedes Sánchez-Barba & Javier Merchán Sánchez-Jara. (2020) A Computational Model of Tonal Tension Profile of Chord Progressions in the Tonal Interval Space. Entropy 22:11, pages 1291.
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Federico Favali. (2020) Entropic dynamics and rhizomatic archetypes in Aeriality by Anna Thorvaldsdottir. Zbornik Akademije umetnosti:8, pages 112-136.
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Song A. An, Daniel A. Tillman & Lawrence M. Lesser. 2018. Transdisciplinarity in Mathematics Education. Transdisciplinarity in Mathematics Education 25 45 .
Jason Yust. (2017) Review of Emmanuel Amiot, Music through Fourier Space: Discrete Fourier Transform in Music Theory (Springer, 2016) . Music Theory Online 23:3.
Crossref
Jason Yust. 2017. The Musical-Mathematical Mind. The Musical-Mathematical Mind 329 337 .
Emmanuel Amiot. 2017. The Musical-Mathematical Mind. The Musical-Mathematical Mind 17 28 .
Jason Yust. (2016) Special Collections. Journal of Music Theory 60:2, pages 213-262.
Crossref
Jason Yust. (2015) Schubert’s Harmonic Language and Fourier Phase Space. Journal of Music Theory 59:1, pages 121-181.
Crossref
Jason Yust. 2015. Mathematics and Computation in Music. Mathematics and Computation in Music 207 218 .
Emmanuel Amiot. 2013. Mathematics and Computation in Music. Mathematics and Computation in Music 1 18 .

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