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The Torii of Phases

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Mathematics and Computation in Music (MCM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7937))

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Abstract

The present paper is concerned with the existence, meaning and use of the phases of the (complex) Fourier coefficients of pc-sets, viewed as maps from ℤ c to . It explores a particular cross-section of the most general torus of phases, representing pc-sets by the phases of the third and fifth coefficients. On this 2D torus, triads take on the well-known configuration of the Tonnetz. Some other (sequences of) chords are viewed in this space as examples of its musical relevance. The end of the paper uses the model as a convenient universe for drawing gestures – continuous paths between pc-sets.

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Author information

Authors and Affiliations

  1. Classes Préparatoire aux Grandes Ecoles, Perpignan, France

    Emmanuel Amiot

Authors
  1. Emmanuel Amiot
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Editor information

Editors and Affiliations

  1. Boston University, USA

    Jason Yust

  2. McGill University, Montreal, Canada

    Jonathan Wild

  3. University of Amsterdam, The Netherlands

    John Ashley Burgoyne

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Amiot, E. (2013). The Torii of Phases. In: Yust, J., Wild, J., Burgoyne, J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science(), vol 7937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39357-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-39357-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39356-3

  • Online ISBN: 978-3-642-39357-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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