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Quantum-Musical Explorations on \(\mathbb {Z}_n\)

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Mathematics and Computation in Music (MCM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13267))

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Abstract

Motivated through recent applications of quantum theory to the music-theoretical conceptualisation of tonal attraction, the paper recapitulates basic facts about quantum wave functions over the finite configuration space \(\mathbb {Z}_n\), and proposes a particular musical application.

After an introduction of position and momentum operators, the Fourier transform as well as the translation and ondulation operators, particular attention is plaid to the Quantum Harmonic Oscillator via its Hamilton operator and its eigenstates. In this setup the time development of chosen wave functions is applied to the control of moving sound sources in a Spatialisation scenario.

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Notes

  1. 1.

    https://forum.ircam.fr/projects/detail/spat/.

  2. 2.

    https://www.wolfram.com/mathematica/.

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Author information

Authors and Affiliations

  1. Departament de Creació i Teoria Musical, Escola Superior de Música de Catalunya, Barcelona, Spain

    Thomas Noll

  2. Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany

    Peter Beim Graben

Authors
  1. Thomas Noll
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  2. Peter Beim Graben
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Corresponding author

Correspondence to Thomas Noll .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Mariana Montiel

  2. Technological University of the Mixteca, Huajuapan de León, Mexico

    Octavio A. Agustín-Aquino

  3. Universidad Politécnica de Madrid, Madrid, Spain

    Francisco Gómez

  4. Life University, Marietta, GA, USA

    Jeremy Kastine

  5. National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Emilio Lluis-Puebla

  6. Georgia State University, Atlanta, GA, USA

    Brent Milam

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Noll, T., Graben, P.B. (2022). Quantum-Musical Explorations on \(\mathbb {Z}_n\). In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_32

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  • DOI: https://doi.org/10.1007/978-3-031-07015-0_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07014-3

  • Online ISBN: 978-3-031-07015-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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