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Toward a Gauge Theory of Musical Forces

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Quantum Interaction (QI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10106))

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Abstract

How well does a given pitch fit into a tonal scale or key, being either a major or minor key? This question addresses the well-known phenomenon of tonal attraction in music psychology. Metaphorically, tonal attraction is often described in terms of attracting and repelling forces that are exerted upon a probe tone of a scale. In modern physics, forces are related to gauge fields expressing fundamental symmetries of a theory. In this study we address the intriguing relationship between musical symmetries and gauge forces in the framework of quantum cognition.

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Notes

  1. 1.

    Note that we chose a natural unit system with particle’s mass \(m = 1/2\) and Planck’s quantum of angular momentum \(\hbar \equiv 1\) as necessary for quantum cognition applications.

  2. 2.

    For the sake of simplicity, we neglect time-dependence of the gauge field in our exposition.

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Author information

Authors and Affiliations

  1. Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Berlin, Germany

    Peter beim Graben

  2. Emeritus ILLC, Universiteit van Amsterdam, 1090, Amsterdam, Georgia, The Netherlands

    Reinhard Blutner

Authors
  1. Peter beim Graben
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  2. Reinhard Blutner
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Corresponding author

Correspondence to Peter beim Graben .

Editor information

Editors and Affiliations

  1. San Francisco State University, San Francisco, California, USA

    Jose Acacio de Barros

  2. University of Oxford, Oxford, United Kingdom

    Bob Coecke

  3. City University of London, London, United Kingdom

    Emmanuel Pothos

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beim Graben, P., Blutner, R. (2017). Toward a Gauge Theory of Musical Forces. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-52289-0_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52288-3

  • Online ISBN: 978-3-319-52289-0

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