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International Conference on Mathematics and Computation in Music

MCM 2007: Mathematics and Computation in Music pp 140–155Cite as

Calculating Tonal Fusion by the Generalized Coincidence Function

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 37))

Abstract

Models of pitch perception in the time domain suggest that the perception of pitch is extracted from neuronal pulse series by networks for periodicity detection. A neuronal mechanism for periodicity detection in the auditory system has been found in the inferior colliculus (Langner 1983). The present paper proposes a mathematical model to compute the degree of coincidence in the periodicity detection mechanism for musical intervals represented by pulse series. The purpose of this model is to study the logical structure of coincidence and to define a measure value for the degree of coincidence.

The model is purely mathematical but has a strong relation to physiological data presented by Langner. As the sensation of consonance depends mostly on pitch, frequency is the only parameter to be regarded in the model. The integration of other parameters and the adaptation to further physiological data should be easy but still lies ahead.

The model is a mathematical basis for a concept of consonance based on pitch perception models in the time domain. In contrast to the concept of the sensory consonance it does not refer to the percept of roughness, which nevertheless is important for the perceived pleasantness of consonances.

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Author information

Authors and Affiliations

  1. Peter-Cornelius-Conservatory of music, Mainz

    Martin Ebeling

Authors
  1. Martin Ebeling
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Editors and Affiliations

  1. Abteilung III Akustik und Musiktechnologie, Staatliches Institut für Musikforschung Preußischer Kulturbesitz, Tiergartenstr. 1, 10785, Berlin, Germany

    Timour Klouche

  2. Departament de Teoria i Composicio i Direccio, Escola Superior de Musica de Catalunya, C. Padilla 155-Edifici L’Auditori, 08013, Barcelona, Spain

    Thomas Noll

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Ebeling, M. (2009). Calculating Tonal Fusion by the Generalized Coincidence Function. In: Klouche, T., Noll, T. (eds) Mathematics and Computation in Music. MCM 2007. Communications in Computer and Information Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04579-0_14

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  • DOI: https://doi.org/10.1007/978-3-642-04579-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04578-3

  • Online ISBN: 978-3-642-04579-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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