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Compatibility of the Different Tuning Systems in an Orchestra

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Mathematics and Computation in Music (MCM 2009)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 38))

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Abstract

Focusing on the daily practice of musicians, we give flexibility to the mathematical treatment of musical notes, tuning systems and the relations between them. This allows us to connect the theory and the practice of music. Using the techniques of fuzzy logic, we describe the concepts with fuzzy sets and introduce the α-compatibility as a degree of interchangeability between tuning systems. To show how our proposal works, we use a fragment of Haydn and analyze the compatibility of the notes taken from 48 recordings for the tuning systems of Pythagoras, Zarlino and Equal Temperament of 12 notes.

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Author information

Authors and Affiliations

  1. Taller de Música Jove, Mistral, 22, 46020, Valencia, Spain

    Alfonso del Corral

  2. Dep. Estadística e Investigación Operativa, Universidad de Valencia, Vicente, Andrés Estellés, s/n, 46100, Burjassot, Valencia, Spain

    Teresa León

  3. Dep. Matemáticas para la Economía y la Empresa, Universidad de Valencia, Avda. Tarongers, s/n, 46022, Valencia, Spain

    Vicente Liern

Authors
  1. Alfonso del Corral
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  2. Teresa León
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  3. Vicente Liern
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Editor information

Editors and Affiliations

  1. Viterbi School of Engineering, Integrated Media Systems Center, Epstein Department of Industrial and Systems Engineering, University of Southern California, 3715 McClintock Avenue GER240 MC:0193, P.O. Box, Los Angeles, California, USA

    Elaine Chew

  2. Hugh Hodgson School of Music, University of Georgia, 250 River Road, GA 30602-7278, Athens, USA

    Adrian Childs

  3. Department of Math and Computer Science, Barry University, 11300 NE 2nd Avenue, Miami Shores, FL 33161, USA

    Ching-Hua Chuan

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© 2009 Springer-Verlag Berlin Heidelberg

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del Corral, A., León, T., Liern, V. (2009). Compatibility of the Different Tuning Systems in an Orchestra. In: Chew, E., Childs, A., Chuan, CH. (eds) Mathematics and Computation in Music. MCM 2009. Communications in Computer and Information Science, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02394-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-02394-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02393-4

  • Online ISBN: 978-3-642-02394-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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