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Compatibility of the Different Tuning Systems in an Orchestra

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

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.

Keywords

  • Tuning Systems
  • Fuzzy Sets
  • Fuzzy Numbers

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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)