Skip to main content
SpringerLink
Log in
Book cover

International Conference on Mathematics and Computation in Music

MCM 2009: Mathematics and Computation in Music pp 93–103Cite as

Compatibility of the Different Tuning Systems in an Orchestra

  • Conference paper

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

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benson, D.: Music: a Mathematical Offering. Cambridge University Press, Cambridge (2006)

    CrossRef  MATH  Google Scholar 

  2. Borup, H.: A History of String Intonation, http://www.hasseborup.com/ahistoryofintonationfinal1.pdf

  3. Carlsson, C., Fullér, R.: Fuzzy Reasoning in Decision Making and Optimization. Physica-Verlag, Heidelberg (2002)

    CrossRef  MATH  Google Scholar 

  4. Dubois, D., Prade, H.: Fuzzy Sets and Systems:Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  5. Goldáraz Gaínza, J.J.: Afinación y temperamento en la música occidental, Alianza Editorial, Madrid (1992)

    Google Scholar 

  6. Hall, R.W., Josíc, K.: The mathematics of musical instruments. Amer. Math. Monthly 108, 347–357 (2001)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Halusca, J.: Equal temperament and pythagorean tuning:a geometrical interpretation in the plane. Fuzzy Sets and Systems 114, 261–269 (2000)

    CrossRef  MathSciNet  Google Scholar 

  8. Haluska, J.: The Mathematical Theory of Tone Systems. Marcel Dekker, Inc., Bratislava (2005)

    MATH  Google Scholar 

  9. Lattard, J.: Gammes et tempéraments musicaux, Masson Éditions, Paris (1988)

    Google Scholar 

  10. Liern, V.: Fuzzy tuning systems: the mathematics of the musicians. Fuzzy Sets and Systems 150, 35–52 (2005)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Teresa León
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vicente Liern
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • 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)

search

Navigation