Skip to main content

Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2611)

Abstract

A study on a 220-piece corpus (baroque, classical, romantic, 12-tone, jazz, rock, DNA strings, and random music) reveals that aesthetically pleasing music may be describable under the Zipf-Mandelbrot law. Various Zipf-based metrics have been developed and evaluated. Some focus on music-theoretic attributes such as pitch, pitch and duration, melodic intervals, and harmonic intervals. Others focus on higher-order attributes and fractal aspects of musical balance. Zipf distributions across certain dimensions appear to be a necessary, but not sufficient condition for pleasant music. Statistical analyses suggest that combinations of Zipf-based metrics might be used to identify genre and/or composer. This is supported by a preliminary experiment with a neural network classifier. We describe an evolutionary music framework under development, which utilizes Zipf-based metrics as fitness functions.

Keywords

  • Fractal Dimension
  • Interval Graph
  • Relative Balance
  • Composite Metrics
  • Neural Network Classifier

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/3-540-36605-9_48
  • Chapter length: 13 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   139.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-36605-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   179.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adamic, L.A.: “Zipf, Power-laws, and Pareto — a Ranking Tutorial” (1999) http://ginger.hpl.hp.com/shl/papers/ranking/

  2. Balaban, M., Ebcioğlu, K., and Laske, O., (eds.): Understanding Music with AI: Perspectives on Music Cognition. Cambridge: AAAI Press/MIT Press (1992)

    Google Scholar 

  3. Cope, D.: Virtual Music, MIT Press Cambridge (2001)

    Google Scholar 

  4. Howat, R.: Debussy in Proportion. Cambridge University Press (cited in [16]) Cambridge (1983)

    Google Scholar 

  5. Knott, R.: “Fibonacci Numbers and Nature”. http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html (2002)

  6. Li, W.: “Zipf’s Law”. http://linkage.rockefeller.edu/wli/zipf/ (2002)

  7. Machado, P., Cardoso, A.: “All the truth about NEvAr”. Applied Intelligence, Special issue on Creative Systems, Bentley, P., Corne, D. (eds), 16(2), (2002), 101–119

    Google Scholar 

  8. Manaris, B., Purewal, T., and McCormick, C.: “Progress Towards Recognizing and Classifying Beautiful Music with Computers”. 2002 IEEE SoutheastCon, Columbia, SC (2002) 52–57

    Google Scholar 

  9. Mandelbrot, B.B.: The Fractal Geometry of Nature. W.H. Freeman New York (1977)

    Google Scholar 

  10. Marillier, C.G.: “Computer Assisted Analysis of Tonal Structure in the Classical Symphony”. Haydn Yearbook 14 (1983) 187–199 (cited in [16])

    Google Scholar 

  11. May, M.: “Did Mozart Use the Golden Section?”. American Scientist 84(2). http://www.sigmaxi.org/amsci/issues/Sciobs96/Sciobs96-03MM.html (1996)

  12. Meyer, L.B.: Emotion and Meaning in Music. University of Chicago Press Chicago (1956)

    Google Scholar 

  13. Meyer, L.B.: “Music and Emotion: Distinctions and Uncertainties”. In Music and Emotion — Theory and Research, Juslin, P.N., Sloboda, J.A. (eds), Oxford University Press Oxford (2001) 341–360

    Google Scholar 

  14. Miranda, E.R.: Composing Music with Computers. Focal Press Oxford (2001)

    Google Scholar 

  15. Nettheim, N.: “On the Spectral Analysis of Melody”. Interface: Journal of New Music Research 21 (1992) 135–148

    CrossRef  Google Scholar 

  16. Nettheim, N.: “A Bibliography of Statistical Applications in Musicology”. Musicology Australia 20 (1997) 94–106

    Google Scholar 

  17. Pareto, V.: Cours d’Economie Politique, Rouge (Lausanne et Paris) (1897) Cited in [9]

    Google Scholar 

  18. Salingaros, N..A., and West, B.J.: “A Universal Rule for the Distribution of Sizes”. Environment and Planning B(26) (1999) 909–923

    Google Scholar 

  19. Schroeder, M.: Fractals, Chaos, Power Laws. W.H. Freeman New York (1991)

    MATH  Google Scholar 

  20. Stuttgart Neural Network Simulator (SNNS), http://www-ra.informatik.uni-tuebingen.de/SNNS/).

  21. Taylor, R.P., Micolich, A.P., and Jonas, D.: “Fractal Analysis Of Pollock’s Drip Paintings”. Nature, vol. 399, (1999), 422http://materialscience.uoregon.edu/taylor/art/Nature1.pdf

    CrossRef  Google Scholar 

  22. The Classical Music Archives. http://www.classicalarchives.com.

  23. Voss, R.F., and Clarke, J.: “1/f Noise in Music and Speech”. Nature 258 (1975) 317–318

    CrossRef  Google Scholar 

  24. Voss, R.F., and Clarke, J.: “1/f Noise in Music: Music from 1/f Noise”. Journal of Acoustical Society of America 63(1) (1978) 258–263

    CrossRef  Google Scholar 

  25. Zipf, G.K.: Human Behavior and the Principle of Least Effort. Addison-Wesley New York (1972) (original publication Hafner Publishing Company, 1949)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Manaris, B., Vaughan, D., Wagner, C., Romero, J., Davis, R.B. (2003). Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music. In: , et al. Applications of Evolutionary Computing. EvoWorkshops 2003. Lecture Notes in Computer Science, vol 2611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36605-9_48

Download citation

  • DOI: https://doi.org/10.1007/3-540-36605-9_48

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00976-4

  • Online ISBN: 978-3-540-36605-8

  • eBook Packages: Springer Book Archive