Cross Entropy as a Measure of Musical Contrast

  • Robin Laney
  • Robert Samuels
  • Emilie Capulet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9110)


We present a preliminary study of using the information theoretic concept of cross entropy to measure musical contrast in a symbolic context, with a focus on melody. We measure cross entropy using the Information Dynamics Of Music (IDyOM) framework. Whilst our long term aim is to understand the use of contrast in sonata form, in this paper we take a more general perspective and look at a broad spread of Western art music of the common practice era. Our results suggest that cross entropy has a useful role as an objective measure of contrast, but that a fuller picture will require more work.


Contrast Similarity Cross entropy N gram model Markov model 



We are grateful for discussions and advice to Byron Dueck, Tom Collins, Alan Marsden, Marcus Pearce, Raymond Whorley, Geraint Wiggins, and Alistair Willis.


  1. 1.
    Cleary, J.G., Witten, I.H.: Data compression using adaptive coding and partial string matching. IEEE Trans. Commun. 32(4), 396–402 (1984)CrossRefGoogle Scholar
  2. 2.
    Collins T., Böck S., Krebs, F., Widmer, G.: Bridging the audio-symbolic gap: the discovery of repeated note content directly from polyphonic music audio. In: Proceedings of the Audio Engineering Society’s 53rd Conference on Semantic Audio, London, p. 12 (2014)Google Scholar
  3. 3.
    Collins, T., Laney, R., Willis, A., Garthwaite, P.H.: Developing and evaluating computational models of musical style. In: Jin, Y. (ed.) Artificial Intelligence for Engineering Design, Analysis and Manufacturing, vol. 9, p. 28. Cambridge University Press, Cambridge (1995)Google Scholar
  4. 4.
    Conklin, D., Witten, I.H.: Multiple viewpoint systems for music prediction. J. New Music Res. 24(1), 51–73 (1995)CrossRefGoogle Scholar
  5. 5.
    Marsden, A.: Interrogating melodic similarity: a definitive phenomenon or the product of interpretation? J. New Music Res. 41(4), 323–335 (2012)CrossRefGoogle Scholar
  6. 6.
    Meyer, L.B.: Meaning in music and information theory. J. Aesthet. Art Crit. 15, 412–424 (1957)CrossRefGoogle Scholar
  7. 7.
    Online Chopin Variorum Edition.
  8. 8.
    Pearce, M.: The construction and evaluation of statistical models of melodic structure in music perception and composition, M.T. Ph.D. thesis. City University London, Pearce (2005)Google Scholar
  9. 9.
    Pearce, M.T., GA Wiggins, G.A.: Auditory expectation: the information dynamics of music perception and cognition. Top. Cogn. Sci. 4(4), 625–652 (2012)CrossRefGoogle Scholar
  10. 10.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Tversky, A.: Features of similarity. Psychol. Rev. 84, 327–352 (1977)CrossRefGoogle Scholar
  12. 12.
    Whorley, R.: The construction and evaluation of statistical models of melody and harmony. Whorley, R.P. Ph.D. thesis. Goldsmiths, University of London (2013)Google Scholar
  13. 13.
    Wiggins, G.A., Müllensiefen, D., Pearce, M.T.: On the non-existence of music: why music theory is a figment of the imagination. Musicae Sci. 5, 231–255 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Open UniversityMilton KeynesUK
  2. 2.London College of MusicUniversity of West LondonLondonUK

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