Probabilistic and Logic-Based Modelling of Harmony

  • Simon Dixon
  • Matthias Mauch
  • Amélie Anglade
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6684)


Many computational models of music fail to capture essential aspects of the high-level musical structure and context, and this limits their usefulness, particularly for musically informed users. We describe two recent approaches to modelling musical harmony, using a probabilistic and a logic-based framework respectively, which attempt to reduce the gap between computational models and human understanding of music. The first is a chord transcription system which uses a high-level model of musical context in which chord, key, metrical position, bass note, chroma features and repetition structure are integrated in a Bayesian framework, achieving state-of-the-art performance. The second approach uses inductive logic programming to learn logical descriptions of harmonic sequences which characterise particular styles or genres. Each approach brings us one step closer to modelling music in the way it is conceptualised by musicians.


Chord transcription inductive logic programming musical harmony 


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  1. 1.
    Anglade, A., Benetos, E., Mauch, M., Dixon, S.: Improving music genre classification using automatically induced harmony rules. Journal of New Music Research 39(4), 349–361 (2010)CrossRefGoogle Scholar
  2. 2.
    Anglade, A., Dixon, S.: Characterisation of harmony with inductive logic programming. In: 9th International Conference on Music Information Retrieval, pp. 63–68 (2008)Google Scholar
  3. 3.
    Anglade, A., Ramirez, R., Dixon, S.: First-order logic classification models of musical genres based on harmony. In: 6th Sound and Music Computing Conference, pp. 309–314 (2009)Google Scholar
  4. 4.
    Anglade, A., Ramirez, R., Dixon, S.: Genre classification using harmony rules induced from automatic chord transcriptions. In: 10th International Society for Music Information Retrieval Conference, pp. 669–674 (2009)Google Scholar
  5. 5.
    Aucouturier, J.J., Defréville, B., Pachet, F.: The bag-of-frames approach to audio pattern recognition: A sufficient model for urban soundscapes but not for polyphonic music. Journal of the Acoustical Society of America 122(2), 881–891 (2007)CrossRefGoogle Scholar
  6. 6.
    Aucouturier, J.J., Pachet, F.: Improving timbre similarity: How high is the sky? Journal of Negative Results in Speech and Audio Sciences 1(1) (2004)Google Scholar
  7. 7.
    Bello, J.P., Pickens, J.: A robust mid-level representation for harmonic content in music signals. In: 6th International Conference on Music Information Retrieval, pp. 304–311 (2005)Google Scholar
  8. 8.
    Benetos, E., Kotropoulos, C.: Non-negative tensor factorization applied to music genre classification. IEEE Transactions on Audio, Speech, and Language Processing 18(8), 1955–1967 (2010)CrossRefGoogle Scholar
  9. 9.
    Cathé, P.: Harmonic vectors and stylistic analysis: A computer-aided analysis of the first movement of Brahms’ String Quartet Op. 51-1. Journal of Mathematics and Music 4(2), 107–119 (2010)CrossRefGoogle Scholar
  10. 10.
    Conklin, D.: Representation and discovery of vertical patterns in music. In: Anagnostopoulou, C., Ferrand, M., Smaill, A. (eds.) ICMAI 2002. LNCS (LNAI), vol. 2445, pp. 32–42. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Conklin, D., Bergeron, M.: Discovery of contrapuntal patterns. In: 11th International Society for Music Information Retrieval Conference, pp. 201–206 (2010)Google Scholar
  12. 12.
    Conklin, D., Witten, I.: Multiple viewpoint systems for music prediction. Journal of New Music Research 24(1), 51–73 (1995)CrossRefGoogle Scholar
  13. 13.
    Dixon, S., Pampalk, E., Widmer, G.: Classification of dance music by periodicity patterns. In: 4th International Conference on Music Information Retrieval, pp. 159–165 (2003)Google Scholar
  14. 14.
    Downie, J., Byrd, D., Crawford, T.: Ten years of ISMIR: Reflections on challenges and opportunities. In: 10th International Society for Music Information Retrieval Conference, pp. 13–18 (2009)Google Scholar
  15. 15.
    Ebcioğlu, K.: An expert system for harmonizing chorales in the style of J. S. Bach. In: Balaban, M., Ebcioiğlu, K., Laske, O. (eds.) Understanding Music with AI, pp. 294–333. MIT Press, Cambridge (1992)Google Scholar
  16. 16.
    Fujishima, T.: Realtime chord recognition of musical sound: A system using Common Lisp Music. In: Proceedings of the International Computer Music Conference, pp. 464–467 (1999)Google Scholar
  17. 17.
    Hainsworth, S.W.: Techniques for the Automated Analysis of Musical Audio. Ph.D. thesis, University of Cambridge, Cambridge, UK (2003)Google Scholar
  18. 18.
    Harte, C.: Towards Automatic Extraction of Harmony Information from Music Signals. Ph.D. thesis, Queen Mary University of London, Centre for Digital Music (2010)Google Scholar
  19. 19.
    Krumhansl, C.L.: Cognitive Foundations of Musical Pitch. Oxford University Press, Oxford (1990)Google Scholar
  20. 20.
    Lerdahl, F., Jackendoff, R.: A Generative Theory of Tonal Music. MIT Press, Cambridge (1983)Google Scholar
  21. 21.
    Longuet-Higgins, H., Steedman, M.: On interpreting Bach. Machine Intelligence 6, 221–241 (1971)Google Scholar
  22. 22.
    Mauch, M.: Automatic Chord Transcription from Audio Using Computational Models of Musical Context. Ph.D. thesis, Queen Mary University of London, Centre for Digital Music (2010)Google Scholar
  23. 23.
    Mauch, M., Dixon, S.: Approximate note transcription for the improved identification of difficult chords. In: 11th International Society for Music Information Retrieval Conference, pp. 135–140 (2010)Google Scholar
  24. 24.
    Mauch, M., Dixon, S.: Simultaneous estimation of chords and musical context from audio. IEEE Transactions on Audio, Speech and Language Processing 18(6), 1280–1289 (2010)CrossRefGoogle Scholar
  25. 25.
    Mauch, M., Dixon, S., Harte, C., Casey, M., Fields, B.: Discovering chord idioms through Beatles and Real Book songs. In: 8th International Conference on Music Information Retrieval, pp. 111–114 (2007)Google Scholar
  26. 26.
    Mauch, M., Müllensiefen, D., Dixon, S., Wiggins, G.: Can statistical language models be used for the analysis of harmonic progressions? In: International Conference on Music Perception and Cognition (2008)Google Scholar
  27. 27.
    Mauch, M., Noland, K., Dixon, S.: Using musical structure to enhance automatic chord transcription. In: 10th International Society for Music Information Retrieval Conference, pp. 231–236 (2009)Google Scholar
  28. 28.
    Maxwell, H.: An expert system for harmonizing analysis of tonal music. In: Balaban, M., Ebcioiğlu, K., Laske, O. (eds.) Understanding Music with AI, pp. 334–353. MIT Press, Cambridge (1992)Google Scholar
  29. 29.
    Mearns, L., Tidhar, D., Dixon, S.: Characterisation of composer style using high-level musical features. In: 3rd ACM Workshop on Machine Learning and Music (2010)Google Scholar
  30. 30.
    Morales, E.: PAL: A pattern-based first-order inductive system. Machine Learning 26(2-3), 227–252 (1997)CrossRefzbMATHGoogle Scholar
  31. 31.
    Pachet, F.: Surprising harmonies. International Journal of Computing Anticipatory Systems 4 (February 1999)Google Scholar
  32. 32.
    Papadopoulos, H.: Joint Estimation of Musical Content Information from an Audio Signal. Ph.D. thesis, Université Pierre et Marie Curie – Paris 6 (2010)Google Scholar
  33. 33.
    Pardo, B., Birmingham, W.: Algorithms for chordal analysis. Computer Music Journal 26(2), 27–49 (2002)CrossRefGoogle Scholar
  34. 34.
    Pérez-Sancho, C., Rizo, D., Iñesta, J.M.: Genre classification using chords and stochastic language models. Connection Science 21(2-3), 145–159 (2009)CrossRefGoogle Scholar
  35. 35.
    Pérez-Sancho, C., Rizo, D., Iñesta, J.M., de León, P.J.P., Kersten, S., Ramirez, R.: Genre classification of music by tonal harmony. Intelligent Data Analysis 14, 533–545 (2010)Google Scholar
  36. 36.
    Pickens, J., Bello, J., Monti, G., Sandler, M., Crawford, T., Dovey, M., Byrd, D.: Polyphonic score retrieval using polyphonic audio queries: A harmonic modelling approach. Journal of New Music Research 32(2), 223–236 (2003)CrossRefGoogle Scholar
  37. 37.
    Ramirez, R.: Inducing musical rules with ILP. In: Proceedings of the International Conference on Logic Programming, pp. 502–504 (2003)Google Scholar
  38. 38.
    Raphael, C., Stoddard, J.: Functional harmonic analysis using probabilistic models. Computer Music Journal 28(3), 45–52 (2004)CrossRefGoogle Scholar
  39. 39.
    Scholz, R., Vincent, E., Bimbot, F.: Robust modeling of musical chord sequences using probabilistic N-grams. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 53–56 (2009)Google Scholar
  40. 40.
    Steedman, M.: A generative grammar for jazz chord sequences. Music Perception 2(1), 52–77 (1984)CrossRefGoogle Scholar
  41. 41.
    Temperley, D., Sleator, D.: Modeling meter and harmony: A preference rule approach. Computer Music Journal 23(1), 10–27 (1999)CrossRefGoogle Scholar
  42. 42.
    Whorley, R., Wiggins, G., Rhodes, C., Pearce, M.: Development of techniques for the computational modelling of harmony. In: First International Conference on Computational Creativity, pp. 11–15 (2010)Google Scholar
  43. 43.
    Widmer, G.: Discovering simple rules in complex data: A meta-learning algorithm and some surprising musical discoveries. Artificial Intelligence 146(2), 129–148 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Winograd, T.: Linguistics and the computer analysis of tonal harmony. Journal of Music Theory 12(1), 2–49 (1968)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Simon Dixon
    • 1
  • Matthias Mauch
    • 1
  • Amélie Anglade
    • 1
  1. 1.Centre for Digital MusicQueen Mary University of LondonLondonUK

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