The Harmonic Musical Surface and Two Novel Chord Representation Schemes

  • Emilios CambouropoulosEmail author


Selecting an appropriate representation for chords is important for encoding pertinent harmonic aspects of the musical surface, and, at the same time, is crucial for building effective computational models for music analysis. This chapter, initially, addresses musicological, perceptual and computational aspects of the harmonic musical surface. Then, two novel general chord representations are presented: the first, the General Chord Type (GCT) representation, is inspired by the standard Roman numeral chord type labelling, but is more general and flexible so as to be applicable to any idiom; the second, the Directed Interval Class (DIC) vector, captures the intervallic content of a transition between two chords in a transposition-invariant idiom-independent manner. Musical examples and preliminary evaluations of both encoding schemes are given, illustrating their potential to form a basis for harmonic processing in the domain of computational musicology.


Music Information Retrieval Pitch Interval Tonal Music Pitch Class Tonal Context 
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.


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  1. Bregman, A. S. (1994). Auditory Scene Analysis: The Perceptual Organization of Sound. MIT Press.Google Scholar
  2. Burns, E. M. (1999). Intervals, scales and tuning. In Deutsch, D., editor, The Psychology of Music, pages 215–264. Academic Press, second edition.Google Scholar
  3. Cambouropoulos, E. (2008). Voice and stream: Perceptual and computational modeling of voice separation. Music Perception, 26(1):75–94.Google Scholar
  4. Cambouropoulos, E. (2010). The musical surface: Challenging basic assumptions. Musicae Scientiae, 14(2):131–147.Google Scholar
  5. Cambouropoulos, E. (2012). A directional interval class representation of chord transitions. In Proceedings of the Joint 12th International Conference for Music Perception and Cognition & 8th Conference of the European Society for the Cognitive Sciences of Music (ICMPC-ESCOM 2012), Thessaloniki, Greece.Google Scholar
  6. Cambouropoulos, E., Crochemore, M., Iliopoulos, C. S., Mouchard, L., and Pinzon, Y. J. (2002). Algorithms for computing approximate repetitions in musical sequences. International Journal of Computer Mathematics, 79(11):1135–1148.Google Scholar
  7. Cambouropoulos, E., Kaliakatsos-Papakostas, M., and Tsougras, C. (2014). An idiom-independent representation of chords for computational music analysis and generation. In Proceeding of the Joint 11th Sound and Music Computing Conference (SMC) and 40th International Computer Music Conference (ICMC), ICMC–SMC 2014, Athens, Greece.Google Scholar
  8. Cambouropoulos, E., Katsiavalos, A., and Tsougras, C. (2013). Idiom-independent harmonic pattern recognition based on a novel chord transition representation. In Proceedings of the 3rd InternationalWorkshop on Folk Music Analysis (FMA2013), Amsterdam, Netherlands.Google Scholar
  9. Cemgil, A. T., Kappen, H. J., and Barber, D. (2006). A generative model for music transcription. IEEE Transactions on Audio, Speech, and Language Processing, 14(2):679–694.Google Scholar
  10. de Haas, W. B., Veltkamp, R. C., and Wiering, F. (2008). Tonal pitch step distance: a similarity measure for chord progressions. In 9th International Conference on Music Information Retrieval (ISMIR 2008), pages 51–56, Philadelphia, PA.Google Scholar
  11. de Haas, W. B., Wiering, F., and Veltkamp, R. C. (2013). A geometrical distance measure for determining the similarity of musical harmony. International Journal of Multimedia Information Retrieval, 2(3):189–202.Google Scholar
  12. Deutsch, D. (2012). The processing of pitch combinations. In Deutsch, D., editor, The Psychology of Music, pages 249–326. Academic Press, third edition.Google Scholar
  13. Forte, A. (1973). The Structure of Atonal Music. Yale University Press.Google Scholar
  14. Handel, S. (1989). Listening: An Introduction to the Perception of Auditory Events. MIT Press.Google Scholar
  15. Harte, C., Sandler, M., Abdallah, S. A., and Gómez, E. (2005). Symbolic representation of musical chords: A proposed syntax for text annotations. In Proceedings of the 6th International Conference on Music Information Retrieval (ISMIR 2005), pages 66–71, London, UK.Google Scholar
  16. Hubbard, T. L. and Datteri, D. L. (2001). Recognizing the component tones of a major chord. The American Journal of Psychology, 114(4):569–589.Google Scholar
  17. Huron, D. (2001). Tone and voice: A derivation of the rules of voice-leading from perceptual principles. Music Perception, 19(1):1–64.Google Scholar
  18. Hutchinson, W. and Knopoff, L. (1978). The acoustic component of Western consonance. Interface, 7(1):1–29.Google Scholar
  19. Jackendoff, R. (1987). Consciousness and the Computational Mind. MIT Press.Google Scholar
  20. Jackendoff, R. and Lerdahl, F. (2006). The capacity for music: What is it, and what’s special about it? Cognition, 100(1):33–72.Google Scholar
  21. Jordanous, A. (2008). Voice separation in polyphonic music: A data-driven approach. In Proceedings of the International Computer Music Conference 2008, Belfast, UK.Google Scholar
  22. Kaliakatsos-Papakostas, M. and Cambouropoulos, E. (2014). Probabilistic harmonisation with fixed intermediate chord constraints. In Proceedings of the Joint 11th Sound and Music Computing Conference (SMC) and 40th International Computer Music Conference (ICMC), Athens, Greece.Google Scholar
  23. Kaliakatsos-Papakostas, M., Katsiavalos, A., Tsougras, C., and Cambouropoulos, E. (2014). Harmony in the polyphonic songs of Epirus: Representation, statistical analysis and generation. In 4th International Workshop on Folk Music Analysis (FMA 2014), Istanbul, Turkey.Google Scholar
  24. Kaliakatsos-Papakostas, M., Zacharakis, A., Tsougras, C., and Cambouropoulos, E. (2015). Evaluating the General Chord Type algorithm in tonal music and organising its output in higher-level functional chord categories. In Proceedings of the 16th International Society for Music Information Retrieval Conference (ISMIR 2015), Malaga, Spain.Google Scholar
  25. Kostka, S. and Payne, D. (1995). Tonal Harmony. McGraw-Hill.Google Scholar
  26. Laitz, S. G. (2012). The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening. Oxford University Press.Google Scholar
  27. Lerdahl, F. (2001). Tonal Pitch Space. Oxford University Press.Google Scholar
  28. Lerdahl, F. and Jackendoff, R. (1983). A Generative Theory of Tonal Music. MIT Press.Google Scholar
  29. Lewin, D. (1959). Intervallic relations between two collections of notes. Journal of Music Theory, 3(2):298–301.Google Scholar
  30. Lewin, D. (2001). Special cases of the interval function between pitch-class sets x and y. Journal of Music Theory, 45(1):1–29.Google Scholar
  31. Lewin, D. (2007). Generalized Musical Intervals and Transformations. Oxford University Press.Google Scholar
  32. Locke, S. and Kellar, L. (1973). Categorical perception in a non-linguistic mode. Cortex, 9(4):355–369.Google Scholar
  33. Mauch, M., Cannam, C., Davies, M., Dixon, S., Harte, C., Kolozali, S., Tidhar, D., and Sandler, M. (2010). OMRAS2 metadata project 2009. In Proceedings of the 11 th International Society for Music Information Retrieval Conference (ISMIR 2010), Utrecht, The Netherlands.Google Scholar
  34. Parncutt, R. (1989). Harmony: A Psychoacoustical Approach. Springer.Google Scholar
  35. Parncutt, R. (1994). Template-matching models of musical pitch and rhythm perception. Journal of New Music Research, 23(2):145–167.Google Scholar
  36. Parncutt, R. (1997). A model of the perceptual root(s) of a chord accounting for voicing and prevailing tonality. In Leman, M., editor, Music, Gestalt, and Computing, volume 1317 of Lecture Notes in Computer Science, pages 181–199. Springer.Google Scholar
  37. Piston, W. (1978). Harmony. Norton. Revised and expanded by M. DeVoto.Google Scholar
  38. Povel, D.-J. and Jansen, E. (2001). Perceptual mechanisms in music processing. Music Perception, 19(2):169–197.Google Scholar
  39. Ryynänen, M. P. and Klapuri, A. P. (2008). Automatic transcription of melody, bass line, and chords in polyphonic music. Computer Music Journal, 32(3):72–86.Google Scholar
  40. Schorlemmer, M., Smaill, A., Kühnberger, K.-U., Kutz, O., Colton, S., Cambouropoulos, E., and Pease, A. (2014). COINVENT: Towards a computational concept invention theory. In 5th International Conference on Computational Creativity (ICCC) 2014, Ljubljana, Slovenia.Google Scholar
  41. Sloboda, J. A. (1985). The Musical Mind. Oxford University Press.Google Scholar
  42. Smith, J. D., Nelson, D. G., Grohskopf, L. A., and Appleton, T. (1994). What child is this? What interval was that? Familiar tunes and music perception in novice listeners. Cognition, 52(1):23–54.Google Scholar
  43. Temperley, D. (2001a). The Cognition of Basic Musical Structures. MIT Press.Google Scholar
  44. Temperley, D. (2001b). Kostka–Payne dataset. Available online at Last accessed 5 September 2015.
  45. Temperley, D. (2012). Computational models of music cognition. In Deutsch, D., editor, The Psychology of Music, pages 327–368. Academic Press, third edition.Google Scholar
  46. Tymoczko, D. (2011). A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford University Press.Google Scholar
  47. Vernon, P. E. (1934). Auditory perception. I. The Gestalt approach. II. The evolutionary approach. British Journal of Psychology, 25:123–139, 265–283.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Music StudiesAristotle University of ThessalonikiThessalonikiGreece

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