Analysing Music with Point-Set Compression Algorithms

Chapter

Abstract

Several point-set pattern-discovery and compression algorithms designed for analysing music are reviewed and evaluated. Each algorithm takes as input a point-set representation of a score in which each note is represented as a point in pitch-time space. Each algorithm computes the maximal translatable patterns (MTPs) in this input and the translational equivalence classes (TECs) of these MTPs, where each TEC contains all the occurrences of a given MTP. Each TEC is encoded as a 〈pattern, vector set〉 pair, in which the vector set gives all the vectors by which the pattern can be translated in pitch-time space to give other patterns in the input dataset. Encoding TECs in this way leads, in general, to compression, since each occurrence of a pattern within a TEC (apart from one) is encoded by a single vector, that has the same information content as one point. The algorithms reviewed here adopt different strategies aimed at selecting a set of MTP TECs that collectively cover (or almost cover) the input dataset in a way that maximizes compression. The algorithms are evaluated on two musicological tasks: classifying folk song melodies into tune families and discovering repeated themes and sections in pieces of classical music. On the first task, the best-performing algorithms achieved success rates of around 84%. In the second task, the best algorithms achieved mean F1 scores of around 0.49, with scores for individual pieces rising as high as 0.71.

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References

  1. Bayard, S. (1950). Prolegomena to a study of the principal melodic families of British-American folk song. Journal of American Folklore, 63(247):1–44.Google Scholar
  2. Bent, I. (1987). Analysis. The New Grove Handbooks in Music. Macmillan. (Glossary by W. Drabkin).Google Scholar
  3. Chaitin, G. J. (1966). On the length of programs for computing finite binary sequences. Journal of the Association for Computing Machinery, 13(4):547–569.Google Scholar
  4. Collins, T. (2011). Improved methods for pattern discovery in music, with applications in automated stylistic composition. PhD thesis, Faculty of Mathematics, Computing and Technology, The Open University, Milton Keynes. Collins, T. (2013a). JKU Patterns Development Database. Available at https://dl.dropbox.com/u/11997856/JKU/JKUPDD-Aug2013.zip.
  5. Collins, T. (2013b). MIREX 2013 Competition: Discovery of Repeated Themes and Sections. http://tinyurl.com/o9227qg. Accessed on 5 January 2015.
  6. Collins, T. (2013c). PattDisc-Jul2013. Available online at http://www.tomcollinsresearch.net/publications.html. Accessed 29 December 2013.
  7. Collins, T., Arzt, A., Flossmann, S., and Widmer, G. (2013). SIARCT-CFP: Improving precision and the discovery of inexact musical patterns in point-set representations. In Fourteenth International Society for Music Information Retrieval Conference (ISMIR 2013), Curitiba, Brazil.Google Scholar
  8. Collins, T., Laney, R., Willis, A., and Garthwaite, P. H. (2011). Modeling pattern importance in Chopin’s Mazurkas. Music Perception, 28(4):387–414.Google Scholar
  9. Collins, T., Thurlow, J., Laney, R., Willis, A., and Garthwaite, P. H. (2010). A comparative evaluation of algorithms for discovering translational patterns in baroque keyboard works. In Proceedings of the 11th International Society for Music Information Retrieval Conference (ISMIR 2010), pages 3–8, Utrecht, The Netherlands.Google Scholar
  10. Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. (2009). Introduction to Algorithms. MIT Press, 3rd edition.Google Scholar
  11. Dice, L. R. (1945). Measures of the amount of ecologic association between species. Ecology, 26(3):297–302.Google Scholar
  12. Forth, J. and Wiggins, G. A. (2009). An approach for identifying salient repetition in multidimensional representations of polyphonic music. In Chan, J., Daykin, J. W., and Rahman, M. S., editors, London Algorithmics 2008: Theory and Practice, pages 44–58. College Publications.Google Scholar
  13. Forth, J. C. (2012). Cognitively-motivated geometric methods of pattern discovery and models of similarity in music. PhD thesis, Department of Computing, Goldsmiths, University of London.Google Scholar
  14. Grijp, L. P. (2008). Introduction. In Grijp, L. P. and van Beersum, I., editors, Under the Green Linden—163 Dutch Ballads from the Oral Tradition, pages 18–27. Meertens Institute/Music & Words.Google Scholar
  15. Kolmogorov, A. N. (1965). Three approaches to the quantitative definition of information. Problems of Information Transmission, 1(1):1–7.Google Scholar
  16. Lerdahl, F. and Jackendoff, R. S. (1983). A Generative Theory of Tonal Music. MIT Press.Google Scholar
  17. Li, M., Chen, X., Li, X., Ma, B., and Vitányi, P. M. B. (2004). The similarity metric. IEEE Transactions on Information Theory, 50(12):3250–3264.Google Scholar
  18. Li, M. and Vitányi, P. (2008). An Introduction to Kolmogorov Complexity and Its Applications. Springer, third edition.Google Scholar
  19. Meredith, D. (2006a). Point-set algorithms for pattern discovery and pattern matching in music. In Proceedings of the Dagstuhl Seminar on Content-based Retrieval (No. 06171, 23–28 April, 2006), Schloss Dagstuhl, Germany. Available online at http://drops.dagstuhl.de/opus/volltexte/2006/652.
  20. Meredith, D. (2006b). The ps13 pitch spelling algorithm. Journal of New Music Research, 35(2):121–159.Google Scholar
  21. Meredith, D. (2007). Computing pitch names in tonal music: A comparative analysis of pitch spelling algorithms. PhD thesis, Faculty of Music, University of Oxford.Google Scholar
  22. Meredith, D. (2013). Three-layer precision, three-layer recall, and three-layer F1 score. http://tinyurl.com/owtz79v.
  23. Meredith, D., Lemström, K., and Wiggins, G. A. (2002). Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music. Journal of New Music Research, 31(4):321–345.Google Scholar
  24. Meredith, D., Lemström, K., and Wiggins, G. A. (2003). Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music. In Cambridge Music Processing Colloquium, Department of Engineering, University of Cambridge. Available online at http://www.titanmusic.com/papers.php.
  25. Meredith, D., Wiggins, G. A., and Lemstrm, K. (2001). Pattern induction and matching in polyphonic music and other multi-dimensional datasets. In Callaos, N., Zong, X., Verges, C., and Pelaez, J. R., editors, Proceedings of the 5th World Multiconference on Systemics, Cybernetics and Informatics (SCI2001), volume X, pages 61–66.Google Scholar
  26. Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14(5):465–471.Google Scholar
  27. Salomon, D. and Motta, G. (2010). Handbook of Data Compression. Springer, fifth edition.Google Scholar
  28. Scheurleer, D. (1900). Preisfrage. Zeitschrift der Internationalen Musikgesellschaft, 1(7):219–220.Google Scholar
  29. Simon, H. A. and Sumner, R. K. (1968). Pattern in music. In Kleinmuntz, B., editor, Formal representation of human judgment. Wiley.Google Scholar
  30. Simon, H. A. and Sumner, R. K. (1993). Pattern in music. In Schwanauer, S. M. and Levitt, D. A., editors, Machine Models of Music, pages 83–110. MIT Press.Google Scholar
  31. Solomonoff, R. J. (1964a). A formal theory of inductive inference (Part I). Information and Control, 7(1):1–22.Google Scholar
  32. Solomonoff, R. J. (1964b). A formal theory of inductive inference (Part II). Information and Control, 7(2):224–254.Google Scholar
  33. Sørensen, T. (1948). A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons. Kongelige Danske Videnskabernes Selskab, 5(4):1–34.Google Scholar
  34. van Kranenburg, P., Volk, A., and Wiering, F. (2013). A comparison between global and local features for computational classification of folk song melodies. Journal of New Music Research, 42(1):1–18.Google Scholar
  35. Velarde, G., Weyde, T., and Meredith, D. (2013). An approach to melodic segmentation and classification based on filtering with the Haar-wavelet. Journal of New Music Research, 42(4):325–345.Google Scholar
  36. Volk, A. and van Kranenburg, P. (2012). Melodic similarity among folk songs: An annotation study on similarity-based categorization in music. Musicae Scientiae, 16(3):317–339.Google Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Architecture, Design and Media TechnologyAalborg UniversityAalborgDenmark

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