Comparison of musical sequences

Abstract

Concepts from the theory of sequence comparison are adapted to measure the overall similarity or dissimilarity between two musical scores. A key element is the notion of consolidation and fragmentation, different both from the deletions and insertions familiar in sequence comparison, and from the compressions and expansions of time warping in automatic speech recognition. The measure of comparison is defined so as to detect similarities in melodic line despite gross differences in key, mode or tempo. A dynamic programming algorithm is presented for calculating the measure, and is programmed and applied to a set of variations on a theme by Mozart. Cluster analysis and spatial representation of the results confirm subjective impressions of the patterns of similarities among the variations. A generalization of the algorithm is presented for detecting locally similar portions in two scores, and is then applied.

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References

  1. Anonymous.Radio City Album of Soprano Solos. New York: Edward B. Music Corporation, 1932, pp. 2–7.

  2. Dillon, M. and M. Hunter. “Automated Identification of Melodic Variants in Folk Music.”Computers and the Humanities, 16 (1982), 107–17.

    Google Scholar 

  3. Duschenes, M.Méthodes de flûte à bec. Vol. II. BMI Canada Ltd, Toronto, 1962, pp. 69–72.

    Google Scholar 

  4. Kruskal, J. B. and D. Sankoff. “An Anthology of Algorithms and Concepts for Sequence Comparison.” InTime Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Ed. D. Sankoff and J. B. Kruskal. Reading, MA: Addison-Wesley, 1983, pp. 293–96.

    Google Scholar 

  5. Kruskal, J. B. and M. Liberman. “The Symmetric TimeWarping Problem: From Continuous to Discrete.” InTime Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Ed. D. Sankoff and J. B. Kruskal. Reading, MA: Addison-Wesley, 1983, pp. 125–59.

    Google Scholar 

  6. Logrippo, L. and B. Stepien. “Cluster Analysis for the Computer-Assisted Statistical Analysis of Melodies.”Computers and the Humanities, 20 (1986), 19–33.

    Google Scholar 

  7. Mozart, W. A. Ah! vous dirai-je, maman. K300, 1781-82 .

  8. Mozart, W. A. Alleluja. Extract of motet “Exultate.” K165, 1773.

  9. Rao, C. R. “Use and Interpretation of Principal Components Analysis in Applied Research.” InSankhya. The Indian Journal of Statistics. Series A, 26 (1965), 329-58.

  10. Sankoff, D. and J. B. Kruskal, eds.Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Reading, MA: Addison-Wesley, 1983.

    Google Scholar 

  11. Smith, T. F. and M. S. Waterman. “Identification of Common Molecular Subsequences.”Journal of Molecular Biology, 147 (1981), 195–97.

    Google Scholar 

  12. Stech, D. A. “A Computer-Assisted Approach to MicroAnalysis of Melodic Lines.”Computers and the Humanities, 15 (1981), 211–21.

    Google Scholar 

  13. Williams, W. T. and G. N. Lance. “Hierarchical Classificatory Methods.” InStatistical Methods for Digital Computers. Vol. III ofMathematical Methods for Digital Computers. Ed. K. Enslein, A. Ralston, H. S. Wilf. New York: Wiley, 1977,p.280.

    Google Scholar 

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Marcel Mongeau obtained his B.Sc. and M.Sc. degrees at the Université de Montréal and is currently completing his doctorate at the University of Waterloo.

David Sankoff (Ph.D., McGill) is a Professor in the Département de mathématiques et statistique and is also attached to the Centre de recherches mathématiques at the Université de Montréal. His research intersts include sociolinguistics — specifically the quantitative approach inherent in linguistic variation theory — statistical classification theory, biomathematics and computational biology — particularly algorithms for macromolecular sequence analysis and the reconstruction of phylogenetic trees.

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Mongeau, M., Sankoff, D. Comparison of musical sequences. Comput Hum 24, 161–175 (1990). https://doi.org/10.1007/BF00117340

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Key Words

  • sequence comparison
  • dynamic programming
  • musical pattern recognition
  • melodic line