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Contextual Set-Class Analysis

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Computational Music Analysis

Abstract

In this chapter, we review and elaborate a methodology for contextual multi-scale set-class analysis of pieces of music. The proposed method provides a systematic approach to segmentation, description and representation in the analysis of the musical surface. The introduction of a set-class description domain provides a systematic, mid-level, and standard analytical lexicon, which allows for the description of any notated music based on a fixed temperament. The method benefits from representation completeness, a balance between generalization and discrimination of the set-class spaces, and access to hierarchical inclusion relations over time. Three new data structures are derived from the method: class-scapes, class-matrices and class-vectors. A class-scape represents, in a visual way, the set-class content of each possible segment in a piece of music. The class-matrix represents the presence of each possible set class over time, and is invariant to time scale and to several transformations of analytical interest. The class-vector summarizes a piece by quantifying the temporal presence of each possible set class. The balance between dimensionality and informativeness provided by these descriptors is discussed in relation to standard content-based tonal descriptors and music information retrieval applications. The interfacing possibilities of the method are also discussed.

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References

  • Babbitt, M. (1955). Some aspects of twelve-tone composition. The Score and I.M.A. Magazine, 12:53–61.

    Google Scholar 

  • Castrén, M. (1994). RECREL. A similarity measure for set-classes. PhD thesis, Sibelius Academy, Helsinki.

    Google Scholar 

  • Clough, J. and Douthett, J. (1991). Maximally even sets. Journal of Music Theory, 35(1/2):93–173.

    Google Scholar 

  • Cook, N. (1987). A Guide to Musical Analysis. J. M. Dent and Sons.

    Google Scholar 

  • Deliège, C. (1989). La set-theory ou les enjeux du pléonasme. Analyse Musicale, 17:64–79.

    Google Scholar 

  • Foote, J. (1999). Visualizing music and audio using self-similarity. In Proceedings of the Seventh ACM International Conference on Multimedia (MM99), pages 77–80, Orlando, FL.

    Google Scholar 

  • Forte, A. (1964). A theory of set-complexes for music. Journal of Music Theory, 8(2):136–183.

    Google Scholar 

  • Forte, A. (1973). The Structure of Atonal Music. Yale University Press.

    Google Scholar 

  • Forte, A. (1988). Pitch-class set genera and the origin of modern harmonic species. Journal of Music Theory, 32(2):187–270.

    Google Scholar 

  • Forte, A. (1989). La set-complex theory: Elevons les enjeux! Analyse Musicale, 17:80–86.

    Google Scholar 

  • Hanson, H. (1960). The Harmonic Materials of Modern Music: Resources of the Tempered Scale. Appleton-Century-Crofts.

    Google Scholar 

  • Harley, N. (2014). Evaluation of set class similarity measures for tonal analysis. Master’s thesis, Universitat Pompeu Fabra.

    Google Scholar 

  • Hasty, C. (1981). Segmentation and process in post-tonal music. Music Theory Spectrum, 3:54–73.

    Google Scholar 

  • Huovinen, E. and Tenkanen, A. (2007). Bird’s-eye views of the musical surface: Methods for systematic pitch-class set analysis. Music Analysis, 26(1–2):159–214.

    Google Scholar 

  • Huron, D. (1992). Design principles in computer-based music representations. In Mardsen, A. and Pople, A., editors, Computer Representations and Models in Music, pages 5–39. Academic Press.

    Google Scholar 

  • Leman, M. (2008). Embodied Music: Cognition and Mediation Technology. MIT Press.

    Google Scholar 

  • Lerdahl, F. (2001). Tonal Pitch Space. Oxford University Press.

    Google Scholar 

  • Lewin, D. (1959). Re : Intervallic relations between two collections of notes. Journal of Music Theory, 3(2):298–301.

    Google Scholar 

  • Lewin, D. (1979). Some new constructs involving abstract pcsets and probabilistic applications. Perspectives of New Music, 18(1–2):433–444.

    Google Scholar 

  • Martorell, A. (2013). Modelling tonal context dynamics by temporal multi-scale analysis. PhD thesis, Universitat Pompeu Fabra.

    Google Scholar 

  • Martorell, A. and Gémez, E. (2015). Hierarchical multi-scale set-class analysis. Journal of Mathematics and Music, 9(1):95–108.

    Google Scholar 

  • Müller, M. (2007). Information Retrieval for Music and Motion. Springer.

    Google Scholar 

  • Nattiez, J. J. (2003). Allen Forte’s set theory, neutral level analysis and poietics. In Andreatta, M., Bardez, J. M., and Rahn, J., editors, Around Set Theory. Delatour/Ircam.

    Google Scholar 

  • Rahn, J. (1979). Relating sets. Perspectives of New Music, 18(1):483–498.

    Google Scholar 

  • Rahn, J. (1980). Basic Atonal Theory. Schirmer.

    Google Scholar 

  • Rive, T. N. (1969). An examination of Victoria’s technique of adaptation and reworking in his parody masses - with particular attention to harmonic and cadential procedure. Anuario Musical, 24:133–152.

    Google Scholar 

  • Sapp, C. S. (2005). Visual hierarchical key analysis. ACM Computers in Entertainment, 4(4):1–19.

    Google Scholar 

  • Straus, J. N. (1990). Introduction to Post-Tonal Theory. Prentice-Hall.

    Google Scholar 

  • Tufte, E. R. (2001). The Visual Display of Quantitative Information. Graphics Press.

    Google Scholar 

  • Tymoczko, D. (2011). A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford University Press.

    Google Scholar 

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Correspondence to Agustín Martorell .

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Martorell, A., Gómez, E. (2016). Contextual Set-Class Analysis. In: Meredith, D. (eds) Computational Music Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-25931-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-25931-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25929-1

  • Online ISBN: 978-3-319-25931-4

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