Interval Cycles, Affinity Spaces, and Transpositional Networks

  • José Oliveira Martins
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6726)

Abstract

The paper proposes a framework that coordinates several models of pitch space whose constructive features rely on the concept of interval cycles and transpositional relations. This general model brings under a focused perspective diverse pitch structures such as Tonnetze, affinity spaces, Alban Berg’s “master array” of interval-cycles, and several types of transpositional networks (T-nets). This paper argues that applying incremental changes on some of the constructive features of the generic Tonnetz (Cohn 1997) results in a set of coherent and analytically versatile transpositional networks (T-nets), here classified as homogeneous, progressive, and dynamic. In this context, several properties of the networks are investigated, including voice-leading and common-tone relations. The paper also explores the music-modeling potential of progressive and dynamic T-nets by attending to characteristic compositional deployments in the music of Witold Lutosławski and György Kurtág.

Keywords

Interval cycles Affinity spaces Dasian Transposition Tonnetz neo-Riemannian theory Network T-nets 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cohn, R.: Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective. Journal of Music Theory 42(2), 167–180 (1998)CrossRefGoogle Scholar
  2. 2.
    Journal of Music Theory 42(2), 167–348 (1998)Google Scholar
  3. 3.
    Cohn, R.: Neo-Riemannian Operations, Parsimonious Trichords and Their Tonnetz Representations. Journal of Music Theory 41(1), 1–66 (1997)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Douthett, J., Steinbach, P.: Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition. Journal of Music Theory 42(2), 241–263 (1998)CrossRefGoogle Scholar
  5. 5.
    Lewin, D.: Notes on the Opening of the F# Minor Fugue from WTCI. Journal of Music Theory 42(2), 235–239 (1998)CrossRefGoogle Scholar
  6. 6.
    Martins, J.O.: Dasian, Guidonian, and Affinity Spaces in Twentieth-century Music. Ph.D. diss, U Chicago (2006)Google Scholar
  7. 7.
    Pesce, D.: The Affinities and Medieval Transposition. Indiana University Press, Bloomington (1987)Google Scholar
  8. 8.
    Gollin, E.: Multi-Aggregate Cycles and Multi-Aggregate Serial Techniques in the Music of Bla Bartk. Music Theory Spectrum 29(2), 143–176 (2007)CrossRefGoogle Scholar
  9. 9.
    Lambert, P.: Interval Cycles as Compositional Resources in the Music of Charles Ives. Music Theory Spectrum 12(1), 43–82 (1990)CrossRefGoogle Scholar
  10. 10.
    Carey, N., Clampitt, D.: Regions: A Theory of Tonal Spaces in Early Medieval Treatises. Journal of Music Theory 40(1), 113–147 (1996)CrossRefGoogle Scholar
  11. 11.
    Martins, J.O.: Affinity Spaces and Their Host Set Classes. In: Klouche, T., Noll, T. (eds.) MCM 2007. Communications in Computer and Information Science, vol. 37, pp. 499–511. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Perle, G.: Berg’s Master Array of the Interval Cycles. The Musical Quarterly 63(1), 1–30 (1977)CrossRefGoogle Scholar
  13. 13.
    Headlam, D.: George Perle: An Appreciation. Perspectives of New Music 47(2), 59–195 (2009)Google Scholar
  14. 14.
    Hoffmann, P.: Die Kakerlake sucht den Weg zum Licht: Zum Streichquartett op. 1 von Gyrgy Kurtg. Die Musikforschung 44, 32–48 (1991)Google Scholar
  15. 15.
    Martins, J.O.: Bartók’s Vocabulary and Kurtág’s Syntax in the First Movement of the ‘Quartetto per Archi’, op. 1. Presented at the symposium: Bartók’s String Quartets: Tradition and Legacy, University of Victoria (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • José Oliveira Martins
    • 1
  1. 1.Eastman School of MusicUnited States

Personalised recommendations