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Decontextualizing Contextual Inversion

  • Jason YustEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively de-contextualizing contextual inversions.

Keywords

Pitch-class set theory Contextual inversion Neo-Riemannian theory Transformational theory 

References

  1. 1.
    Amiot, E.: The torii of phases. In: Yust, J., Wild, J., Burgoyne, J.A. (eds.) MCM 2013. LNCS (LNAI), vol. 7937, pp. 1–18. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-39357-0_1CrossRefzbMATHGoogle Scholar
  2. 2.
    Amiot, E.: Discrete Fourier Transform in Music Theory. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-319-45581-5CrossRefzbMATHGoogle Scholar
  3. 3.
    Amiot, E.: Strange symmetries. In: Agustín-Aquino, O.A., Lluis-Puebla, E., Montiel, M. (eds.) MCM 2017. LNCS (LNAI), vol. 10527, pp. 135–150. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-71827-9_11CrossRefGoogle Scholar
  4. 4.
    Childs, A.: Moving beyond neo-Riemannian triads: exploring a transformational model for seventh chords. J. Music Theory 42(2), 181–93 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cohn, R.: Neo-Riemannian operations, parsimonious triads, and their ‘Tonnetz’ representations. J. Music Theory 41(1), 1–66 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cohn, R.: Audacious Euphony: Chromaticism and the Triad’s Second Nature. Oxford University Press, Oxford (2011)Google Scholar
  7. 7.
    Fiore, T.M., Noll, T.: Voicing transformations and a linear representations of uniform triadic transformations. arXiv:1603.09636 (2016)
  8. 8.
    Fiore, T.M., Noll, T., Satyendra, R.: Incorporating voice permutations into the theory of neo-Riemannian groups and Lewinian duality. In: Yust, J., Wild, J., Burgoyne, J.A. (eds.) MCM 2013. LNCS (LNAI), vol. 7937, pp. 100–114. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-39357-0_8CrossRefzbMATHGoogle Scholar
  9. 9.
    Fiore, T.M., Noll, T., Satyendra, R.: Morphisms of generalized interval systems and \(PR\)-groups. J. Math. Music 7(1), 3–27 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hall, R.W.: Linear contextual transformations. In: Di Maio, G., Naimpally, S. (eds.) Theory and Applications of Proximity, Nearness, and Uniformity, pp. 101–29. Aracne Editrice, Rome (2009)Google Scholar
  11. 11.
    Hall, R.W., Tymoczko, D.: Submajorization and the geometry of unordered collections. Am. Math. Monthly 119(4), 263–83 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hook, J.: Uniform triadic transformations. J. Music Theory 46(1–2), 57–126 (2002)CrossRefGoogle Scholar
  13. 13.
    Hook, J., Douthett, J.: Uniform triadic transformations and the music of Webern. Perspect. New Music 46(1), 91–151 (2008)Google Scholar
  14. 14.
    Kochavi, J.: Contextually defined musical transformations. Ph.D. diss., State University of New York at Buffalo (2002)Google Scholar
  15. 15.
    Milne, A.J., Bulger, D., Herff, S.A.: Exploring the space of perfectly balanced rhythms and scales. of Math. Music 11(3), 101–33 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Lambert, P.: On contextual inversion. Perspect. New Music 38(1), 45–76 (2000)CrossRefGoogle Scholar
  17. 17.
    Lewin, D.: Forte’s interval vector, my interval function, and Regener’s common-note function. J. Music Theory 21(2), 194–237 (1977)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Lewin, D.: Re: intervallic relations between two collections of notes. J. Music Theory 3, 298–301 (1959)CrossRefGoogle Scholar
  19. 19.
    Lewin, D.: Special cases of the interval function between pitch-class sets X and Y. J. Music Theory 45, 1–29 (2001)CrossRefGoogle Scholar
  20. 20.
    Lewin, D.: Generalized Musical Intervals and Transformations, 2nd edn. Oxford University Press, Oxford (2011)Google Scholar
  21. 21.
    Lewin, D.: Musical Form and Transformation: Four Analytic Essays. Yale University Press, New Haven (1993)Google Scholar
  22. 22.
    Straus, J.: Contextual-inversion spaces. J. Music Theory 55(1), 43–88 (2011)CrossRefGoogle Scholar
  23. 23.
    Tymoczko, D.: Scale theory, serial theory, and voice leading. Mus. Anal. 27(1), 1–49 (2008)CrossRefGoogle Scholar
  24. 24.
    Tymoczko, D.: The generalized Tonnetz. J. Music Theory 56(1), 1–52 (2012)CrossRefGoogle Scholar
  25. 25.
    Tymoczko, D.: Tonality: an owners manual. Unpub. MSGoogle Scholar
  26. 26.
    Yust, J.: Applications of DFT to the theory of twentieth-century harmony. In: Collins, T., Meredith, D., Volk, A. (eds.) MCM 2015. LNCS (LNAI), vol. 9110, pp. 207–218. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-20603-5_22CrossRefGoogle Scholar
  27. 27.
    Yust, J.: Schubert’s harmonic language and Fourier phase space. J. Music Theory 59(1), 121–81 (2015)CrossRefGoogle Scholar
  28. 28.
    Yust, J.: Special collections: renewing set theory. J. Music Theory 60(2), 213–62 (2016)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Yust, J.: Organized Time: Rhythm, Tonality, and Form. Oxford University Press, Oxford (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Boston UniversityBostonUSA

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