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Embedded Structural Modes: Unifying Scale Degrees and Harmonic Functions

  • Thomas NollEmail author
  • Karst De Jong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

The paper offers an integration of the theory of structural modes, functional theory and diatonic scale degrees. In analogy to the parsimonious voice leading between generic diatonic triads we study parsimonious function leading between embedded structural modes. A combinatorics of diatonic embeddings of structural modes is given. In four analytical examples we study the interaction of relative minor and major modes within an encompassing diatonic collection. Finally we discuss alternative possibilities for the interpretation of the diminished fifth as a fundament progression.

Keywords

Structural modes Functional harmony Scale degree theory Hierarchy Diabolus in musica 

Notes

Acknowledgement

We wish to thank Jason Yust, David Clampitt and the anonymous reviewers for valuable feedback.

References

  1. 1.
    Biamonte, N.: Augmented-sixth chords vs. tritone substitutes. Music Theory Online 14(2) (2008). http://www.mtosmt.org/issues/mto.08.14.2/mto.08.14.2.biamonte.html
  2. 2.
    Caplin, W.E.: Harmony and cadence in Gjerdingen’s ‘Prinner’. In: Neuwirth, M., Bergé, P. (eds.) What Is a Cadence? Theoretical and Analytical Perspectives on Cadences in the Classical Repertoire. Leuven University Press, Leuven (2015)Google Scholar
  3. 3.
    Dahlhaus, C.: Untersuchungen über die Entstehung der harmonischen Tonalität. Kassel et al.: Bärenreiter (1967)Google Scholar
  4. 4.
    de Jong, K., Noll, T.: Fundamental passacaglia: harmonic functions and the modes of the musical tetractys. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS (LNAI), vol. 6726, pp. 98–114. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-21590-2_8CrossRefzbMATHGoogle Scholar
  5. 5.
    De Jong, K., Noll, T.: FFundamental bass and real bass in dialogue: tonal aspects of the structural modes. Music Theory Online 24(4) (2018). http://mtosmt.org/issues/mto.18.24.4/mto.18.24.4.de_jong_noll.html
  6. 6.
    Cork, C.: The New Guide to Harmony with Lego Bricks: Revised and Extended Edition. Tadley Ewing Publications, Leicester (1996)Google Scholar
  7. 7.
    Elliott, J.: Insights In Jazz: An Inside View of Jazz Standard Chord Progressions. Jazzwise Publications, London (2009)Google Scholar
  8. 8.
    Gjerdingen, R.: Music in the Galant Style. Oxford University Press, New York (2007)Google Scholar
  9. 9.
    Harrison, D.: Harmonic Function in Chromatic Music. The University of Chicago Press, Chicago and London (1994)Google Scholar
  10. 10.
    Mazzola, G.: Die Geometrie der Töne. Birkhäuser, Basel (1990)CrossRefGoogle Scholar
  11. 11.
    Noll, T.: Die Vernunft in der Tradition: Neue mathematische Untersuchungen zu den alten Begriffen der Diatonizität. ZGMTH 13. Special Issue (2016). https://doi.org/10.31751/864
  12. 12.
    Quinn, I.: Harmonic function without primary triads. Paper delivered at the annual meeting of the Society for Music Theory in Boston, November 2005Google Scholar
  13. 13.
    Rohrmeier, M.: Towards a generative syntax of tonal harmony. J. Math. Music 5(1), 35–53 (2011)CrossRefGoogle Scholar
  14. 14.
    Yust, J.: Distorted continuity: chromatic harmony, uniform sequences, and quantized voice leadings. Music Theor. Spectr. 37(1), 120–143 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departament de Teoria, Composició i DireccióEscola Superior de Música de CatalunyaBarcelonaSpain
  2. 2.Royal Conservatoire Den HaagHagueThe Netherlands

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