Abstract
In this paper we take the three tonal functions tonic, subdominant and dominant out of their usual theoretical domicile—the combinatorics of fifth-related triads enriched by a dialectical interpretation—and redeploy them within an alternative theoretical framework: the combinatorics of the modes of the musical tetractys, enriched by musical-theoretical interpretations of selected mathematical facts. Section 1 introduces tonal perspectives of the analysis of the fundamental bass. Section 2 provides a short overview of the combinatorics of the three modes of the musical tetractys. The concluding Section 3 binds the two strands of investigation together.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Carey, N., Clampitt, D.: Aspects of Well Formed Scales. Music Theory Spectrum 11(2), 187–206 (1989)
De Jong, K., Noll, T.: Contiguous Fundamental Bass Progressions. Dutch Journal of Music Theory (2008)
Hauptmann, M.: Die Natur der Harmonik und der Metrik, Leipzig, Breitkopf und Härtel (1853)
Riemann, H.: Musikalische Logik: Hauptzüge der physiologischen und psychologischen Begründung unseres Musiksystems. Verlag von C. F. Kahnt, Leipzig (1874)
Clampitt, D., Noll, T.: Modes, the Height-Width Duality, and Handschin’s Tone Character. Theory Online 17(1) (2011)
Noll, T.: Ionian Theorem. JMM 3(3), 137–151 (2009)
Glareanus, H.: Dodecachordon, Basel (1547); Reprint: Hildesheim: Olms (1970)
Hook, J.: Signature Transformations. In: Douthett, J., Hyde, M.M., Smith, C.J. (eds.) Music Theory and Mathematics: Chords, Collections, and Transformations, pp. 137–160. University of Rochester Press, Rochester (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Jong, K., Noll, T. (2011). 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) Mathematics and Computation in Music. MCM 2011. Lecture Notes in Computer Science(), vol 6726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21590-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-21590-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21589-6
Online ISBN: 978-3-642-21590-2
eBook Packages: Computer ScienceComputer Science (R0)