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The Spinnen-Tonnetz: New Musical Dimensions in the 2D Network for Tonal Music Analysis

Using Polarization and Tonal Regions in a Dynamic Environment

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Book cover Mathematics and Computation in Music (MCM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9110))

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Abstract

The Polarized Tonnetz developed by Hugues Seress [4] is an innovative two-dimensional representation system for visualizing statically and dynamically some triadic or post-triadic organization, harmonic and tonal paths, as well as tonal regions and musical relations. As for the traditional Tonnetz, the Polarized one relates to transformational design and parsimonious voice leading. Its originality resides however in the introduction of three differentiated criteria concerning the transformation (chromatic distance, modal orientation, polarity) and a fourth parameter: the upward or downward direction of the voice leading. We then enhanced the Polarized Tonnetz with the Planet-4D colorization and animation system developed by Gilles Baroin [1], and finally add a new dynamic graphical layer that illustrates the tonal regions. This paper describes the construction and features of the Spinnen-Tonnetz as well as some musical analysis performed. All videos concerning the construction of the Spinnen-Tonnetz and the musical sample studied are available online at www.MatheMusic.net.

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References

  1. Baroin, G.: The planet-4D model: an original hypersymmetric music space based on graph theory. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds.) MCM 2011. LNCS, vol. 6726, pp. 326–329. Springer, Heidelberg (2011)

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  2. Cohn, R.: Neo-riemannian operations, parsimonious trichords, and their “tonnetz” representations. J. Music Theor. 41, 1–66 (1997)

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  3. Schönberg, A.: Structural Functions of Harmony. Faber and Faber, London (1954)

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  4. Seress, H.: La musique folklorique pour piano (1907–1920) de Béla Bartók: emprunt symbolique, matriau combinatoire (Doctoral dissertation, Paris 4) (2012)

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  5. Seress, H.: Trois exemples datonalité chez Beethoven, Bartk et Faur: une rflexion no-riemannienne sur la perte du sentiment tonal, Analyse Music Analysis Today, 315–332, Paris: Delatour (2014)

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Authors and Affiliations

  1. Labo MAIAA, Ecole Nationale de l’Aviation Civile, Université de Toulouse, Toulouse, France

    Gilles Baroin

  2. IReMus, Centre dÉtudes Supérieures de Musique de Poitiers, University of Paris Sorbonne, Paris, France

    Hugues Seress

Authors
  1. Gilles Baroin
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  2. Hugues Seress
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Corresponding author

Correspondence to Gilles Baroin .

Editor information

Editors and Affiliations

  1. De Montfort University, Leicester, United Kingdom

    Tom Collins

  2. Aalborg University, Aalborg, Denmark

    David Meredith

  3. Utrecht University, Utrecht, The Netherlands

    Anja Volk

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© 2015 Springer International Publishing Switzerland

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Baroin, G., Seress, H. (2015). The Spinnen-Tonnetz: New Musical Dimensions in the 2D Network for Tonal Music Analysis. In: Collins, T., Meredith, D., Volk, A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science(), vol 9110. Springer, Cham. https://doi.org/10.1007/978-3-319-20603-5_32

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  • DOI: https://doi.org/10.1007/978-3-319-20603-5_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20602-8

  • Online ISBN: 978-3-319-20603-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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