Abstract
Beside a geometrical part that has been calculated with the help of the graph theory, the Planet-4D model includes twelve ideograms that can either symbolize notes, chords or scales depending on the context. Based on symmetry principles, it presents the following innovations:
-
the hyper spherical environment grants each symbol an equivalent physical position, and involves more symmetries than any 3D model,
-
the concept of bi-dimensional ideograms provides an intuitive understanding of pitch relationships,
-
it contains implicitly the chromatic and fourth circles as well as the original Tonnetz.
NB: the pertinence of this model is effective when demonstrated in motion with colored CGI animations of the 4D Space including sound examples. Videos shown during this conference are available on the web at www.planetes.info .
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Byers, N.: E.Noether’s Discovery of the Deep Connection Between Symmetries and Conservation Laws. IMC 12 (1999)
Lederman, L., Hill, C.: Symmetry and the Beautiful Universe. Prometheus Books (2004)
Andreatta, M., Agon, C.: Formalisation algébrique des structures musicales aide de la Set-Theory: aspects théoriques et analytiques. Actes des Journées d’Informatique Musicale (2003)
Forte, A.: The Structure of Atonal Music. Yale University Press, New Haven (1973)
Balzano, G.: The group-theoretic description of 12-fold and microtonal pitch systems. Computer Music Journal, 66–84 (1980)
Mazzola, G.: The Topos of Music. Birkhuser Verlag, Basel (2003)
Noll, T.: Geometry of Chords. In: Puebla, E.L. (ed.) Electronic Bulletin of the Sociedad Matematica Mexicana, vol. 1 (2001)
Baroin, G., Ferré, L.: Representation of musical pitch space using graphs, spectrum and hyperspaces. In: Proceedings of 8FCC Combinatorical Conference, Paris (2010)
Baroin, G.: De Newton à Riemann, Graphes et Graphisme: Interactions Mathématico-Musico-Plastiques. Litter@incognita (3), 41–57 (2010)
Leys, J., Ghys, E., Alvarez, A.: Dimensions: A walk through mathematics! (CGI movie) (2008), http://www.dimensions-math.org
Cohn, R.: Dramatization of hypermetric conflicts in the Scherzo of Beethoven’s Ninth Symphony. 19th-Century Music 15, 22–40 (1992)
Crans, A., Fiore, T., Satyendra, R.: Musical Actions of Dihedral Groups. Amer. Math. Monthly 116(6), 479–495 (2009)
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
Baroin, G. (2011). 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) 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_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-21590-2_25
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)