The Escher Theorem

  • Guerino Mazzola
  • Joomi Park
  • Florian Thalmann
Part of the Computational Music Science book series (CMS)


The Escher Theorem was first proved and discussed in the context of mathematical gesture theory (Mazzola and Andreatta, 2007; Mazzola, 2009). We shall review the theorem here as a case study relating to explicit strategies for creativity. This theorem was first applied to describe creative strategies in free jazz, see (Mazzola and Cherlin, 2009).


Topological Space Directed Graph Critical Concept Creative Strategy Pitch Class 
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  1. 84.
    Mazzola G and M Andreatta: Diagrams, Gestures, and Formulas in Music. Journal of Mathematics and Music 2007, Vol. 1, no. 1, 2007 Google Scholar
  2. 85.
    Mazzola G and P B Cherlin: Flow, Gesture, and Spaces in Free Jazz—Towards a Theory of Collaboration. Springer Series Computational Music Science, Heidelberg et al. 2009 Google Scholar
  3. 87.
    Mazzola G: Categorical Gestures, the Diamond Conjecture, Lewin’s Question, and the Hammerklavier Sonata. Journal of Mathematics and Music Vol. 3, no. 1, 2009 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Guerino Mazzola
    • 1
    • 2
  • Joomi Park
    • 3
  • Florian Thalmann
    • 1
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of InformaticsUniversity of ZurichZurichSwitzerland
  3. 3.McNally Smith College of MusicSaint PaulUSA

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