Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes

  • Louis Bigo
  • Moreno Andreatta
  • Jean-Louis Giavitto
  • Olivier Michel
  • Antoine Spicher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7937)


We represent chord collections by simplicial complexes. A temporal organization of the chords corresponds to a path in the complex. A set of n-note chords equivalent up to transposition and inversion is represented by a complex related by its 1-skeleton to a generalized Tonnetz. Complexes are computed with MGS, a spatial computing language, and analyzed and visualized in Hexachord, a computer-aided music analysis environment. We introduce the notion of compliance, a measure of the ability of a chord-based simplicial complex to represent a musical object compactly. Some examples illustrate the use of this notion to characterize musical pieces and styles.


MGS simplicial complexes generalized Tonnetze compliance Hexachord chord spaces 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Louis Bigo
    • 1
    • 2
  • Moreno Andreatta
    • 2
  • Jean-Louis Giavitto
    • 2
  • Olivier Michel
    • 1
  • Antoine Spicher
    • 1
  1. 1.LACL/Université Paris-Est CreteilFrance
  2. 2.UMR CNRS STMS 9912/IRCAMFrance

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