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A Transformational Space for Elliott Carter’s Recent Complement-Union Music

  • John Roeder
Part of the Communications in Computer and Information Science book series (CCIS, volume 37)

Abstract

Elliott Carter’s recent music exploits a special combinatorial property of the all-trichord hexachord. I show how this property can be reconceived in terms of interesting and analytically significant musical transformations: three involutions on the pitch-class aggregate which constitute a Klein four-group, and which have a natural interpretation as the symmetry group on a particular 12-vertex geometrical structure. Accordingly the opening of Carter’s Figment II for solo cello can be analyzed transformationally as a complete traversal of this structure by just a few, striking, characteristic gestures.

Keywords

Transformational Space Transformational Analysis Music Theory Pitch Interval Pitch Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • John Roeder
    • 1
  1. 1.University of British Columbia School of MusicCanada

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