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)


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.


Transformational Space Transformational Analysis Music Theory Pitch Interval Pitch Class 
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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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