A transformational space for Elliott Carter's recent complement-union music

Author: Roeder, John
Publication details: Communications in Computer and Information Science (CCIS). Vol. 37, pp. 300-307
Weblink: http://download.springer.com

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.