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.
This research is supported by a Standard Research Grant from the Social Sciences and Humanities Research Council of Canada.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Capuzzo, G.: Variety within Unity: Expressive Means and Their Technical Ends in the Music of Elliott Carter. Ph.D. dissertation, University of Rochester (1983–1994)
Capuzzo, G.: The Complement Union Property and the Music of Elliott Carter. Journal of Music Theory 48(1), 1–24 (2004)
Carter, E.: Harmony Book. Hopkins, N., Link, J.F. (eds.). Carl Fischer, New York (2002)
Childs, A.: Structural and Transformational Properties of All-Interval Tetrachords. Music Theory Online 12(4) (2006)
Gollin, E.: Representations of Space and Conceptions of Distance in Transformational Music Theories. Ph.D. diss., Harvard University (2000)
Lewin, D.: Generalized Musical Intervals and Transformations. Yale University Press, New Haven (1987)
Lewin, D.: Musical Form and Transformation: 4 Analytic Essays. Yale University Press, New Haven (1993)
Morris, R.: Pitch Class Complementation and its Generalizations. Journal of Music Theory 34(2), 175–245 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Roeder, J. (2009). A Transformational Space for Elliott Carter’s Recent Complement-Union Music. In: Klouche, T., Noll, T. (eds) Mathematics and Computation in Music. MCM 2007. Communications in Computer and Information Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04579-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-04579-0_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04578-3
Online ISBN: 978-3-642-04579-0
eBook Packages: Computer ScienceComputer Science (R0)