A Tetrahedral Graph of Tetrachordal Voice-Leading Space

Richard Cohn

KEYWORDS: voice leading, tetrachord, simplex, atonality, P relation, transpositional combination

ABSTRACT: A tetrahedral graph models voice leading among the 29 T/I-type tetrachord classes. Transpositional combination plays a crucial role in the structure of the tetrahedron. A dipyramid, fusing two tetrahedra, models similar relations among the 43 T-type |4|-classes. The two graphs generalize to n-dimensional simplexes for relations among |n + 1|-classes, in modulo 12 and in other universes of even cardinality. A peculiarity is that the symmetrical graphs are a bit too large to hold the asymmetrical collection of abstract objects that they are designed to contain. A handful of set-class duplications serve as bubble wrap; the article devotes considerable attention to investigating their status.

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Received July 2003
Volume 9, Number 4, October 2003
Copyright © 2003 Society for Music Theory

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Richard Cohn
Professor of Music
University of Chicago

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