A Tetrahedral Graph of Tetrachordal Voice-Leading Space

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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