Cycles of Cycles: Ordering Principles Suggested by George Perle's Twelve-Tone Tonality (Absract)

This thesis investigates correspondences between transformational networks developed by Henry Klumpenhouwer and David Lewin and the compositional system, Twelve-Tone Tonality, of George Perle. These correspondences are then utilized to generate an ordering system utilizing certain aspects of Perle’s cyclic sets. The first portion traces the origin of cyclic sets from the usage of interval cycles in the late 19th and early 20th Centuries. This discussion is followed by an introduction to Perle’s cyclic sets and how they intersect with Klumpenhouwer networks. After this introduction the relationship between different cyclic set array alignments and the representative K-net transformations is explored more fully. The section dealing with ordering principles demonstrates how one can generate ordered chord progressions drawn from Perle sets and the relevant K-net analyses. This section is followed by a similar demonstration using triadic arrays. Finally two compositional designs illustrate possible foreground projections of the ordered chord progressions. (full paper - pdf)

Cyclic Harmony

Cyclic Harmony is a java-based program which will generate all possible cyclic set arrays from a given seed sonority. As of this version the generated arrays are comprised of a single cyclic interval and its complement (IS 5/7, 1/e, etc.). The array is presented with dual sliders so that one can analyze axis-dyad chords drawn from multiple alignments of the array (set-class, ICV, Forte name, and K-Net representation). From an alignment the program can then generate a series of ordered progressions of axis-dyad chords. This ordering is generated by the resultant sum scale of the cyclic set array. These progressions can then be implemented in many ways as a compositional design. The previous discussion is a very basic introduction to how Cyclic Harmony implements the relationships described in my thesis.

If anyone is interested in this program, feel free to contact me directly.

Toward a Structural Ordering Within George Perle's Twelve-Tone Tonality

This article (to be published in an upcoming Festschrift for George Perle, is an earlier incarnation of the ordering principles outlined in my dissertation. It outlines the idea of ordering through the use of resultant sum cycles, however it more fully explores middle and background Klupenhouwer relations between cyclic set arrays which share a common resultant cycle. (full paper - pdf)