Author: Romig, James
Title: Twelve-Tone Rhythmic Structure and its Application to Form: Time-Point Nesting and Rotation in 'Spin'
Institution: Rutgers University
Begun: September 1999
Completed: April 2000
In the mid-twentieth century, as harmonic aspects of musical composition became increasingly complex and algorithmically structured, composers experimented with equally rigorous methods of determining rhythm. In Europe, "total serialism," associating duration with pitch-class, was introduced by Olivier Messiaen and later employed by Pierre Boulez and Karlheinz Stockhausen. In America, Milton Babbitt experimented with similar duration rows before introducing the seminal "time-point" system, in which durational interval is associated not with pitch-class, but with interval-class. This shift in thinking allowed rhythmic rows to function isomorphically with their pitch-class counterparts, and provided the means for meaningful manipulation of rhythm by the classic twelve-tone operations originated by Arnold Schoenberg, as well as by subsequent transformational methods.
The problem of large-scale structure in serial music is of great concern to Charles Wuorinen, who introduced the concept of using time-point intervals, in a modulus-free environment, to determine a composition's large-scale dimensions. While Babbitt's structural forms are often amalgamations of durational or time-point rows, and many of Elliott Carter's works are structured on multiple polyrhythms, Wuorinen uses time-point intervals to determine the lengths of large compositional sections, dividing each of these sections similarly, then often producing a composition's surface with still another level of time-point division. This "nesting" approach guarantees motivic self-similarity, from a composition's deep structure to its surface.
By layering two or more strands of multi-level time-point divisions across the length of a composition or movement, a composer can create a rich counterpoint of rhythmic interaction on several scales of time. Such an approach constitutes an explicit recognition of the notion that "rhythm is form in the small, and form is rhythm in the large." "Spin" utilizes four similar time-point strands, time- shifted and cyclically arranged to contribute to the overall shape and structure of the composition.
Keywords: twelve-tone, time-point, nesting, rotation, Romig, rhythmic, form, serial
53-B Phelps Ave.
New Brunswick, NJ 08901