In his study of Steve Reich’s phase–shifting music, Richard Cohn points to a specific analytical challenge that transcends the repertoire at hand: “Given the relative poverty of our rhythmic terminology, the challenge for the theorist is to discover a means to characterize this material that is not only descriptively adequate, but also allows for exploration of its properties, its behavior under transformation, and its relations to other potential material” (1992, 149).1 This essay responds to Cohn’s call to action, singling out one of the many under–determined modes of rhythmic continuity in post–tonal music—(asymmetrical) composite meters. It rehearses a wide– ranging application of a new conceptual framework that can be used in accounting for the frequency and formal salience of composite meters in twentieth–century repertoire. Through analysis of select musical examples, I relate composite asymmetrical meters to compound and aksak meters, showing how certain types of “asymmetrical” meter exemplify non–isochronous duple and triple meters and, further, how composite meters combine two or more different metric units into a recurring whole (e.g., isochronous duple followed by non–isochronous triple meter). Along the way, I introduce a number of new concepts (meta–measures, duplication) and a new form of graphic representation (the time signature map).
Isochronicity refers to the durational equality of temporal units such as beats and beat groups. Isochronous beats cohere into symmetrical meters, such as symmetrical duple meter, or 2/4, whereas non–isochronous beats give rise to asymmetrical meters. The examples in this essay are chosen because they outline similar metric patterns, rather than for their exclusivity—a wealth of examples in the twentieth–century repertoire pursue similar metric patterns. An analytical approach to this repertory can take a perceptual or a formal stance but will likely suffer from a lack of a working methodology because approaches to rhythmic and metric analysis are not standardized and are often incompatible with one another. In lieu of following an established analytical methodology for this repertoire or a widely accepted theoretical framework for understanding beat hierarchy in asymmetrical meters, I consider various approaches and develop a performer–sensitive method of analysis.
- While the “material” Cohn singles out in Reich’s phasing works represents a repeated pattern of eight or twelve pulses (hence the beat–class set), the material I refer to is more generally derived from the organization of the rhythmic parameter and is not restricted to twelve–pulse cycles. ↵