Some Problems in Rhythmic Theory and Analysis

WE KNOW LESS about the rhythm of contemporary music than the numerical precision of many fashionable descriptions would suggest.' Such descriptions usually consider the organization of factors (such as duration) without respect to other factors.2 We are, however, accustomed to hearing music in terms of the complicated interaction of many factors. This difficulty is of course easily avoided in analyses of those special cases (so striking in Stravinsky) where nonrhythmic factors are used chiefly to differentiate between elements of a purely rhythmic design.3 Such special cases only seem problematic in that they neither look nor sound like anything in the eighteenth or nineteenth centuries; they are in fact much easier to analyze than music based on more traditional rhythmic procedures. Special cases must be simple to be effective; an evolving tradition usually implies increasing complexity. Analogous complexities of pitch organization in Bart6k or even Schonberg have yielded to extensions of Schenkerian analytic concepts.4 Yet the underlying structure (if not the detail) of Schonberg's