Strange dimensions: regularity and irregularity in deep levels of rhythmic reduction

Abstract

The guiding idea for this article is well expressed in a famous quotation from Renaissance philosopher Francis Bacon: “There is no excellent beauty that hath not some strangeness in the proportion.” This statement is excerpted from one of Bacon's forays into what was then a developing literary form, the essay. Like Montaigne, who invented this form, Bacon sought in his essays to encapsulate a world of observation in a handful of pithy statements. In many ways, modern-day music theorists do something similar in that they often seek to summarize complex artistic statements with simpler aphoristic models. Also like Montaigne and Bacon, some theorists are testing a new form of summary, an essay into rhythmic structure. I refer of course to the application of Schenker's theories to the analysis of rhythm, as developed by Carl Schachter and William Rothstein. The aim of this method of rhythmic reduction is to create a hierarchy of rhythm both analogous to and closely in rapport with the hierarchy of tonal structure: groups of measures are combined to form groups of hypermeasures, while their significance is evaluated in coordination with the underlying voice leading. Hierarchies in Schenkerian theory are generally assumed to have a structure that proceeds in a uniform progression from complexity to simplicity, that is, from a complex surface to ever simpler explanatory models. In this way irregular features are resolved into regular schemata, individualities are consumed by generalities.

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