John Roeder, "Pulse Streams and Problems of Grouping and Metrical Dissonance in Bartók's 'With Drums and Pipes,'" Music Theory Online 7.1 (2001) << TOC Section 1a Sect. 2a >>
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[1] Introduction

[1.1] Polyphony, the concurrence of two or more musical streams, has many interesting rhythmic properties. Many of them do not obtain in the monophonic or homophonic textures that are modeled by most rhythmic theories. The difference between rhythm in polyphony and in homophony becomes apparent when we consider accent and grouping, the basic, though not neatly separable, aspects of rhythm identified by Lerdahl and Jackendoff (1983), among others. It is also apparent when we consider meter, which I take here to be a mental construction of a regular hierarchy of beats in conformance with grouping structure and accentual patterns presented in the piece.

[1.2] In polyphony, accent is not simply a property of a timepoint. To the extent that any given accent arises from features of a particular stream, it must be attributable to that stream only, and not to other concurrent streams. Consequently when at any given moment more than one stream is proceeding, accent may appear in one stream and not the other. Similarly, grouping can be different in concurrent voices. In many polyphonic textures the boundaries and durations of groups in one stream are different from those in concurrent streams.

[1.3] One familiar process that may result from these rhythmic properties of polyphony is polymeter, which is familiar in the hemiolas of Handel and Brahms, but also appears ubiquitously in music from medieval polyphony to jazz. Composers in the early twentieth century, such as Stravinsky and Bartók, had a marked predilection for textures of this sort. Music theorists--most thoroughly, Harald Krebs (1987, 1997, 1999), in his adaptations of Yeston's (1976) notions of "metrical consonance and dissonance"--have analyzed polymetric passages by investigating and classifying them according to the ways that a single underlying rapid pulse is grouped simultaneously into different "layers" or "levels" that have different characteristic durations. These investigations focus on special passages in which the groups are repeated, so that levels are maintained in each voice, and they treat the ratios of level durations as significant.

[1.4] A more complete picture of such polyphony can be obtained by considering the accentual properties of the groups in more detail. This paper will demonstrate how, in an extended two-part polyphony, streams of pulse are created by accents, how these streams interact with the rapidly changing groups in both parts, and how those interactions contribute to the processes and form of the piece.

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