||John Roeder, "Pulse Streams and Problems of Grouping and Metrical Dissonance in Bartók's 'With Drums and Pipes,'" Music Theory Online 7.1 (2001)||<< Sect. 3||Section 4||Sect. 5a >>|
[4.1] Many of the questions raised in the context of grouping and metrical dissonance theory about the rhythms of Bartók's piano piece can be addressed productively by attending to the timing of phenomenal accents. (Click here for a brief surview of the types of phenomenal accent that are pertinent to the passage at hand.) Each series of regular accents is heard as a "pulse stream," that is, as a series of repeated durations (Roeder 1994). At any given moment, several such pulse streams may be proceeding, each with its own characteristic duration. In this respect the theory resembles that of metrical dissonance. But since the accents that create a pulse stream may be located in any voice, the theory better accommodates varying polyphonic textures, even textures in which voices drop in and out, or in which there are no consistent timbral continuities at all. Moreover, rather than simply labeling the mathematical relation of the characteristic durations, pulse-stream theory treats the streams as actual rhythms that take on increasing impetus as they are reinforced by subsequent accents. That is, each pulse stream possesses musical continuity and direction, so that analysis focuses on how the pulses are created and sustained, how (once established) they interact with the grouping structures of the voices, and thus how they create musical form.
[4.2] Figure 2 gives a pulse-stream analysis of the first eleven measures of the passage at hand. The score is shown in the center of the example. Above and below the score, placed to clarify certain relations with the actual music, are shown various pulses that arise from regularities of phenomenal accent. Each horizontal line represents a pulse stream that is created when at least two equal timespans are marked off by three accented timepoints.
[4.3] The figure shows that for a pulse stream to be sustained it must be constantly reinforced, more so in the presence of conflicting accents, and less so the longer it has been in existence. Consider, for example, the quarter-note pulse stream (numbered 1) created at the beginning of the passage. Its first three durations arise from fairly clear accents--an accent of inter-onset duration at the first -left-hand attack, then another left-hand attack, then a dynamic accent in the right hand. But its next duration is articulated quite weakly--only by the unaccented attack of the right hand--and so are several of its subsequent durations. The weakness is symbolized on the line that indicates the stream by enclosing these durations in parentheses. Indeed, in m. 26 stream 1 disappears quickly in the absence of a sustaining accent and in the presence of strong contradictory accents. This can be heard in the following audio Example IV.7, in which the quarter-note pulse (1) and the dotted-quarter pulse (4) that displaces it in m. 26 are doubled by snare drum and whistle, respectively. (The instruments that double the pulse streams in this and subsequent examples, selected from the General MIDI drum kit, allude to Bartók's title for this piece.)
(Example IV.7) [click here
if the movie does not appear or play correctly]
[4.4] Some pulse streams in Figure 2 feature durations that correspond exactly to the grouping structures that have been identified in the analysis above, for example, the 5-eighth-note pulse stream (labeled 5) in mm. 26-29. This occurs naturally in repetitive passages, since phenomenal accent creates group boundaries (Lerdahl and Jackendoff 1983: 46). A pulse stream may also correspond to a succession of strong beats in a regular meter, as is evident at the beginning of this passage, when the phenomenal accents do. On the other hand, since the pulse-stream analysis is nonhierarchical, a pulse stream may connect timepoints that are weak beats in a metrical reading, if those beats take phenomenal accent. This is evident at the top of the Figure 2, where odd- and even-numbered down beats are assigned to distinct whole-note pulse streams (numbered 2 and 3), as will be discussed below. Obviously, such a reading goes against our preference for hierarchical meter, but when such meter is absent, or when accentual cues give more emphasis than expected to ostensibly weak beats, a pulse-stream analysis provides an attractive explanation of the musical continuity.
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