Metric Dissonance in Non-Isochronous Meters Page: 15
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music as a result of varying types of accent, including contour accents, dynamic accents, and
agogic accents. He points out the relationship between violin's dotted-half note pulse (letter A)
with its augmentation, A' (dotted whole note) and the half-note pulse (B) with its augmentation
(B'). After discussing the pulse streams that occur, he claims "the interaction of pulse streams is
essential to the rhythmic form of this passage."28
Roeder's methodology can account for rhythmic dissonance involving non-isochronous
pulses. For example, on Bart6k's "With Drums and Pipes," Roeder discusses both displacement
dissonances and grouping dissonances involving a non-isochronous 3+2 grouping in 5/8 against
a persistent grouping of 3 (Example 1.14).29 He references Krebs's methodology, claiming the
grouping dissonance involves a conflict between 5 and 3.30 In Krebs's terms, this grouping
dissonance would be expressed as G5/3. Although this expression accounts for the conflict
between the 5/8 meter in the right hand and the persistent 3-group in the left hand, it does not
account for the non-isochronous pulses of the 5/8 meter against the 3-group in the left hand, in
other words of the conflict between a pulse stream of 3+2 eighth notes and one of 3 eighth notes.
The example begins in misalignment by one eighth note as a result of the grouping dissonance
between the 5-group and the 3-groups. Although Roeder is able to explain this misalignment in
his prose, he is unable to use Krebs's displacement dissonance methodology because Krebs's
displacement dissonances must have a shared cardinality as the first integer of the superscript.
Thus, this example exhibits a key issue in terms of Krebs's methodology: grouping dissonance
involving non-isochronous pulses. Whereas Roeder's methodology has fewer restrictions than
28 Ibid., 247.
29 John Roeder, "Pulse Streams and Problems of Grouping and Metrical Dissonance in Bart6k's
With Drums and Pipes," Music Theory Online 7, no. 1 (January 2001).
30 Ibid., par. 2.7.
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Smith, Jayson. Metric Dissonance in Non-Isochronous Meters, dissertation, August 2018; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc1248499/m1/26/: accessed April 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .