Metric Dissonance in Non-Isochronous Meters Page: 13
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Example 1.12 really exhibits grouping dissonance at multiple levels rather than a shared
cardinality displacement dissonance. Regardless of labels, Krebs's methodologies do not work
for dissonances of these sort. These types of dissonance require a new methodology, which I will
discuss in Chapter 3.
Example 1.11. Misaligned 7/8 involving grouping and displacement dissonances (points of
consonance shown with arrows).
- I u - I
mdL so IIIIW
Example 1.12. Misaligned 9/8 (3+3+3) and 7/8 (2+3+2) (points of consonance shown with
John Roeder's pulse streams, which constitute the majority of his discussions, are not
metric in nature, but rather rhythmic in nature. Roeder's methodology has fewer limitations than
Cohn's or Krebs's. He does not require metrical pulses to be isochronous, and he does not
require shared time spans. His theory "represents rhythmic polyphony as two or more concurrent
'pulse streams' created by regularly recurring accents."25 These pulse streams are not groupings
25 John Roeder, "Interacting Pulse Streams in Schoenberg's Atonal Polyphony," Music Theory Spectrum 16, no. 2
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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/m1/24/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .