Metric Dissonance in Non-Isochronous Meters Page: 10
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Example 1.9. Cohn's metric space'7
A E F_
Cohn's methodology allows him to only consider musical passages that both share a time
span and contain isochronous pulses that are divided by 2 or 3. He recognizes the limitations of
his methodology, stating, "The theory of complex hemiolas has, at present, no means for
accounting for... the asymmetrical partitioning of a time-span."'8 This limitation is also present
in Yeston's and Krebs's approaches to grouping dissonance. Perhaps, these authors have these
limitations because of the repertoire they discuss, which primarily spans music of the 18th and
19th centuries. This music, unlike more recent music, does not typically require considerations of
asymmetrical partitioning of time spans. To account for asymmetrical meters, Cohn and Krebs
would both need to alter their methodologies. In their current state, Cohn's ski-hill graphs only
allow for divisions of 2 or 3, and Krebs's grouping dissonances only allow for isochronous
One of the few authors to discuss grouping dissonances in non-isochronous meters is
Zachary Cairns, who defines "shared cardinality grouping dissonances" in asymmetrical
meters.19 In Example 1.10, for instance, Cairns shows dissonance between a 3+2 grouping and a
2+3 grouping, highlighting the relative strength and weaknesses of the pulses using Lerdahl and
7 Ibid., 310.
19 Zachary Cairns, "Juggling 2s and 3s" (lecture, Society for Music Theory Annual Meeting, Baltimore, November
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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/m1/21/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .