Metric Dissonance in Non-Isochronous Meters Page: 1
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Meter involves the interaction of various pulse layers, including the division of the beat,
the beat, the measure, and the hypermeasure. These interactions result in recurring patterns of
pulses on multiple levels. Meters are either isochronous, meaning they consist of evenly-spaced
pulses at every level (i.e., 4/4 or 6/8), or non-isochronous, meaning they consist of unevenly-
spaced pulses at one or more levels (i.e., 5/4 or 7/8). The current literature addresses conflicts
that occur on a level when the pulses on that level are isochronous.
Non-isochronous meters and metric dissonance are prevalent in music of the twentieth
and twenty-first centuries, but the literature on metric dissonance primarily focuses on
isochronous meters. My dissertation fills this gap by expanding upon the current literature,
addressing two problems related to metric dissonance in non-isochronous meters. The first
problem involves grouping dissonances that occur in non-isochronous meters. Harald Krebs
defines grouping dissonances as "superpositions of levels of different cardinalities" when those
levels are metrical or hypermetrical beats.' Example 1.1 shows the isochronous beats in a
measure of 3/4 compared to the isochronous beats in a measure of 6/8. Although consonance
occurs at the downbeats of each measure, dissonance occurs at the beat level, resulting in
grouping dissonance. To account for grouping dissonances involving non-isochronous meters, I
expand upon Richard Cohn's research regarding hemiolas by modifying his ski-hill graphs. Ski-
hill graphs allow Cohn to show hemiolas at various metric levels, and my modifications allow
me to show hemiolas involving non-isochronous meters.2 The second problem I seek to address
' Krebs, "Robert Schumann's Metrical Revisions," 37.
2 Richard Cohn, "Complex Hemiolas, Ski-Hill Graphs and Metric Spaces," Music Analysis 20, no. 3 (October 2001).
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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/m1/12/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .