Metric Dissonance in Non-Isochronous Meters Page: 5
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melody and the displaced alto grouping). Krebs recognizes that dissonances are not all equal in
intensity. He refers to Gretchen Horlacher's "cycles" to determine the relative intensity of
grouping dissonances. Horlacher's cycles appear in discussions of the music of Stravinsky.
Cycles are "the larger pattern[s] created by the simultaneous repetitions of...strata."8 The longer
the cycle, the greater the dissonance, according to Krebs. In other words, the more attacks that
occur before the two strata align, the more dissonant the relationship. G3/2, which contains a
cycle of 6 pulses, is therefore less dissonant than G5/4, which contains a cycle of 20 pulses.9
Example 1.3. Krebs's grouping and displacement dissonances'0
Example 1. Schumann, Sonata in F minor, op. 1: Scherzo e Intermezzo., mm. 51-56
1 = . ni
G3/ 2 3 3 3 3 3 3
2 2 (2) 2 2 (2) 2 2 (2)
6 6 6
Although Krebs's conception of grouping relies on metrical considerations, Lerdahl and
Jackendoff distinguish grouping structure from metrical structure. They claim, "Grouping
structure consists of units organized hierarchically; metrical structure consists of beats organized
hierarchically."" Example 1.4 reproduces Lerdahl and Jackendoff's grouping and metrical
analysis of the opening of Mozart's G Minor Symphony. They show hierarchical groupings with
the curved brackets and hierarchical metrical structures with dots. Note that the three-note
8 Gretchen Horlacher, "The Rhythms of Reiteration: Formal Development in Stravinsky's Ostinati," Music Theory
Spectrum 14 (1992): 174.
9 Krebs, "Robert Schumann's Metrical Revisions," 38.
0 Ibid., 37.
" Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983), 25.
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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/m1/16/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .