Metric Dissonance in Non-Isochronous Meters Page: 27
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APPROACHING THE LIMITS OF MODIFIED SKI-HILL GRAPHS
As mentioned before, the second problem I seek to address involves shared time spans.
When displacement dissonances occur with non-isochronous pulses, both Cohn's (including the
modified ski-hill graphs) and Krebs's methodologies struggle to show the dissonances and the
degree of conflict that occurs. Considering Example 3.1, it would be impossible to show all of
the conflict that occurs using those methodologies. Bart6k's String Quartet, No. 4, II exhibits
both metric dissonances that may be shown with Cohn's modified ski-hill graphs and some that
cannot. Example 3.1 begins with 6/8 vs. 2/4. The eighth-notes in 2/4 are in a 3:2 ratio with the
eighth notes of 6/8. Although the viola line is beamed in 3s, and that beaming may influence the
performer's conception of the passage, I believe these eighth notes would more accurately be
grouped in 2s because of the repetition of the motion from C to B. The cello line's grouping of
2s, however, is accurately represented in Bart6k's beaming. I show the grouping below the score,
where the first line of 2s represents the viola's groupings and the second line of 2s represents the
cello's groupings. The 2s here are not equivalent because they are performed in a 3:2 ratio.
Example 3.1. Eighth-note groupings in Bart6k's String Quartet, no. 4, II, mm. 76-80
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 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/m1/38/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .