Metric Dissonance in Non-Isochronous Meters Page: 21
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Example 2.3. Modified ski-hill graph for Bart6k, Mikrokosmos, no. 115, "Bulgarian Rhythm,"
Path Takeii by Measures 1-8
Path Tukcn by 1azsur s 9-16
Gabriel Piern6's Piano Quintet, No. 41, III
In some music, conflicts involve asymmetrical groupings and ratios other than 3:2.
Gabriel Piern6's Piano Quintet, No. 41, III contains passages of 10/8 against 2/2, 10/8 against
6/4, and 10/8, 2/2, and 6/4 at the same time. Measures 8-12 (Example 2.4), feature 10/8 against
2/2, in which a 3+2+3+2 pulse grouping occurs in the ostinato (second staff from the bottom)
and a 2+2+2+2 pulse grouping in the conflicting string parts (top staves). Each element of the
groupings, however, is not equal in duration, as the ostinato is in a 5:4 ratio with the strings.
Thus, five eighth-notes in the ostinato are equal to the duration of one half-note in the strings.
Example 2.5 shows the two conflicting groupings, normalizing the strings to 10/8 to reflect
consistent durations. One quarter note in 2/2 is the duration of a quarter note tied to a sixteenth
note in 10/8.
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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/m1/32/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .