Metric Dissonance in Non-Isochronous Meters Page: 24
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Example 2.7. Pulses in Piern6's Piano Quintet, no. 41, mm. 20-27
M m. 20-27
Although the ratios are different from the Bart6k example, the metrical conflict that
occurs in this passage can be shown with a modified ski-hill graph, provided in Example 2.8. To
determine the graph required for this passage, I found the durational greatest common factor
between the three meters, which is the triplet thirty-second-note (from the perspective of 10/8).
Although the triplet thirty-second-note does not appear in the music itself and would not be
readily perceived as a tactus, it is the longest possible duration to represent each beat in each
meter with whole-number divisions and is necessary to conceptually show the points of conflict.
Each number on the graph represents the number of triplet thirty second notes at each metrical
level. The measure has 60, and because the meters align at the halfway point of the measure,
each takes the path from 60 to 30. The blue path represents 6/4, ending on 10 triplet thirty-
second-notes. The green path represents 2/2, ending on 15 triplet thirty-second-notes. The red
path represents 10/8, ending on both 18 and 12 triplet thirty-second-notes because of the 3+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/m1/35/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .