Metric Dissonance in Non-Isochronous Meters Page: 35
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The way in which I combine the attacks from different layers into one composite layer
resembles Yeston's. In his discussion of the simple hemiola, Yeston combines the two strata into
a string of integers, 2112. Krebs also discusses "resultant rhythms," which is a similar principle.
These integers, however, do not succeed in showing which voice or collection of voices or
timbres contributed the attack points. Furthermore, the integer method does not show metric
dissonance. My methodology takes Yeston's integer strings as a point of departure and expands
it to show both which voices or timbres are involved and dissonance at the metric level.
Although our understanding of the Bart6k example profits from the use of the CBAP
system, It is possible to show examples such as Piern6's Piano Quintet with CBAP visuals rather
than modified ski-hill graphs. Both methodologies, however, have their advantages and
disadvantages. Example 3.9 shows a CBAP visual for Piern6's Piano Quintet. The = represent
the 18+12 10/8, the represent the 2/2, and the ' represent the 6/4. This visual, representing
multiple ratios in simultaneity, stretches the limits of our musical notation and is not readily
comprehensible as a visual of metric states, which is more easily shown with a ski-hill graph.
This visual does have its benefits, however. Because this example involves non-isochronous
pulses with diverse ratios, it is possible to conclude that some at some moments within the metric
state, the dissonance is greater than others. As previously mentioned, using Krebs's principle of
proximity, the points of non-coinciding attacks are greater when the dissonant attack points occur
closer together. In this example, the points of greatest dissonance occur at the sixteenth-note
triangle note head followed by the triplet sixteenth-note x notehead, occurring twice in the
measure. Modified ski-hill graphs are better at showing the metric state itself and its relationship
to other metric states in passages that involve asymmetrical dissonances that occur over a shared
time span. Furthermore, modified ski-hill graphs can show an unlimited number of metrical
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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/m1/46/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .