Metric Dissonance in Non-Isochronous Meters Page: 42
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ostinato this time around. Because quintuple meters are asymmetrical, a superposition of this sort
creates metric dissonance. To illustrate, I adopt a modified version of Cohn's (2001) metric
states visuals. The figure on the right of Example 4 shows the metric states of the two meters at
mm. 43-44. The left column represents the metric states of two measures of 5/4, and the right
column represents the metric states of one measure of 5/2. The meters are consonant at the
highest level, I o , or 10 quarter notes long. At the first stage, 5/4 requires a symmetrical
division- ,or 5 quarter notes. 5/2 may be interpreted as having a 2+3 (J) or 4+6 ( )
asymmetrical division, requiring a c and a c . This is where I depart from Cohn's metric
states and show a slash to denote the uneven division. A dissonance occurs at this level, shown
by the double arrow connecting the columns. At the second stage, 5/2 requires a symmetrical
division of r), while 5/4 requires an asymmetrical 3+2 division. This 3+2 division is shown asJ
/ . Dissonance occurs at this level because of the conflict between the Jof 5/4 and the J of
5/2. At the third division, the two meters are consonant, each sharing a duration. At the fourth
division, dissonance occurs at the triplet figure in the ostinato. When these triplets occur, the
meters are in a complex hemiola relationship. Otherwise, they are in a double hemiola
relationship. In other words, the level of dissonance is greater when the 0- occur than when the "
occur. 5/2 and 5/4 x 2 do share a cardinality (10 ), but not all of the pulses are isochronous (4+6
and 3+2). Furthermore, the divisions of pulses are not all exactly by 2 or 3. 5/2 on the second
level is divided into a Oand a h . 5/4 on the third level is divided into a - and aJ.
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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/m1/53/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .