Metric Dissonance in Non-Isochronous Meters Page: 34
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around. Whereas the yellow states contained consonant attacks at the beginning of the measures
and at the third eighth note of the measure, in mm. 109 and 112, these attacks are all dissonant.
In m. 102, conflict occurs not only at the eighth-note level and the beat level, but also
the metrical level. In Example 3.6, I marked metrical groupings for the passage with brackets.
Bart6k uses meters of a cardinality of 6 and 9 in the Violin I/Viola pair and meters of a
cardinality of 6, 4, 5, 7, and 8 in the Violin II/Cello pair. Note that 6 in the Violin I/Viola pair
equals 2/3 of the 6 of the Violin II/Cello pair. These overlapping metrical groupings at different
ratios can also be shown with a composite visual. For this, CDAP (Composite Downbeat Attack
Point) is a more appropriate label (Example 3.8). The downbeats of the Violin I/Viola pair are
shown with , and the downbeats of the Violin II/Cello pair are shown with . The metric
cardinalities for the Violin I/Viola pair are shown above the staff, and those for the Violin
II/Cello pair are shown below the staff. Note that when the Violin I/Viola pair has a meter with a
cardinality of 6 or 9, it is consonant with a Violin II/Cello pair meter of 4 or 6 respectively. This
is because of the 3:2 ratio between the two pairs. With ski-hill graphs, CBAP and CDAP visuals,
I am able to show dissonance that occurs at the eighth-note level, the beat level, and the metrical
Example 3.8. Composite Downbeat Attack Point (CDAP) visual for Bart6k's String Quartet, no.
4, II, mm. 102-112
102 103 104 105 106 107 108 109 110 111 112
6 6 9 6 6 6 6 6 6
6I 4 4KK K 6 , *
6 4 4 4 6 5 7 S
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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/m1/45/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .