Developing Ogolevets's Doubly Augmented Prime: Semitonal Voice Leading in the Music of Shostakovich Page: 50
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indicate raised or lowered versions of the whole numbers 1-7.139 Through the line of fifths, any
diatonic mode may be produced by using seven consecutive syllables (equivalent to letter names)
on the line. The line expands indefinitely in both directions to accommodate other modal centers.
In the following illustration (Example 3.2), Ogolevets analyzes J.S. Bach excerpts and adjusts
the line of fifths to present the keys represented in various sections. 140 On the far right side, the
line begins with Do and descends to Fa#, replicating a part of the line previously in Example 3.1;
however, the left-hand side continues towards sharped pitches not represented in the previous
graph. This graph provides insight into the flexibility of the line for musical analysis.141
Example 3.2: Ogolevets's Expansion of the line of fifths. From Ogolevets (1941, 592).
i -F ti1b- (L~ -i C 14-.,4 1- J7 9 Pe -co,1m -,7
Mi# la# re# sol# do# fa# Si mi a re Sol do
In Ogolevets's system, augmented primes occur in a total of fourteen diatonic modes:
five eight-tone modes (hybrid diatonic modes), four nine-tone modes, three ten-tone modes, and
two eleven-tone modes. Carpenter begins her discussion of Ogolevets's augmented primes
starting with his views of attraction and repulsion (ommaueanwi) within modes.142 While
many theories, such as those of Yavorsky, highlight resolutions of tendency tones (i.e. tritone
resolving to a major third), Ogolevets focuses on the tendencies themselves, or the repulsive
139 See Bazayev (2014) for more explanation on Ogolevets's "alpha" and "beta" for flats and sharps, which is not
represented in this graph.
140 Ogolevets (1941), 592. See Chapter 1 for a summary of the line of fifths..
14' The "moving window" concept is similar to the derivation of scales within the Ancient Greek Greater Perfect
System, where one could highlight different scales (lower, middle, and higher) by selecting seven adjacent tones
within a fixed system. Ogolevets's system includes many more fixed tones because he uses a twelve-tone system,
but the concept of moving up and down in a system to include a certain number of tones is similar. See Thomas J.
Mathiesen, Apollo's Lyre. University of Nebraska Press, 1999, 382.
142 Carpenter (1988), 1195-96.50
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Hatch, Amy M. Developing Ogolevets's Doubly Augmented Prime: Semitonal Voice Leading in the Music of Shostakovich, dissertation, May 2022; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc1944286/m1/61/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .