Developing Ogolevets's Doubly Augmented Prime: Semitonal Voice Leading in the Music of Shostakovich Page: 23
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Like Yavorsky's symmetrical systems, the duplex systems also include single and double
systems. Example 2.5 presents the duplex double system. Below the staff, 'dS' represents a
duplex subdominant and 'dt' as duplex tonic, but with a lowercase 't' because it refers to minor
thirds.52 Notice that the bottom dyads, starting with D-A, copies exactly from the DSS. The
dyads above relate to the bottom dyads by a tritone.
Example 2.5: Converging duplex double system.
dS dt
The duplex single and double systems combine to form two complete triads. Example 2.6
provides this visual. The duplex single system appears first and the double system second, with
their function labels below the staff. The dashed lines connect the opposite pairs of tonic chord
members (dT) and appear in the last measure in triadic form. The single and double duplex
system results in two triads related by a tritone: C major and F# major. Because the double
system included a Bb-Db dyad, I have enharmonically interpreted the full Gb major triad in
parentheses adjacent to F# major.
Example 2.6: Duplex single and double systems.
dD dT dS di dT
52 McQuere's text shows this tonic as a 'dT,' but following the process of Yavorsky's symmetrical systems, this
should be labeled as 'dt' with a lowercase 't.' Ewell (2018) [4.19] also corrects this tonic to a lowercase.23
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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/m1/34/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .