In this dissertation, I develop and apply an original voice-leading method to the music of Shostakovich. Between the years of 1926 and 1948, his music involved extreme chromaticism that required analytical views from both Russia and the West. In the mid-twentieth century, Russian theorists such as Lev Mazel' and Alexandr Dolzhansky wrote about the modal language of Shostakovich's works, but their writings lacked how to identify them within extremely chromatic passages. In the West, scholars describe his music as both tonal and atonal, sometimes combined within one work. I unify these two views with my voice-leading system consisting of an intervallic resolution of the doubly augmented prime (DAP), which appears seemingly random on the musical surface, but occurs for specific compositional reasons. First mentioned by name in Aleksei Ogolevets' 1946 "An Introduction into Contemporary Musical Thought," the DAP served no harmonic or modal purpose. While Ogolevets mentions and includes examples that show this interval, he does not discuss its resolutions nor how it functions in musical contexts. This structure, however, has broader conceptual and analytical implications. Therefore, I develop a method based on the voice leading and semitonal resolutions of the DAP, which I apply to the music of Shostakovich. The DAP contributes to his compositional style by functioning in three ways: 1) identifying one mode or two simultaneous modes, 2) completing traditional triadic harmonies, and 3) facilitating both tonal and modal modulations.