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The expression P 3,0 refers to one class of parsimonious voice-leading transformations between seventh chords introduced in a 1998 article by Jack Douthett and Peter Steinbach as P m,n ( Journal of Music Theory 42 (2): 241–63). In addition to tones that may be held in common, the subscripts indicate the number of voices that move by half step (m) or whole step (n) in connecting one seventh chord to the next. P 3,0 designates a transformation in which one of the chord members is held in common while each of the other three moves by half step. P 3,0 transformations produce some of the most striking chromatic harmonic progressions in the late Romantic repertoire. This study focuses on aspects of P 3,0 transformations that include 1) their place in the broader context of neo-Riemannian voice-leading transformations; 2) their properties and a specific means of notating all possible P 3,0 types; 3) explications of how the various types are integrated within late nineteenth-century harmonic practice and interact with traditional tonal harmony; and 4) analytic applications that demonstrate how P 3,0 transformations operate within and contribute to musical structure, including the opening of the Prelude to Wagner’s Tristan und Isolde , and a complete song (“ Ruhe, meine Seele! ” op. 27 no. 1) by Richard Strauss.

Types and Applications of P3,0 Seventh-Chord Transformations in Late Nineteenth-Century Music