Signature Transformations

Abstract

Among the many distinctive features of the Schubert Valse sentimentale in A major reproduced in figure 6.1, the various adventures of the four-eighth-note pickup figure (first appearing as C#–E–D–C# in measure 2) merit special attention, as does the sudden appearance of the key of C# major in the second strain. We consider the latter first. This chromatic mediant C# major could be explained in traditional terms as a product of mixture, a sort of parallel substitution for the diatonic mediant, C# minor. This explanation could be modeled using neo- Riemannian transformations as shown in the simple network of figure 6.2, in which the Riemannian Leittonwechsel L describes the relationship between A major and C# minor, and P is the parallel relation between C# minor and C# major. It might be objected that figure 6.2 is only marginally relevant to Schubert's waltz, inasmuch as C# minor never actually appears in the piece: there is neither a C# minor triad nor a tonicization of the key of C# minor. There is, however, at least a suggestion of C# minor in the form taken by the four-note melodic fragment at the point where the mixture first appears, in measure 18: C#–E–D#–C#. Two measures later, the figure takes its C# major form, C#–Eƒ–D#–C#. The latter, it should be noted, is not simply measure 2 transposed from A major to C# major; rather, both forms start on the same note, C-sharp, which is scale degree 3 in A major but 1 in C# major. All three of these forms of the four-note motive are shown in figure 6.3. The melodic transformations shown here precisely reflect the harmonic structure outlined in figure 6.2, but in a way that is more apparent in the waltz. The variants of the melodic figure are represented here by changes of key signature rather than the accidentals that Schubert used. When shifts of diatonic collection are implied, appropriate key signatures are a convenient means of representation for analytical purposes, and will be used thus throughout this paper, sometimes without regard to a composer's original notation. The transformations relating the melodic forms in figure 6.3 are signature transformations. The first signature transformation, s 1 , adds one sharp to the key signature, and s 3 adds three more sharps, all while leaving the written notes unchanged.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 84 citations exist upstream.