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Chopin’s mazurka in B major, op. 56, no. 1, provides a clear-cut example of a harmonic structure determined by major-third affinity pairs arranged symmetrically around a tonic. The mazurka’s form is tripartite: A B1 – A B2 – A C. The recurring A section, which begins and ends in tonic B major, prepares the chromatic mediant relations to come by dramatically tonicizing the lower flat mediant before settling on the tonic. The two B sections begin at opposite major thirds from the tonic and continue moving away from it symmetrically. The final A section and coda remain in tonic B major, withconsiderab le use of sequence and chromatic elaboration (Ex. 9.1).

The mazurka’s opening section (shown as a network diagram and bass sketch in Figure 9.1) projects tonal ambiguity for muchof its duration. After an indefinite beginning on an open third, E–G , the bass continues downward to trace an unstable C minor 6 4 chord, which finally gains context in the next two beats as the initiating chord of a ii 6 4–V6 5 –I progression arriving in m. 2. This process occurs twice again in sequence, descending by whole step through A major in m. 4 to G major in m. 6, for cumulative motion of M, a major third. G major remains as a pedal point for several measures, as if the descending sequence had reached bottom and settled on the tonic. At this point rising motion takes over. The melody ascends a full octave by scalar motion above the pedal while the opening bass motive repeats on G, confirming the arrival. A second octave ascent by the melody, however, overshoots by a step as, along the way, the G major triad is transformed at m. 12 into a German augmented-sixth chord, whose resolution initiates a return to B major. The arrival to B at m. 16 sounds even more final than that to G, and is affirmed by several V–I cadences. In retrospect, then, G major is heard as the lower flat mediant, returning to the tonic through the familiar augmented-sixth route described often above. Chopin’s innovation is to expand the I–LFM juxtaposition at the beginning of the basic cadential framework (I–LFM–Ger+6–cad. 6 4–V–I, as in the Schubert B  major sonata) into a three-element descending sequence. While B major, which sounded like a false tonic at the beginning, is revealed to be the true tonic, G major, the LFM, has been strongly tonicized by the sequential expansion as well. In this way Chopin sets up a chromatic mediant relation as the governing harmonic polarity of the mazurka’s first section.

At the transition into the first B section, Chopin treats B major as he had G major, transforming it into a German augmented-sixthch ord, resolving properly up by M−1 to E  major (enharmonically D major, the USM) at m. 24. Thus, having just confirmed its tonic, the music immediately wanders off in the opposite direction. Notwithstanding this abrupt sharpward chromatic transition, and in contrast
to the earlier dramatic play between chromatically third-related keys, this new section proceeds by a series of stable eight-measure pedal points alternating calmly by pivot-chord modulation between E  and A major, the other member of the sharp mediant affinity pair (enharmonically G major, the LSM). The appearance of these new harmonies in the absence of any focus on fifth-related keys makes it clear that Chopin is intent on exploiting the oppositional qualities of chromatic third relations to the tonic. The last phrase of this section, in A, dissolves before it ends into a single suspended line at m. 46 in preparation for the return to opening material. Direct

Example 9.1 Chopin, Mazurka op. 56 no. 1, opening

Figure 9.1 Chromatic-mediant transformation structure of section of Chopin’s Mazurka op. 56 no. 1

motion back from A is potentially quite smooth despite its chromatic relation to the tonic, since the A section begins with a C minor chord, and G/A  major may act as its dominant. Chopin chooses to move slowly, though, first changing A major to A minor, and only then moving to C minor. In so doing, Chopin decomposes the chromatically tinged dominant relation F into a subtler modal fifthr elation PD
whose sound and effect are less marked than the chromatic mediant relations controlling the piece’s structure. This eases back into the beginning in an indefinite manner more appropriate to its tentative quality than a straightforward V–I progression would be. Figure 9.2 recounts this process and that of the following sections.

The second B section transpires as the mirror reflection of the first. The transition into this section from the repeat of the opening takes B major down a major third rather than up, flatward toward G major, already familiar from its tonicizations in the opening section.1 Once settled in G at m. 82, B2 proceeds withpedal-point material equivalent to that of B1, including the modulations by fifth at the end of each eight-measure phrase. But these modulations are the opposite of the earlier ones: where E  major had moved down a fifth to A major, G major moves up a fifth to D major, the UFM and last chromatic mediant to appear, at m. 90. The alternating pedals repeat as before, dissolving again into a single line in anticipation of the return to the tonic. The relation between D major and the opening is more distant than the one at the end of B1, and Chopin pads the return with a lo

Figure 9.2 Transformation structure of Chopin’s Mazurka op. 56 no. 1, up to the final section

Figure 9.3 Symmetrical transformation network, formed by the middle sections of Chopin’s Mazurka op. 56 no. 1, incorporating all four chromatic mediants and all four chromatic mediant relations

and subtle stepwise approachr eviving the indefinite feel of earlier events, moving downward chromatically in parallel 6 3 chords from D major (m. 106) to the same G minor he previously used to prepare C minor (m. 123).

The change in B2 is crucial, for it allows for a symmetrical harmonic structure (Fig. 9.3). Where the A–B1 sections move from B major up a major third to E  and down a fifthto A (M−1D), the A–B2 sections move down a major third to G and up a fifthto D (MD−1). Defining this symmetry through this change in B2 allows Chopin to visit all four chromatically third-related keys: G, the LFM; G/A , th e
LSM; D, the UFM; and D/E , the USM. Clearly a deliberate construction, this smooth, regular structure unites the tonic with all of its chromatic mediants in a harmonic formation more complex and sophisticated than Schubert produced in Die Sterne, although without the marked effect of direct surface mediant relations, except at the transitions into the B sections.

Following the third iteration of the opening material, Chopin lets loose with section C, a vigorous coda full of sequential passages tonicizing “neglected” diatonic harmonies vi, IV, ii, and V, along with cadential reaffirmations of tonic B major. There is a regularizing effect, to be sure, and in retrospect Chopin appears to have isolated and emphasized the qualities of the chromatic mediants’ greater harmonic remove from the tonic in the earlier sections in order to set up the diatonic return. But this in no way invalidates the coherence of the earlier sections. In fact, it is exactly the coherence of the chromatic mediant relations as chromatic mediant relations that allows for the definite contrast between the first two sections and the last to be drawn.

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