Opus 7/2
Consequently the B section stands out more boldly than do the b regions. Whereas b resides within an internal rounded ternary form, B is a more independent entity – what musicians often call a trio. Given how often the tonic pillar recurs, it is not surprising that its internal binary structure (the antecedent and consequent phrases shown in 1.19) is truncated during the a2 statements, where only its consequent half is presented.
The embellishing chord that occurs during the a region’s first measure influenced how Chopin shaped the b region. Whereas in its initial statement the chord might be imagined as deriving from concurrent neighboring motions – E<F>E and (C)<D>C – another common context for a would be corresponding upper-third shift occurs as the circle draws to a close – in measure 24, where E-G-B♭-D arrives as if rooted on C, but is departed as if rooted on E. Over the
course of the b region the melody fills in the tonic’s E>A fifth, while the bass concurrently fills in its A>E fourth. (These expanses are slurred in 2.15.) The continuation in measure 25 (which corresponds to measure 1) is unfurled into position to accommodate the inverted A chord of 243.
Example 2.15 Analysis of Mazurka in A Minor (op. 7/2).
The B section’s internal ternary form juxtaposes tonic prolongations during the outer parts (labeled x in 2.15) with a motion to the dominant (via a conventional I5–6 II➔ V harmonic progression) during the middle part (labeled y).19 I propose that whereas E (=
) serves as the Kopfton for the mazurka as a whole, the B section’s melodic focus is the third from C♯ to A (with interruption).20
Kopfton regains prominence with the onset of A2. The background descent from to occurs during that section’s a2 region, bringing the mazurka to a close [2.15].
Opus 17/3
During the Mazurka in A♭ Major’s tonic pillar the Kopfton C (= ) serves as the starting point for a descending third-progression to the tonic root [1.16]. In the context of the A1 section’s internal a1 b a2 form (in measures 0|1 through 40), that third-progression’s C leads through B♭ during b to the restored pillar’s endpoint A♭ during a2 [2.16]. (These pitches will constitute the background descent during the reprise after the mazurka’s B section.) The b region begins with six measures of strumming on II, focused melodically on the chromatic filling-in of II’s F>D♭ third, thereby prolonging the Kopfton’s upper neighbor, D♭. The next two measures feature an evolved dominant, during which the region’s melodic goal – (B♭) – is attained.21
Example 2.16 Analysis of Mazurka in A♭ Major (op. 17/3).
The B section (likewise ternary) is in the key of F♭ Major (which Chopin presents as E Major), a chromatic variant of I6, as noted in 2.16.22 Consequently the Kopfton wobbles from C to C♭. Harmonically there are no surprises: the x regions proceed from the tonic to the dominant in their antecedent phrases (where a descending fifth-progression from C♭ is interrupted at G♭ [F♯]),23 and through the dominant to the tonic in their consequent phrases (where the fifth-progression is completed). The y region that intervenes proceeds from II➔ to V, supporting a prolonged C♭ in the upper line, here covered by E♭. The ascending C♭<D♭<E♭ that is repeated several times during measures 57 through 64 (where it undergoes an internal upward registral shift, not shown in 2.16) is one of numerous upward motions from deep structural pitches throughout the mazurka: compare this C♭<E♭ third (tenth) with C<E♭ in measure 2 and D♭<F in measure 17. That upward drive
also energizes measures 41|42 through 45|46, where the arpeggiated bass from the tonic root to the dominant root (F♭<A♭<C♭) is mimicked in the soprano as C♭<E♭<G♭, after which C♭ is restored preceding the descent to F♭. For locomotion, Chopin deploys a circular progression with one omitted element: F♭ (B♭) E♭ A♭ D♭ G♭ C♭. Consequently the bald parallel motion on display in 2.16 does not occur in the musical foreground.
Opus 33/3 [a.k.a. opus 33/2]
The Mazurka in D Major offers an interesting study in contrasts. The outer A sections (first heard in measures 0|1 through 48) are uncommonly repetitive and uncomplicated in their harmonic fabric, whereas the interior B section is strikingly original, displaying chromatic writing that likely baffled many of Chopin’s contemporaries. Whereas the initial tonic pillar (a1 within A1) succeeds in establishing D Major via an interrupted third-progression (F♯>E>D) descending from Kopfton [1.18], the transfer of that material to a dominant context for the b region that follows offers no successor to : the C♯ of its C♯>B>A third-progression relates to the tonic’s interior D, rather than to F♯. Though some may find my parenthetical E in measures 17 and 89 of 2.17 dubious, it is consistent with my imaginative approach to analysis, which tolerates some discrepancies between the musical surface and a work’s foundational conception. In this case it even constitutes a
“motivic” relationship, since a parenthetical E occurs in my reading of the tonic pillar as
moves beyond the B♭ chord, ultimately to D Major’s dominant, A-C♯-E. Consequently the soprano F♮ here functions broadly as a chromatic passing note, rather than as a wobbly note, even if its successor E sounds in the bass (at 691) rather than in the soprano, where
Observe that in this mazurka Chopin in fact proceeds from B♭-D-F♮ (the I6 from the parallel minor key) to E-G♯-B (II♯). How is this accomplished?
Though B♭<E is an awkward relationship within diatonic tonality (modulo 7), it is a favored relationship within chromatic tonal space (modulo 12), since it represents exactly half the span of an octave. It can be traversed with ease once the bounds of diatonic tonality are removed: for example, as 2+2+2 or as 3+3. Chopin pursues the latter course:
10 1 4 in modulo 12 numerical notation (where C = 0). Because music notation was designed to accommodate compositions conceived in modulo 7, composers had to contend with infelicities such as a succession from B♭ to D♭ (the first +3) followed by one from D♭ [C♯] to E (the second +3).
Turning now to some details not conveyed in 2.17, note that the D Major tonic’s chromaticized 6-phase chord (B♭-D-F♮) is tonicized during an eight-measure phrase leading from B♭ to a cadence on its F dominant (measures 49 through 56). The following phrase, charged with undertaking the first +3 ascent, first converts to the parallel minor (B♭-D♭-F), thereby placing goal D♭ within a locally diatonic context. The D♭-F-A♭ chord that arrives in measure 62 plays no role within D Major. It instead is a connector (within an obstinate circular progression: 3+3) between two chords that do function within that broad context.
Chopin deals with the task of enharmonic conversion at 651, where a dominant-emulating evolved state of the D♭/C♯ chord targets F♯. Yet the F♯-A-C♯ chord does not take hold. Chopin backtracks, resolving the E♯-G♯-B♮-D♮ chord repeatedly. Only on the third try does its resolution endure and function within the broader harmonic progression.
That chord is not F♯ minor, but instead A major (in measure 70). The accomplishment of the second +3 is sudden and unexpected, yet alert listeners would of course be aware of the special properties of the particular evolved chord that Chopin introduces in measure 65. Whereas C♯-E♯-G♯-B♮ would have targeted F♯ forthrightly, E♯-G♯-B♮-D♮ offers alternatives. Chopin demonstrates that its root might be C♯, or that it might be E. By measure 69 we come to understand that E♯-G♯-B♮-D♮ stands for G♯-B♮-D♮-F♮, an interpretation confirmed when ninth F♮ yields to root E♮. Having achieved II➔ (thereby completing the 3+3 ascent), the dominant goal is easily attained in measure 70. The mapping of A1’s structure into the A2 space rounds out the mazurka, as shown in 2.17.
The background arrival on is followed by a tonic-focused coda.