The fourth movement is in 2/4, E-flat major, at a fast Allegro vivace. Its layout is A–B–A–C–A–B a rondo in which the final A is omitted.
A
The A section begins in E-flat major and consists of A–a (8 bars) and A–b (16 bars). It opens with an anacrusis; both hands start in the low register. In the first two bars the right hand shows a leap up a 4th then down a 3rd, followed by a stepwise descent in 2nds—the main motive. The left hand answers after a rest, entering with 16th-note stepwise motion that drives the tempo. From m. 3 both hands move together in 16ths. There is no separate cadence at m. 4; the line keeps flowing and only at m. 8 do we hear a V–I perfect authentic cadence (PAC), then on to A–b.
A–b also stays in E-flat major. It starts on V, and in the first two bars the harmony is stated plainly. The right hand spans octaves leaping by 3rds, striking chord tones literally; staccatos sharpen the profile. After two bars of leaps, two bars of stepwise motion follow. The left hand keeps the 16th-note drive. The subsection is built from a four-bar unit repeated four times. Cadences occur twice, once every 8 bars, both as PACs in E-flat.
A transition then follows. Its opening part is a chain of short sequences in which the hands alternate low and high registers.
From m. 37 comes the latter half of the transition, preparing the move to B: in the left hand a chromatic line F–F♯–G–A reaches B♭, then a B♭-major V7–I establishes the new key and leads into B.
B
B begins in B♭ major. Phrases are articulated in 2-bar and 4-bar spans. The first 4-bar sentence is made from a 2-bar motive repeated; the next 4-bar sentence forms a single phrase contrasting with the first (notably legato vs. staccato writing, different sfz placements, and different phrase lengths).
The next passage repeats and extends that second 4-bar idea. At m. 71 the line doesn’t cadence but lengthens its figure to propel the continuation. The harmony naturally modulates to E-flat major; the bass holds B♭ as a pedal, strongly emphasizing the dominant. Cadential material appears at mm. 79–80, but Beethoven delays the cadence by two bars; at m. 82 I in E-flat arrives and the music turns to A′.
A′
A′ repeats A almost literally. From m. 100 the pitch G♭ begins to color the harmony; at mm. 104–106 there is a modulation to G♭ major with an imperfect authentic cadence (V–I). This additional preparation foreshadows the key scheme of C.
C
C proceeds in G♭ major. It starts from a motive that seems to draw on A–a’s shapes. Elements of both A and B are audible here: in the first phrase the left hand keeps 16th-note motion while the right hand carries slower melodic lines. The harmony modulates to B♭ minor; from m. 121 octave-leaping 8ths appear in both hands. These can be heard as fragmentations of the immediately preceding left-hand idea together with earlier figures.
The prior processes are expanded and developed. After the final phrase highlighting octave motion (from m. 126), a varied return of C’s opening figure appears from m. 131. The music modulates to B♭ minor again; to underline the drive to the cadence, the bass centers on F. At m. 135 the right hand leaps widely over the same bass line, and with a cadence in B♭ minor the music passes to a transition.
The transition uses comparatively simple figuration: the right hand continues octaves in 8ths, while the left hand presents sequential 3rd-chords. From m. 156 comes the true preparation for A″: B♭ (V of E-flat) is stressed; both hands pedal B♭, extending V until m. 167, where V–I ushers in A″.
A″
A″ reproduces A. Because B will now be restated in the home key (E-flat), only small intervallic adjustments are needed in the following transition.
B′
B′ flows almost exactly like B, the difference being key: it is now recast in E-flat major (whereas B began in B♭ and moved to E-flat). From m. 250 the music drives toward the cadence; mm. 250–255 feature contrary motion in the two hands, reaching extreme registers and producing a strong half cadence. A Coda follows.
Coda
The Coda divides into two parts.
Coda I begins with a metric shift to 3/4. It develops a motive from the third movement, making the organic linkage among movements explicit. At m. 265 another strong half cadence appears, and the music proceeds to the second coda.
Coda II returns to 2/4. It opens with simpler quarter-note writing; leaps by 3rds and 4ths recur, recalling the movement’s earlier leaping figures. After V–I at mm. 277–278, the figuration accelerates in 16ths, and at m. 285 the work ends forcefully on a full E-flat-major I chord.
The fourth movement is in 2/4, E-flat major, at a fast Allegro vivace. Its layout is A–B–A–C–A–B a rondo in which the final A is omitted.
A
The A section begins in E-flat major and consists of A–a (8 bars) and A–b (16 bars). It opens with an anacrusis; both hands start in the low register. In the first two bars the right hand shows a leap up a 4th then down a 3rd, followed by a stepwise descent in 2nds—the main motive. The left hand answers after a rest, entering with 16th-note stepwise motion that drives the tempo. From m. 3 both hands move together in 16ths. There is no separate cadence at m. 4; the line keeps flowing and only at m. 8 do we hear a V–I perfect authentic cadence (PAC), then on to A–b.
A–b also stays in E-flat major. It starts on V, and in the first two bars the harmony is stated plainly. The right hand spans octaves leaping by 3rds, striking chord tones literally; staccatos sharpen the profile. After two bars of leaps, two bars of stepwise motion follow. The left hand keeps the 16th-note drive. The subsection is built from a four-bar unit repeated four times. Cadences occur twice, once every 8 bars, both as PACs in E-flat.
A transition then follows. Its opening part is a chain of short sequences in which the hands alternate low and high registers.
From m. 37 comes the latter half of the transition, preparing the move to B: in the left hand a chromatic line F–F♯–G–A reaches B♭, then a B♭-major V7–I establishes the new key and leads into B.
B
B begins in B♭ major. Phrases are articulated in 2-bar and 4-bar spans. The first 4-bar sentence is made from a 2-bar motive repeated; the next 4-bar sentence forms a single phrase contrasting with the first (notably legato vs. staccato writing, different sfz placements, and different phrase lengths).
The next passage repeats and extends that second 4-bar idea. At m. 71 the line doesn’t cadence but lengthens its figure to propel the continuation. The harmony naturally modulates to E-flat major; the bass holds B♭ as a pedal, strongly emphasizing the dominant. Cadential material appears at mm. 79–80, but Beethoven delays the cadence by two bars; at m. 82 I in E-flat arrives and the music turns to A′.
A′
A′ repeats A almost literally. From m. 100 the pitch G♭ begins to color the harmony; at mm. 104–106 there is a modulation to G♭ major with an imperfect authentic cadence (V–I). This additional preparation foreshadows the key scheme of C.
C
C proceeds in G♭ major. It starts from a motive that seems to draw on A–a’s shapes. Elements of both A and B are audible here: in the first phrase the left hand keeps 16th-note motion while the right hand carries slower melodic lines. The harmony modulates to B♭ minor; from m. 121 octave-leaping 8ths appear in both hands. These can be heard as fragmentations of the immediately preceding left-hand idea together with earlier figures.
The prior processes are expanded and developed. After the final phrase highlighting octave motion (from m. 126), a varied return of C’s opening figure appears from m. 131. The music modulates to B♭ minor again; to underline the drive to the cadence, the bass centers on F. At m. 135 the right hand leaps widely over the same bass line, and with a cadence in B♭ minor the music passes to a transition.
The transition uses comparatively simple figuration: the right hand continues octaves in 8ths, while the left hand presents sequential 3rd-chords. From m. 156 comes the true preparation for A″: B♭ (V of E-flat) is stressed; both hands pedal B♭, extending V until m. 167, where V–I ushers in A″.
A″
A″ reproduces A. Because B will now be restated in the home key (E-flat), only small intervallic adjustments are needed in the following transition.
B′
B′ flows almost exactly like B, the difference being key: it is now recast in E-flat major (whereas B began in B♭ and moved to E-flat). From m. 250 the music drives toward the cadence; mm. 250–255 feature contrary motion in the two hands, reaching extreme registers and producing a strong half cadence. A Coda follows.
Coda
The Coda divides into two parts.
Coda I begins with a metric shift to 3/4. It develops a motive from the third movement, making the organic linkage among movements explicit. At m. 265 another strong half cadence appears, and the music proceeds to the second coda.
Coda II returns to 2/4. It opens with simpler quarter-note writing; leaps by 3rds and 4ths recur, recalling the movement’s earlier leaping figures. After V–I at mm. 277–278, the figuration accelerates in 16ths, and at m. 285 the work ends forcefully on a full E-flat-major I chord.