Recording: Yo-Yo Ma, cello and Emanuel Ax, piano [RCA Red Seal 82876-59415-2]
Published 1866.  Dedicated to Dr. Josef Gänsbacher.

Brahms had considered a violin sonata in A minor for inclusion among his earliest publications, but the piece was rejected and destroyed.  This cello sonata is the earliest published work for solo instrument and piano, and the only example from the period of first maturity, which is rich in other chamber music genres.  Brahms appreciated the cello’s qualities as a melodic voice, and had given it the opening themes of the B-major Piano Trio and the B-flat-major String Sextet.  It was composed for and dedicated to Josef Gänsbacher, a singing teacher and amateur cellist.  It comes from the time when Brahms was transitioning to full-time residence in Vienna.  The sonata is known for its generally somber character and consciously archaic elements.  Brahms, like Beethoven, emphasized the equality of the two instruments by publishing it as “Sonata for Piano with Violoncello.”  He had originally written a slow movement, but rejected and discarded it before publication, settling on the unusual three-movement design with the scherzo-type movement (in this case a minuet) in the middle.  The most original movement is the finale, much of which can properly be described as a fugue, but which has a non-fugal second theme and certain elements of sonata form.  The main fugue theme, or “subject,” is explicitly related to that of Contrapunctus 13 from Bach’s “The Art of Fugue.”  There also seems to be some homage to Beethoven, who wrote a fugue as the finale for his late D-major cello sonata, Op. 102, No. 2.  The middle movement also has a retrospective character.  In addition to the minuet dance rhythms from an earlier era, the movement contains austere modal elements reminiscent of Renaissance harmony.  The central trio section is more “romantic” in character, and skillfully uses the minuet’s opening gesture as a departure.  The more expansive opening movement relies heavily on the cello’s low register, especially in the very broad opening theme.  This theme also has a certain affinity to Bach’s “The Art of Fugue,” in this case the inverted form of that work’s main subject as seen in Contrapunctus 3 and 4, but this connection is more tenuous than that of the fugal finale.  The extensive second group closes with a striking lullaby.  The exposition repeat is less effective than usual in Brahms because of the somewhat literal recapitulation.  The major-key ending provides respite from the sonata’s severe overall mood.  After it was rejected by the publisher to whom it was first offered, Brahms sold the sonata to a second firm, stating that the piece was “certainly not difficult to play” for either instrument.  This is surely one of the most disingenuous statements ever made by a major composer about his own work.  The piano part is thick and active throughout, becoming downright treacherous in the finale’s main fugue sections, and a wide range of cello technique is also demanded.

ONLINE SCORE FROM IMSLP (First Edition from Brahms-Institut Lübeck)
ONLINE SCORE FROM IMSLP (Later Issue of First Edition with Cello Part)
ONLINE SCORE FROM IMSLP (from Breitkopf & Härtel Sämtliche Werke)

1st Movement: Allegro non troppo (Sonata-Allegro form).  E MINOR, 4/4 time.
0:00 [m. 1]--Theme 1, Part 1.  The cello begins in its lowest range and presents the expressive, melancholy melody, which starts on its low E.  The piano accompanies with simple chords on the weak beats.  It rises with a prominent dotted rhythm (long-short) and then moves to a characteristic turn figure.  Rising higher, the cello melody turns toward the harmony of the “dominant” key, B major.  After two wide downward leaps of an octave and a ninth, it reaches a cadence on B.  The piano continues its chords on weak beats. 
0:25 [m. 9]--Theme 1, Part 2.  The cello line, now marked dolce, moves to the higher register in a continuation of the melody.  The dotted rhythm is still prominent.  The piano continues to play chords on the weak second and fourth beats of the measure, defining the harmony.  At first, the key seems to veer toward the “relative” major key, G major.  After a slow triplet rhythm, the cello soars even higher and the harmony moves back to E minor as the volume builds.  As the cello reaches its highest note, the piano finally breaks its steady chords, rolling and holding a dissonant “diminished seventh.”  The cello, exposed, winds and settles back down, leading to the next phrase.
0:53 [m. 21]--Theme 1, Part 3.  The piano takes the opening melody, doubling it in high octaves between the hands with some harmonic decoration.  Meanwhile, the cello continues its downward line, utilizing some broad triplet rhythms and working back to its original low register.  After the turn figure, the piano’s upward line suddenly builds, making a harmonic move toward C major.  The cello follows with its own upward line, culminating in a large leap and further moving the harmony toward F.  Another such exchange follows on F with the piano lower and the cello higher.  The piano settles into rising arpeggios doubled in octaves and moving back to E minor.  The cello returns to its low register and reaches a close in E minor.
1:18 [m. 33]--Transition.  The piano holds its cadence chord while the cello moves up to the note G.  This note is used to pivot to C major, and the piano confirms the motion.  On C, the cello begins to elaborate dreamily on the main melody.  The piano breaks into rippling high triplet figures in the right hand and colorful chords, also in the treble range, in the left.  The harmony and melody are both very chromatic, and the inflections toward the minor key are strong enough that it is really a C major/minor mix.  After four bars, the cello moves to octave leaps, the minor-key inflections disappear, and a weak cadence is reached.
1:38 [m. 42]--The piano left hand moves to the bass and establishes a “pedal point” on C, leaping down the octave.  The triplet rhythms move to the right hand and are all downward.  The key wavers between C and F major.  At the same time, the cello begins a sequence based on a motion down a step, a repeated note, and a motion up a step.  The first two times, the pattern, building in volume, leads to a held note and a yearning downward motion.  This echoes the last cadence hidden in the piano triplets.  After four bars, the held notes are omitted and the simple arch pattern prevails.  At that point, the hands of the piano reverse roles.  The right hand takes the “pedal point” octaves in the high range while the triplets, now rising, move to the bass.
1:54 [m. 50]--At the end of the last passage, both instruments introduced chromatic notes suggesting C or F minor.  But the piano bass touched on the foreign note F-sharp, which now becomes the new “pedal point.”  It moves back to the bass, and the triplets go back to the high treble, again descending.  The cello continues to surge forward on the same pattern.  After four bars, the pattern halts with a sharp chord.  Both hands of the piano and the cello begin to outline a chord on F-sharp in rising arpeggios, but descending notes in the cello, then the piano, reveal this harmony as the preparatory “dominant” of B minor, the key of Theme 2.
2:09 [m. 58]--Theme 2.  It begins with a canon between the cello and the piano right hand.  The cello leads, beginning with an upbeat and repeatedly outlining the chord of the new key (B minor).  The piano follows in imitation.  The line is harmonized using the notes of the chord.  The left hand also uses these notes in downward arpeggios.  The canon continues until the cello breaks free with a more passionate melody.  At first, the piano accompaniment retains the rhythm and syncopation of the canon, but then supports the cello melody.  After an expressive turn, the cello works to a cadence on F-sharp (the “dominant” of B minor).
2:26 [m. 66]--The piano right hand, in the middle range, returns to B minor and starts to outline the chord again.  The volume is suddenly hushed.  The left hand follows, but not in canon.  Instead, it begins a low murmur with stepwise motion.  The right hand continues to outline the chord.  After three bars, the cello enters and joins the piano bass on the low murmur.  The piano then begins a more subdued version of the passionate melody.  The cello works downward, playing in counterpoint.  The piano begins to play in octaves, and its melody stalls, then trails down to a halting cadence with a descending fifth.  The last cadence motion is repeated an octave higher, and the cello follows it a beat later in another brief canon.
3:00 [m. 79]--Closing theme.  With an atmospheric change to B major, the piano right hand begins a gentle, almost lullaby-like melody.  Meanwhile, the cello and the piano bass continue to play the descending fifth, the piano bass beginning on the upbeat and the cello following on the downbeat. 
3:10 [m. 83]--After four bars of the lullaby melody, the cello takes it over and the piano right hand briefly continues the imitation of the bass, which moves away from the fifth and reaches an octave.  This imitation only continues for two measures, and then the right hand harmonizes the cello, leaving the piano bass alone on the octave.  The cello statement is much more chromatic, but remains in major.  At its cadence, the piano bass returns to the fifth, and the melody reaches a full close, the piano right hand moving above the cello.
3:24 [m. 88]--Transition.  The cello drops out, and the piano right hand, in the tenor range, plays descending thirds, moving to the home key of E minor.  The bass subtly shifts toward broken octaves on C and B to help facilitate the move back.  The right hand thirds repeat their last motion, setting up the repeat.
3:32 [m. 91a (1)]--Theme 1, Part 1, as at the beginning.  The last measure of the first ending is identical to the first measure of the movement.
3:55 [m. 9]--Theme 1, Part 2, as at 0:25.
4:22 [m. 21]--Theme 1, Part 3, as at 0:53.
4:47 [m. 33]--Transition with theme in C major/minor, as at 1:18.
5:08 [m. 42]--Pedal point on C and buildup with stepwise arching pattern in cello, as at 1:38.
5:24 [m. 50]--Pedal point on F-sharp, then arpeggios leading to second theme in B minor, as at 1:54.
5:39 [m. 58]--Theme 2, beginning with canon on B-minor chord, then passionate melody, as at 2:09.
5:56 [m. 66]--Softer murmuring motion in bass, then motion to cadence, as at 2:26.
6:29 [m. 79]--Closing theme.  Lullaby-like melody in piano with continuing bass fifth canon, as at 3:00.
6:39 [m. 83]--Chromatic cello statement of B-major lullaby melody, as at 3:10.
6:53 [m. 88]--Transition, as at 3:24.  At the second ending (m. 90b), the piano bass makes a subtle change by staying on the broken C octave instead of moving to B.  The right hand has the same notes, but the last third is notated as an augmented second instead of a minor third.  These subtle changes help to make the harmonic change to G major (and minor) instead of E minor.  The development begins in G.
7:02 [m. 91b]--The cello makes the opening gesture of the main theme in a mixture of G major and minor, supported by middle-range harmonies in the right hand and the continuing broken octaves in the left.  The piano right hand moves up and echoes the gesture with chordal harmonies.  It then moves an octave higher, and altered harmonies immediately change the key to B-flat major.  The cello takes over the bass rocking motion, with varying wide intervals.  The piano chords seem very bright after this change to B-flat.  They continue, adding a gentle decorative turn figure in the left hand, to an expressive cadence.
7:22 [m. 99]--The previous pattern is repeated and varied.  The piano begins with another Theme 1 gesture, adding minor-key elements.  The cello echoes it, and the rocking motion moves to the piano bass.  The same harmonic motion also follows, from B-flat to D-flat (using the same key relationships).  This time, the cello has the top melodic note of the chords as well as the gentle decorative turn, the right hand adds internal motion, the rocking motion remains in the piano bass, and the expressive cadence arrives in D-flat.
7:41 [m. 107]--The cello establishes a “pedal point” on D-flat, leaping up and down octaves on the note.  Meanwhile, the piano bass begins Theme 1 in that key, mixing major and minor again.  The right hand has the rocking motion, now in close harmonies.  After four measures, the cello leaps up, taking over the Theme 1 material.  But it then leaps back down to a low F, anticipating the next harmonic motion. 
7:55 [m. 113]--With another leap up against octave motion in the piano bass, along with steadily building volume, the cello makes the shift to F major.  At this point, the rocking motion in the piano right hand becomes wider and changes to full chords, some with colorful chromatic notes.  The piano bass quickly establishes another “pedal point,” now on F, and the cello utilizes a yearning figure from the main theme to further establish F as the new key center.  The intensity builds to a climax.
8:06 [m. 118]--At the climax, the piano, in full harmony with leaping bass, takes over the yearning figures just played by the cello.  The harmony freely shifts between major and minor.  The cello now begins a new and powerful motion in wide downward leaps from a high F down two octaves to a low F.  These leaps are decorated with grace notes, creating arpeggios.  These maintain the harmony on F, but also shift between major and minor, following the piano.  The climax is sustained until both instruments reach an arrival point.
8:25 [m. 126]--The arrival point is a huge statement of Theme 2 in F minor, which wins out over major.  The piano, fully harmonized, leads the initial canon in both hands, and the cello follows in its low register.  The piano continues with the passionate melody and moves to the expected cadence on the “dominant” (C major), with the cello adding wide upbeat figures, including an emphatic triple stop at the end of the phrase.
8:42 [m. 134]--Suddenly quiet, a harmonically adventurous version of Theme 2 begins, again with the piano leading.  The piano seems to return to F, major this time, while the cello line appears to outline C minor.  The canon is now merely rhythmic, as the notes and intervals are different in piano and cello.  The piano reaches a descent in double thirds in both hands while the cello has an isolated plucked note.  This appears to move to G minor.  The “non-canon” version of Theme 2 begins again, with both instruments appearing to linger on the “dominant” harmony in C major (the expectant “seventh” chord, now on G).
8:57 [m. 141]--Re-transition.  A cadence is averted, and the piano right hand begins a series of descending arpeggios in triplet rhythm on colorful and mysterious “diminished seventh” harmonies.  The right hand plays bass notes leaping up to “diminished
chords, but the combination of these chords with the bass notes results in more stable “dominant seventh” chords.  These move down the circle of fifths, from E to A to D.  Meanwhile, the cello plays descending lines.  The fourth bar is a repetition of the third one, except that the piano left hand joins the cello line instead of playing the bass note leaping to the chord.
9:06 [m. 145]--The piano bass establishes a low “pedal point” on B, the “dominant” note that prepares for the return of E minor, the home key.  It holds a low B then leaps up an octave on the upbeat.  The right hand plays a wide arpeggio, still in triplet rhythm and still on a “diminished seventh,” and stays on this harmony.  The cello fills in between the piano bass motion by playing its own plucked descending octave on the second and third beats of the bar.  After three bars, the right hand arpeggio begins an arching motion in the treble and the cello drops its plucked octaves.
9:14 [m. 149]--The cello plays a mysterious minor-key version of the closing lullaby theme.  The piano continues its pattern with the pedal point and the arpeggios, but the arpeggios change harmony with the melody.  The lullaby tune appears to begin in B minor before changing to E minor, but it avoids a cadence.  After the first phrase, the piano right hand takes over the melody in octaves.  The triplet rhythm moves to the left hand, but the arpeggios now tumble down the keyboard.  The low “dominant” pedal  is maintained on  the downbeats.  The cello adds slower lines beginning off the beat.  The melody still avoids a cadence.
9:33 [m. 157]--The melody stalls on the fourth bar.  The left hand arpeggios slow down to a straight rhythm, and the right hand is reduced to descents in thirds.  The slower piano arpeggio turns around and ascends up the keyboard.  The cello line descends against it, leading into the return of Theme 1 in E minor.
9:48 [m. 162]--Theme 1, Part 1.  The cello melody is as it was at the beginning and at 3:32, but the piano right hand adds melancholy descending arpeggios beginning after the downbeat.  The left hand retains a vestige of the former block chords.
10:09 [m. 170]--Theme 1, Part 2.  The cello melody continues as at 0:25 and 3:55 [m. 9].  The intensity builds as before.  The piano right hand continues with the decorative descending arpeggios.  These become shorter when the cello reaches its highest note.  In the winding cello descent that follows, the piano adds a longer descending arpeggio, extending into the first measure where the cello had previously been exposed.  The left hand plays the dissonant “diminished seventh” chord that had been rolled here before.
10:36 [m. 182]--Theme 1, Part 3.  Here neither instrument has changes from 0:53 and 4:22 [m. 21].
11:00 [m. 194]--Transition.  A very subtle change brings the transition where it needs to go in order for the recapitulation to end in the home key instead of in B.  Against the held cadence chord in the piano, the cello moves down to C instead of up to G.  The piano motion following this is higher than the cadence chord rather than lower, but it otherwise follows the pattern.  These changes cause the key to pivot to F major (and minor) instead of C.  From that point, the transition follows corresponding to 1:18 and 4:47 [m. 33].  Because it is higher, the right hand takes some of the harmonic notes along with its rippling triplets.  The cello octaves, however, are actually able to be set lower because the low notes are in the instrument’s range.
11:21 [m. 203]--Pedal point on F and buildup with stepwise arching pattern in cello, analogous to 1:38 and 5:08 [m. 42].
11:37 [m. 211]--Analogous to 1:54 and 5:25 [m. 50].  The pedal point is now on B (the “dominant” note in E minor or major), and the arpeggios lead to the second theme, now in the home key of E minor.  The first rising cello arpeggio on B is set an octave lower than in the exposition, but then moves back up.
11:53 [m. 219]--Theme 2.  Now in E minor, analogous to 2:09 and 5:39 [m. 58].  Canon and passionate melody, with the cello noticeably higher than in the exposition.
12:10 [m. 227]--Analogous to 2:26 and 5:56 [m. 66].  The piano right hand and the cello essentially reverse roles through this passage with the murmuring bass motion.  At the outset, the cello includes double stops to approximate the piano harmonies.  At the point where the piano began to play in octaves in the corresponding exposition passage, the instrument is also set in octaves here on the material that had been played by the cello.  At the cadence motion and brief canon, the cello and piano right hand return to their original material.
12:45 [m. 240]--Closing material in E major.  The key signature changes to the four sharps of E major, and the major key remains in effect until the end of the movement.  Lullaby-like melody in piano right hand with bass fifth canon in piano bass and cello, analogous to 3:00 and 6:29 [m. 79].  The bass in both instruments is set lower, and the piano bass adds resonant octaves.
12:55 [m. 244]--Cello statement of lullaby melody in E major, analogous to 3:10 and 6:39 [m. 83].  The cello makes an octave shift upward halfway through the statement, and the piano bass abandons the low E octave.  It settles on broken octaves on B, the “dominant” note.
13:09 [m. 249]--The transition from 3:24 and 6:53 [m. 88] is transformed into a closing phrase for the melody that reaches a full cadence on E.  This corresponds to the beginning of the coda.  In this closing phrase, the cello continues, moving back to its middle register and settling down with great warmth into the cadence and the following coda.
13:19 [m. 253]--At the cadence, the cello takes over the low rocking motion on a fifth.  The piano, in full  harmony, plays the opening of the main theme in a major-key version colored by chromatic notes, including some from the original minor-key version.  It is played first in the high register, then an octave lower, dolce.  Following this, the rocking motion, now on octaves, moves to the piano bass.  These broken octaves work upward chromatically, supported by chromatic harmonies played by the right hand in the tenor range.  The cello, meanwhile, echoes the thematic fragment in long notes that expand to a larger descent over the piano motion.  This is rounded off by a yearning upward leap and a faster descent to a cadence.
13:43 [m. 262]--In a parallel passage, the rocking motion now moves to the piano right hand, harmonized in thirds.  It is very chromatic, and it leaps by octave or sixth.  The left hand, in octaves, plays the same opening gesture from Theme 1, with the second statement an octave higher rather than lower.  The cello, having paused for this, now enters.  The piano bass takes over the descent in long notes that the cello had played.  The rocking thirds in the piano right hand begin to descend with the bass, and the cello line consists of slurred half-steps.  The original scoring returns at the end, with the yearning leap in the cello.
14:06 [m. 271]--The yearning leap with descent leads into an extension based on that gesture.  A wide leap up a tenth in the cello turns around to make a very long descent, all over rocking octaves in the bass and a steady descent, also in octaves, in the right hand.  The right hand harmonizes the cello in thirds.  Finally, after a small swell, Brahms settles back into the last two bars of the warm cadence that preceded the coda.
14:29 [m. 279]--The final cadence arrives on a very subdued pianissimo.  The cello plays the third of the chord, G-sharp.  The piano right hand, in the tenor range, completes the chord with the open fifth E—G.  The left hand continues the rocking octaves, which now move down to the low E.  The measure is repeated twice for a total of three statements.  On the third and last of these, the piano bass holds the octave.
14:50--END OF MOVEMENT [281 mm.]

nd Movement: Allegretto quasi Menuetto (Minuet [Scherzo] and Trio).  A MINOR, 3/4 time.
0:00 [m. 1]--Part 1.  The piano leads into the minuet with a rhetorical introduction in triple octaves beginning on an upbeat descent.  The cello enters on the next upbeat to play the actual minuet melody.  It is characterized by a long-short-short-short rhythm, lilting upward leaps, an arching shape, and a melancholy mood.  It becomes harmonically unstable as it works up and back down.  The piano accompaniment, which is largely doubled in octaves between the hands, with both in the high treble, uses the rhythm of its  introductory figure for its characteristic falling short notes and repeated  (or descending) longer notes.
0:13 [m. 9]--The cello melody suddenly arrives on a shape like the brief piano introduction figure.  The piano itself changes to block chords arriving on preparatory “dominant” harmony.  The cello repeats the introduction figure, then leaps down an octave to twice emphasize the “dominant” arrival.  The harmonic motion here has a “Phrygian” modal character, with half-steps moving down to the dominant note E.  The length of the whole melody is irregular unless the introductory measure is counted, resulting in 14 bars.
0:22 [m. 15]--Part 1, varied repeat.  The instruments reverse roles.  The cello, reasserting the A-minor key, plays the rhetorical introduction.  The piano now plays the minuet melody, adding bass support in octaves or fifths on the downbeats and upbeats, as well as harmonies from the previous accompaniment.  The cello, meanwhile, plays the falling lines, now extended to four short notes landing on a longer upbeat.  After five measures, the familiar pattern of two short notes followed by two longer notes briefly returns for two.  At the same time, the piano bass octaves stop resting on the middle beat.
0:35 [m. 23]--The return of the introduction figure with Phrygian motion to the “dominant” remains in the piano.  The cello here simply contributes to the supporting harmonies along with the piano bass, which is now in active single notes.  The piano right hand does not leap down an octave while reiterating the arrival.
0:44 [m. 29]--Part 2.  The piano begins the introduction figure again in triple octaves, but changes the note C to C-sharp, creating a brief turn to A major.  When the cello enters, it repeatedly plays the opening of the minuet melody over the expected falling short notes and repeated long ones in the piano, which is again mostly doubled in octaves.  The figure moves harmonically and melodically in a sequence before an arrival on C minor.  There, the cello reaches up in a short arpeggio, then a longer one while the piano continues its falling patterns.
0:58 [m. 38]--With the establishment of C minor as a temporary key center, the piano begins a graceful (grazioso) decorative melody with close harmonies over wide arpeggios.  The cello adds a descending chromatic line leading to its own imitation of the decorative piano melody.  At that point, the piano reverses roles and imitates the cello’s descending chromatic line.  With each instrument imitating the other, the counterpoint becomes complex and C minor begins to mix with C major.
1:10 [m. 46]--The piano begins to build with the melody, now beginning in C major, and the cello abandons the imitation, turning instead to the introduction figure.  The left hand continues to anchor the harmony with wide arpeggios.  The harmony becomes active, turning away from C.  Two harmonies, G minor and a “dominant” chord on E (preparatory to the return of the home key center, A) begin to fight for predominance.  The cello, meanwhile, plays rising octaves.  The piano melody now becomes more urgent, with the “dominant” harmony struggling to overcome G minor and the cello, in its low range, helping with that effort.  It finally breaks through on a trill-like motion in piano octaves.
1:28 [m. 59]--The “rounding” typical of the minuet or scherzo form arrives with the return of Part 1 in A minor.  The trill-like motion melts into the downbeat of the introductory gesture, and the cello begins the original minuet melody.  The falling figures in the piano are more embellished, with the left hand continuing the right hand descent and the notes adding harmonies in thirds and fourths.  At the melody’s sixth and seventh bars (seventh and eighth counting the introduction), the cello line is changed to allow it to arrive at home on A instead of on the “dominant.”  A mild surge in volume underscores the alteration.
1:39 [m. 67]--The cello, as expected, turns to the introductory gesture and states it twice, landing on A.  The piano accompaniment is changed, as the right hand plays chords after the beats and is led by the left hand.  Then, in a cross rhythm, the cello further fragments the introductory melody, extracting a two-beat unit and using it in a downward sequence.  Three statements create three implied 2/4 measures against two notated 3/4 measures.  The off-beat right hand piano chords are highly chromatic and descend by half-step against a rising, detached line in the bass on the beats.  The following downbeat restores order.
1:49 [m. 74]--The piano has a last statement of the original introductory figure, now played with rolled chords in the left hand and with plucked chords in the cello.  To close the minuet portion, a final cadence is added two octaves lower in the piano with a faster repetition of the plucked cello chords.
TRIO (F-sharp minor)
1:55 [m. 77]--The trio section is set in F-sharp minor, the “relative” minor key of A major, an oblique relation to the minuet’s A minor.  Starting on the upbeat, the last beat of m. 76, the piano has a very brief prelude introducing its figuration that will prevail throughout the trio section.  The smooth melodic line will be decorated with a lower note after the first half of each beat.  The melodic notes on the second half of the beat do not have the decoration.  This lower note usually stays static for at least a full measure.  Here in the prelude, there are only two halting figures.  They are very clearly identifiable with the first four notes of the minuet’s introductory gesture.
1:59 [m. 79]--Part 1.  The introductory figure is used to begin the flowing melodic line.  The cello doubles the piano’s top line, and the lower-note decorations continue as introduced in the “prelude.”  The left hand has wide rising arpeggios following the rhythm of the melody.  After two melodic “waves,” each of two measures, there is a cross-rhythm with three groups of four melodic notes played over two measures, creating three implied 2/4 measures.  The left hand arpeggios confirm this.  The music also builds at this point, and it turns to the major key.  After this, the rhythmic order is restored over three measures that settle down.  These lead smoothly back into minor and to a restatement of the halting “prelude,” with the left hand completing its arpeggio on the first gesture and the cello continuing to double the top right hand line.
2:19 [m. 79]--Part 1 repeated.
2:39 [m. 90]--Part 2.  The first section of Part 2 has a similar structure to Part 1, except that it shifts at the outset to A major, the “relative” key to F-sharp minor, instead of to the home major key.  The cross-rhythm is present in the expected place.  The passage remains in A major until the final “settling” measures, where it moves back to F-sharp minor.  The “prelude” figures at the end are changed.  The first one has a higher upbeat approach, and the second one leaps to a lower downbeat after the higher upbeat, creating a larger arc.  On this second prelude figure, the cello stops doubling and begins a wide rising arpeggio.
2:58 [m. 101]--The right hand piano figures now no longer double the cello.  At this point, after the upbeat, there is another cross-rhythm with groups of four melodic notes (confirmed by the left hand piano arpeggios).  The right hand figures become fragmented, placing a rest on the weak “beat” of the cross-rhythm.  As before, there are three implied 2/4 measures.  The tension builds across this passage, and then the cello restores order with a triplet figure and a cadence.  The piano figures now create a counterpoint in contrary motion to the cello melody.  After the cadence, the cello moves back up, leading into a repetition.
3:06 [m. 105]--The passage with the cross-rhythm, triplet figure and cadence is repeated.  The cello and piano left hand are the same, but the piano right hand has major changes.  Its motion is continuous, without the cross-rhythm rests, and for the only time, it leaps up rather than down to its off-beat decorations.  Throughout the trio section, it had previously jumped down to these.  This heightens the tension.
3:13 [m. 90 (last beat of m. 108a)]--Part 2 repeated.  First section largely in A major, as at 2:39.
3:32 [m. 101]--Cross-rhythm, triplet figure and cadence, as at 2:58.
3:40 [m. 105]--Repetition with changed piano right hand, as at 3:06.
3:46 [m. 108b]--Transition to minuet reprise.  In the second ending, the piano continues after the cadence, introducing a rippling triplet rhythm that replaces the off-beat decorations with a smoother undulation.  The left hand continues its wide arpeggios in straight rhythm.  The cello repeats the triplet rhythm, stretching out the cadence.  After the second sequence of the triplet rhythm, a mild syncopation leads to a full cadence on a low F-sharp.  After being held for some time, this note descends by half-step to E, the preparatory “dominant” for the minuet’s A-minor key.  A rising piano arpeggio leads into two slower anticipations of the first two notes from the minuet’s distinctive introductory figure.  These seamlessly lead into the reprise.
4:04 [m. 1 (last beat of m. 115)]--Part 1.  Opening melody with piano introduction beginning on the upbeat, as at the beginning.
4:17 [m. 9]--Motion to “dominant” with introductory figure and “Phrygian” character, as at 0:13.
4:26 [m. 15]--Part 1, varied repeat.  Piano statement of opening melody, as at 0:22.
4:39 [m. 23]--Return of introduction figure and motion to “dominant,” still in the piano, as at 0:35.
4:48 [m. 29]--Part 2.  Motion to A major and C minor, as at 0:44.
5:02 [m. 38]--Grazioso melody in C minor, as at 0:58.
5:14 [m. 46]--Buildup, then competition between G minor and “dominant” of A minor, as at 1:10.
5:32 [m. 59]--Return of Part 1 with more active piano remaining in the home key, as at 1:28.
5:43 [m. 67]--Return of introductory figure in A minor, then cross-rhythm, as at 1:39.
5:54 [m. 74]--Last statement of introductory figure with rolled and plucked chords, then final cadence, as at 1:49.
6:02--END OF MOVEMENT [115 (+76) mm.]

rd Movement: Allegro (Combination of Fugue with Sonata form).  E MINOR, 4/4 time.
Fugue Exposition (Theme 1, Part 1)
0:00 [m. 1]--The first of the three “voices” to present the fugue “subject” is the piano left hand.  The “subject” begins with a call to attention in the form of a descending octave.  The right hand supports this, and this descending octave is actually spread over four octaves of the piano since both hands play it in octaves.  After this, the left hand takes over with the subject, which is mostly in triplet rhythm, to the extent that the meter of much of the movement seems to be 12/8 rather than 4/4.  The theme contains upward runs, downward leaps, and syncopated notes.  It is four bars long and ends with an arching run.
0:08 [m. 5]--The cello is the next “voice” to play the subject, which it does in the expected “dominant” key of B major (the typical placement of the second entry).  At the same time, the piano left hand continues by introducing the first “countersubject,” a jagged figure in “straight” 4/4 rhythm.  It has a descending shape, is played with detached notes, and begins on an off-beat.  The jagged figure is played twice, then used to introduce a more continuous jagged motion, now moving upward.  The conflict between straight and triplet rhythms helps to differentiate the subject from the countersubject.
0:16 [m. 9]--Shifting back to the home key, the final fugue “voice” enters, the right hand of the piano.  It plays the subject, playing the opening downward leap with octave doubling, then continues as had the left hand.  The cello now plays the first countersubject with the jagged figures, with some minor alterations, and the piano left hand introduces a second countersubject.  It has distinctive rising leaps up to trills, then more octave jumps.
Continuation of Fugue (Theme 1, Part 2)
0:24 [m. 13]--In a brief “episode,” elements of the subject and countersubject are passed between the voices.  The running triplets from the subject begin in the left hand, then move to the right hand and the cello in harmony, and finally are left to the right hand alone.  The leaping octaves from the countersubject material are heard first in the right hand and cello, then in the left hand alone, and finally in both the left hand and cello.  The key touches on the “dominant” B major again before moving back home.
0:29 [m. 16]--In another full statement of the subject and both countersubjects, the piano left hand has the subject again, in the home key as before.  But it is played an octave lower than the first statement.  The first countersubject, with the jagged lines, is in the right hand and played in octaves, and the second countersubject, with the leaps up to trills, is played by the cello.
0:37 [m. 20]--In another transitional “episode,” the subject is absent, but both countersubjects are present.  The right hand plays the second one, with the leaps and trills, in octaves.  The left hand plays a line in rhythm with this, but in contrary motion.  The cello has the first countersubject, with the jagged lines.  It begins in the “dominant” key, B major, then shifts up to C-sharp major.  Then it stalls with syncopated trills in the piano against continuous jagged figures in the cello, eventually reaching “dominant” harmony again.  But the cello plays a huge descending octave on the note C-natural, disrupting the fortissimo arrival point.
0:48 [m. 26]--Both instruments are held over as the measure begins.  The piano plays doubled thirds in both hands, an octave apart.  These thirds are in triplet rhythm and based on the fugue subject.  The cello plays descending octaves on C and B-flat.  The key is a sort of mixture of E minor and the “dominant” harmony of F major, implied by the cello notes and B-flats in the piano runs.  The piano, still in octaves between the hands, breaks away from the  thirds and becomes more excited, finally introducing F-natural and a brief suggestion of the F-major key.  The active cello octaves narrow to fifths, and these, along with the ever more excited and syncopated piano, now moving in contrary motion again, quickly move back to E minor.
0:58 [m. 31]--The cello uses a huge arrival on E minor to begin the subject again, but it is varied after two bars, introducing large downward leaps and remaining in the home key.  The piano, again playing in octaves between the hands, introduces the inversion of the subject, with downward moving triplets.  To this, harmonies are added, and both instruments arrive at one last large, emphatic E-minor cadence.
Transition from Fugue to Second Subject Group
1:06 [m. 35]--At this point, the fugue and the counterpoint begin to dissipate.  The cello and piano appear to reverse roles from the previous passage, with the cello playing the downward inversion and the piano playing the varied subject with the hands two octaves apart.  After two bars, however, both instruments seem to stall in their motion and the volume abruptly drops to piano for the first time in the movement. The cello plays longer descending notes against the continuing upward triplets in the piano.  The volume quickly increases again over this measure.
1:14 [m. 39]--The cello now plays very wide leaps down and up in long half notes.  The piano triplets continue, introducing chromatic notes and then arpeggios that alternate with the prevalent stepwise motion.  The piano bass arrives on the note C, changing to broken octaves in a straight rhythm while the right hand continues in triplets under a broad descending cello line.  The right hand triplets, along with the bass C (the important “seventh” of the chord), form the “dominant” harmony in G major, where the second subject material will be set.  G major is the “relative” major key to the home key of E minor.  The volume again rapidly diminishes here.
1:24 [m. 44]--As the piano bass continues in broken octaves on C, the right hand and the cello elaborate on the descending inversion of the fugue subject, with the cello leading the right hand in a very close imitation.  It is actually a canon at the distance of a ninth (expanded second).  In the context of a fugue, this close imitation is called stretto.  After a couple of bars, the piano right hand and the cello exchange roles, and the cello follows, but the distance of imitation remains a ninth.  The piano bass octaves in straight rhythm continue, moving narrowly away from C with the implied harmony of the canon.  The volume builds again before the imitation breaks and the right hand emerges into a trill.  Both the cello and right hand then slow down and become quiet, leading into the second subject group.  The piano bass octaves have reached D, the “dominant” note in G major.
Second Subject Group--G major
1:43 [m. 53]--Both instruments are marked tranquillo.  The cello starts with wide, undulating triplet arpeggios.  The piano left hand plays fragments derived from the first countersubject, indicating that the fugue elements are not entirely absent.  When the right hand enters, it is also with triplet arpeggios, the highest notes forming a hidden melodic line.  After two bars, the cello breaks into a passionate descending melody in straight rhythm, the piano right hand works downward, still in triplets, and the left hand moves down to low broken octaves in straight rhythm.  The cello melody twice stalls on the second beat of a repeated measure that makes a brief turn to B minor.  When it resumes its descent, the right hand harmonizes it with another line embedded within the triplets.
1:57 [m. 59]--The cello resumes a more static oscillating motion in triplets.  The countersubject fragments are played by the piano in B minor, first in the right hand in octaves, with the left hand following in an inversion of the fragments.  Jerking back to G major, the cello then plays a jaunty version of the formerly passionate descending melody, using a clipped long-short rhythm.  Under this, the piano has left hand octaves followed by off-beat right hand chords.  The jaunty long-short rhythm then passes to the piano right hand, which includes rolled chords, and the cello plays the original longer lines.
2:10 [m. 65]--The melody, now carried by the piano with cello harmonies, again stalls on the second beat of the measure and appears to move to B minor.  But the material is now greatly extended, and the B-minor motion is averted by notes re-establishing G major.  After the fourth measure, a stronger syncopation crossing the bar line is added.  Then the melody obtains a new closing phrase.  The piano carries the first statement as the cello continues to harmonize, then the cello takes the lead.  The phrase is extended and broken up, and the piano adds close chromatic harmonies in its motion.  Another passage of light syncopation leads into the final cadence on G major, which coincides with the arrival of the development.
2:37 [m. 76]--Starting in G, where the exposition ended, the movement returns to material from the fugue.  The mood is quiet but agitated.  The cello and piano right hand play the ascending triplets from the subject, with the cello leading and the right hand following.  In the piano bass are reiterations of the descending octave that opened the subject.  The harmony is unstable, and as the cello moves to longer notes, it moves down a step, to F-sharp major.  There, the two hands of the piano play in imitation on the ascending triplets with the left hand leading.  The cello now has the descending octave.  The harmony remains unstable.
2:50 [m. 83]--The hands of the piano come together, playing two octaves plus a third apart, continuing with the ascending triplet patterns.  The cello continues to play octave leaps, but now they ascend.  The volume, which has been steadily building, reaches a forte level as the harmony and the key make a strong motion to C minor.  The right hand leaps down so that the hands are an octave apart.  The cello plays strong, detached rising thirds in straight rhythm, always playing the first and third notes of the piano triplets heard against it.  Both instruments work up, then back down, moving to a powerful arrival point.
3:04 [m. 91]--The cello briefly drops out, and the two hands of the piano play another canon at the ninth (or stretto), inverting the direction of the triplets from the fugue subject.  It begins in C minor.  The left hand leads the right, and the octave leaps, now ascending, are reinforced with doubling in both hands.  In the third measure, the right hand compresses the imitation so that it comes at a closer distance.  As the canon breaks, there is another arrival in another key, this time D major.
3:11 [m. 95]--In the new key of D major, the volume suddenly becomes muted.  New material is now used, and it comes from the second countersubject, with the rising leaps.  The cello leads the piano, the hands of which are doubled an octave apart, both playing in harmonies of thirds and sixths.  The cello attempts to continue with this new material, but the piano, still in octave doubling, reintroduces the triplet rhythm, passing arching figures between the two voices of each hand.  The key makes another shift, this time to B minor/major, the “dominant” of the home key, E minor.
3:20 [m. 99]--The two hands of the piano begin another stretto canon at the ninth similar to the one at 3:04 [m. 91], but it quickly breaks after two measures.  The cello then enters with the inverted triplets from the fugue subject.  The hands of the piano come together, two octaves plus a third apart, following the cello, which leads in yet another stretto.  At this point, the key has briefly moved back home to E minor, but after four more measures, it is diverted away again.  The mood is now very agitated.
3:30 [m. 105]--Beginning in C-sharp/D-flat major (it is notated differently in the cello and piano), the cello again leads the piano in the material from the second countersubject, similar to the passage at 3:11 [m. 95].  The music is again subdued.  The hands of the piano are again doubled an octave apart, and again play in thirds and sixths.  The harmony is very unstable, moving down from C-sharp to C and then to B, which is again tentatively established as a preparatory “dominant.”  The cello continues to lead the piano until both instruments stall and reach an intense climax with repeated leaps and syncopation, still over unstable harmony.  The piano right hand, richly harmonized, moves together with the cello ahead of the left, which plays octave leaps.
3:53 [m. 115]--Re-transition.  The piano bass reaches B, which now clearly seems to function as a preparatory “dominant.”  It plays repeated broken octaves on that note.  The right hand and the cello, with the former leading, continue to play the inverted downward triplets from the fugue subject in stretto.  The key has actually reached E minor, with the bass B preparing for a cadence there.  After four measures, the broken octaves on B unexpectedly move to the right hand in a very high register, and the left hand plays the descending triplets in the tenor range, leading the cello, while continuing to reiterate a pedal point B in the bass.  After two measures, and quite unexpectedly, notes from the key of B major are introduced, and the harmony actually shifts there.  The preparatory “dominant” has artfully become the home key.
Second Subject Group--B major
4:08 [m. 123]--Things are “inverted” at the beginning of the recapitulation.  Instead of beginning in the home key, it begins in the “dominant” key.  It also begins with the second subject, appearing in the dominant instead of the “relative” major key.  The second subject group is greatly abbreviated.  The opening figures from the first countersubject are omitted, and the cello begins with the passionate descending melody, now more subdued.  The piano accompanies with a pattern of off-beat chords in the right hand following a rising line in the left, marked dolce.  After two measures, the right hand takes over the melody, but contrasts with the cello by using the “jaunty” long-short rhythm and lightly rolled chords.  The cello plays a soaring line in harmony with the piano melody, continuing in smooth long notes.
4:16 [m. 127]--The melody “stalls” as expected and follows the pattern heard at 2:10 [m. 65], but it is cut off after five measures, and the closing phrase is omitted.  The cello line is slightly embellished from the former passage.
Reprise of Fugue Exposition (Theme 1, Part 1)
4:28 [m. 132]--Brahms’s art in using the second subject in B major to lead into the reprise of the fugue is now made apparent.  The first statement of the subject is omitted, and the reprise begins with the second entry, which was in fact on B major.  This makes the transition out of the second subject smooth.  The pattern from 0:08 [m. 5] is followed, but the instruments are reversed.  The piano left hand plays the subject while the cello plays the first countersubject.  Brahms indicates a slightly softer volume than the beginning.
4:36 [m. 136]--With this entry, the instruments are returned to their original orientation, and it is an exact reprise of 0:16 [m. 9], with the subject in the piano right hand, the first countersubject in the cello, and the second countersubject in the piano left hand.
Continuation of Fugue (Theme 1, Part 2)
4:44 [m. 140]--Exact restatement of episode from 0:24 [m. 13].
4:49 [m. 143]--Statement of subject and both countersubjects, as at 0:29 [m. 16].  The full forte has now been reached.
4:57 [m. 147]--Transitional episode, as at 0:37 [m. 20].
5:09 [m. 153]--Passage in double thirds based on fugue subject, as at 0:48 [m. 26].
5:19 [m. 158]--Climactic arrival point and introduction of fugue subject inversion, as at 0:58 [m. 31].
Transition to Coda
5:26 [m. 162]--This first passage of the transition is identical to that at 1:06 [m. 35], with the instrumental role reversal from the previous passage.
5:34 [m. 166]--The first two measures here are the same as at 1:14 [m. 39].  In the third measure, while the huge upward cello leap is on the same notes, the piano notes are very subtly changed.  Many notes are shifted up a half-step, and the bass prematurely moves to straight-rhythm broken octaves.  The fourth measure, while still similar, makes a more drastic shift in its second half.  The cello and piano right hand leap a third higher, and the bass descends a third lower, to A-sharp.  In the fifth measure, the cello has the broad descending line as expected, and the piano bass has moved again to the straight broken octaves, but the cello line is higher and the harmony of the piano arpeggios and bass forms an unstable “diminished seventh” chord.
5:45 [m. 171]--At this point in the previous transition, the inversion of the fugue subject and the canon at the ninth had been introduced.  These were used heavily in the development section, and are avoided here.  Instead, the music continues in the same vein, with triplet arpeggios in the piano right hand and broken octaves in the left.  The cello is reduced to isolated rising leaps.  The piano bass moves up from A-sharp to B, which again functions as the “dominant” in the home key.  The subtle alterations have allowed the music to remain in E minor instead of changing to G major.  The passage now functions as a dissipation, settling down in both speed and volume in preparation for the faster coda, remaining on the preparatory harmony.
CODA--Più Presto
5:55 [m. 175]--The volume is quiet, but the faster speed creates a suddenly agitated mood.  The cello plays the ascending triplets of the fugue subject while the piano introduces clipped cadence-style chords, with shorter ones moving to longer ones.  After two measures, the ascending triplets move to the piano bass, the cello changes to wailing descents, and the piano right hand supports these with its chords.  More chromatic notes and harmonies are introduced, including borrowings from the major key.
6:01 [m. 179]--With a cadence, the triplets move again, now to the piano right hand.  The cello has brief descents while the piano bass has the short-long cadence figures, now in octaves.  After two measures, the volume rapidly builds.  The cello line becomes passionate, arching up and down.  The triplets move again to the piano bass, and the right hand harmonies support the cello.  After two more measures, the piano bass changes to broken octaves, but remains in the triplet rhythm, leaping down and back up.  The harmonies in the right hand follow behind the arching cello line.  The excitement rapidly builds.
6:11 [m. 185]--The cello stalls on longer notes, again making wide leaps.  The triplet octaves in the left hand leap up, then move back down.  The right hand harmonies surge upward.  As the right hand moves to a very high register, the chords become syncopated.  In contrast, the left hand triplet octaves are now very low.  They are on the unstable “leading tone,” D-sharp.  The increased tension begs for release.
6:18 [m. 189]--The huge arrival on the E-minor harmony begins the rush to the finish.  The piano right hand, still very high, moves back to the ascending triplets, supporting their first notes with a lower harmony of a sixth.  The cello has rising, detached thirds in straight rhythm that shadow the piano triplets, a similar motion to that heard before 3:04 [m. 91].  The piano bass remains on low broken octaves, but changes to rising octaves in straight rhythm.  The right hand and cello feverishly work down while the bass steadily rises.
6:24 [m. 193]--The triplets shift to the cello, and the piano comes together on the cadence-rhythm chords, the left hand leaping up in octaves on the “dominant” note B.  After two measures, the triplets move back to the piano, now in both hands with a strong octave doubling, and the cello changes back to the detached thirds in straight rhythm.  Both instruments forcefully move downward, breaking only for the final cadence, where both instruments play full chords.  Unlike the first movement, the finale ends in a stark, unapologetic, and even tragic E minor, avoiding any hints of a final change to the major key.
6:43--END OF MOVEMENT [198 mm.]