The year 1853 witnessed a confluence of major musical events, including the publication of Liszt’s B-minor piano sonata.  Wagner was beginning to work in earnest on the music for the “Ring” cycle.  And it was the last year in which Robert Schumann was active as a critic and composer before his final mental breakdown.  Late in that year, the young Brahms famously arrived on the Schumanns’ doorstep with some of his music in hand, including what we now know as the first two piano sonatas.  A third sonata, in F minor, was not completed at the time, and was finished in Düsseldorf while he stayed with the Schumanns.  Brahms submitted it to Schumann for consideration shortly after the latter had written his momentous article “Neue Bahnen,” which proclaimed Brahms as the next great musical voice.  It would be the last fruit of this brief, but happy time.  Two months later, Schumann attempted suicide and was admitted to a mental hospital.  The sonata is a tremendous work in every sense, and Brahms’s largest single composition for solo piano.  While following some precedents of the first two sonatas and combining aspects of both, it is much larger in scope, with a broad, unusual five-movement design and, in the case of the second and final movements, codas of almost overwhelming weight.  The first movement is a tight, but intense sonata form that prominently includes the “fate” rhythm from Beethoven’s Fifth Symphony.  It ends in the major key.  The slow movement, unlike those of the first two sonatas, is in the ternary form that would later be favored by Brahms.  But the movement is incredibly diverse, using four tempo markings, five meters, and, most remarkably, ending in a different key center from the one in which it began.  The magnificent, almost self-contained coda, whose climax rivals anything in Beethoven, is responsible for much of this.  Brahms headed the movement with some lines of romantic love poetry that match the movement’s mood and progression precisely.  Indeed, the coda could be described as the consummation of the courtship that happens through the rest of the piece.  The demonic and virtuosic scherzo contains a hymn-like trio section, and has similarities to the corresponding movements of the first two sonatas.  The unexpectedly inserted fourth movement is an “intermezzo” titled “Rückblick,” or “backward glance.”  It transforms the romantic theme of the second movement into a funeral march, complete with drum roll effects in the Beethovenian “fate” rhythm.  The finale, in rondo form, is also expansive and diverse.  Its heroic central episode forms the basis for the wildly extended coda in the major key.  In addition to F, the key of D-flat plays a very prominent role in all five movements.  It is used for the second themes of the first two movements (and the second movement remarkably ends there), a blong with the trio section of the scherzo and the important central episode of the finale.  Its “relative” minor key is the center of the “Rückblick” movement.  The sonata has a strong claim as the greatest since Beethoven, its only close rivals being the last Schubert sonatas (particularly the final one in B-flat) and the Liszt B-minor.  And with that, Brahms was finished with the genre that launched his career.  It is of some interest that, other than the four symphonies, Brahms never published more than three of any multi-movement instrumental genre throughout his career (typically there are two or three examples of any such genre).  He considered revising the sonata several times (as he did the B-major piano trio, Op. 8), but thankfully never did.  Other than perhaps tightening the wild coda of the finale, improvements are rather difficult to imagine.

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1^st Movement: Allegro maestoso (Sonata-Allegro form).  F MINOR/MAJOR, 3/4 time with two 4/4 measures, one 5/4 measure, and one 6/4 measure.
EXPOSITION
0:00 [m. 1]--Theme 1.  The first gestures of the theme are thunderous calls to attention.  A low octave F leaps up to a descending harmonized figure in a dotted rhythm that is prominent throughout the movement: a long note  followed by two very short ones.  This leads to a loud chord on the third beat of the measure.  Two more of these sequences follow, with the initial bass octaves moving down by half-step.  The dotted figures and the following chords are also chromatic.  After the three sequences, two more low octaves, continuing downward by half-step, are broken by a single higher chord on the second beat.  Finally, a forceful cadence on the “dominant” note C, with both hands in the treble register, ends the initial statement.
0:16 [m. 7]--A mysterious episode in C minor breaks up the forceful presentation of the theme.  The right hand plays ominous chords in “straight” rhythm while the left hand plays open fifths and octaves, using a triplet rhythm that is similar to the short-short-short-long “fate” motive known from Beethoven’s Fifth Symphony.  The second, higher five-bar phrase of the episode turns briefly to G minor, but it slows to a quiet full cadence on C major.  The last chord has a fermata, indicating an indefinite pause.
0:42 [m. 17]--A loud, zigzagging upbeat figure in octaves, another element that is extremely prominent in the movement, abruptly and jarringly transitions from the C-minor reverie back to the commanding main theme in F minor.  Its outlines follow the first presentation, but now the left hand takes the original descending dotted rhythm by itself, and the chord on the third beat is replaced by a right hand figure, shooting up in very high octaves, that uses the same rhythm.  The same type of figure replaces the chord that separates the two bass octaves in the measure that follows the three sequences.  It also decorates the cadence on the “dominant,” which is now even more emphatic, with rolled chords and staggered hands.
0:56 [m. 23]--Transition.  The cadence on C leads smoothly to the “relative” major key (A-flat major).  There, the right hand plays a noble, march-like tune in rich chords.  Brahms marks it with the German expression “fest und bestimmt” (“firm and decisive”).  The left hand unexpectedly plays the long-short-short figures from Theme 1, without harmony, still on the second beat, and no longer in a dotted rhythm. The short notes are lengthened from 32^nd notes to sixteenth notes after a straight eighth note.  The figure leaps up to a higher note, becoming almost melodic.  The key very quickly turns to B-flat minor and the harmony includes dissonant “diminished” harmonies.  These smoothly lead back to F, but now F major, as confirmed by the last left hand figure, whose rhythms are doubled in length.
1:14 [m. 31]--A new, much quieter phrase of the same material begins in B-flat major, a key whose minor version was just heard.  The march theme is played by the right hand in the tenor range.  The long-short-short left hand figures derived from Theme 1 now alternate between the low bass and the high treble.  The left hand crosses over the right for the treble statements.  The leap up happens after the beat, and after the right hand changes harmony.  In the bass statements, this leap is a fifth, in the treble statements, an octave.  The chords that had closed the first phrase are manipulated to bring the harmony back through F minor to A-flat, where a highly expectant half-close is reached. This is repeated two octaves higher, even quieter and becoming slower.  The expectant arrival back at A-flat brings this transitional material full circle.
1:34 [m. 39]--Theme 2.  The delayed second theme is marked con espressione.  The right hand plays a gentle, but passionate melody, richly harmonized with moving internal voices.  The left hand plays very widely spaced arpeggios with added high-low alternations over “pedal points.”  After the first phrase in A-flat, a second follows in C-flat with added rolled chords.  The high-low alternations take over completely in the left hand.  The right hand shifts to full-measure chords, which steadily build, then become shorter and syncopated.  The left hand alternations are now extremely wide.  The chords approach an arrival point as the final key of the exposition is reached (D-flat major).
1:51 [m. 51]--The arrival and climax are very grand.  Rolled tenths and chords in the left hand incorporate a long-short rhythm underneath a tolling, joyous outburst in the right hand.  The key of D-flat is triumphantly confirmed, but a cadence is avoided.  The last figure of this climactic passage is repeated with an added triplet rhythm.
2:00 [m. 56]--Closing passage.  The music suddenly becomes quiet again.  The right hand returns to material from the beginning of the Theme 2 melody, adding more chromatic motion.  The left hand moves again to its very wide alternations, now over a long pedal point on A-flat.  The end of the six-bar phrase seems to approach a cadence as it accelerates, then slows, and the left hand narrows as its top line moves down.  The cadence is diverted by a full repetition of the entire phrase with both hands an octave lower.  After the repetition, the warm cadence in D-flat finally arrives and is reiterated three times.  Following this closure, the jagged, zigzagging upbeat figure in octaves heard at 0:42 [m. 17] returns with an equally jarring effect, wrenching the music back to F minor for the repeat.
EXPOSITION REPEATED
2:22 [m. 1]--First statement of Theme 1, as at the beginning.
2:36 [m. 7]--Episode in C minor, as at 0:16.
3:01 [m. 17]--Second statement of Theme 1 leading to cadence on the “dominant” harmony, as at 0:42.
3:15 [m. 23]--March-like transition in A-flat major, as at 0:56.
3:33 [m. 31]--Quieter transitional phrase with hand crossing and high repetition of last phrase, as at 1:14.
3:54 [m. 39]--Theme 2 moving from A-flat to D-flat, as at 1:34.
4:11 [m. 51]--Arrival and grand climax, as at 1:51.
4:20 [m. 56]--Closing passage with repetition an octave lower and cadence in D-flat, as at 2:00.  The second ending (m. 71b), removes the highest level from the zigzagging upbeat figure in octaves, a very slight change.  The figure leads into the development section, as it had led into the exposition repeat.
DEVELOPMENT
4:43 [m. 72]--The F of the zigzag figure is diverted to F-sharp.  Two inserted 4/4 measures follow.  In them, Brahms alternates the zigzag figure in octaves between the right and left hands.  In the first measure, it begins on A in both hands, and in the second, it starts on B-sharp (C-natural) and F-sharp.  The key is heading to C-sharp minor, a direct shift in mode from the D-flat major at the end of the exposition.  The octaves and the chords that accompany them are intense and almost wild.  After the two 4/4 measures, another zigzag pattern begins in right hand octaves.  It is extended, creating a great anticipation for an arrival on C-sharp that is intensified by the lengthening of this measure to an irregular 5/4.  The left hand in this measure leaps up from low bass notes to more passionate rolled chords.
4:52 [m. 75]--The prevailing 3/4 meter returns, and Theme 1 appears to begin in C-sharp minor.  The bass line makes a chromatic half-step descent in octaves.  After the first chord, minor reverts back to major, and after four of the long-short-short figures, the harmony lands on the “dominant” chord of C-sharp.  The left hand then quiets and begins the triplet “fate” rhythm as heard in the C-minor episode at 0:16 [m. 7].
5:00 [m. 79]--The episode from 0:16 [m. 7] is now heard in a C-sharp-minor variant.  The “fate” triplets are in right hand octaves, holding steadily to the note G-sharp.  The “straight” rhythm figures are now heard in both hands, in octaves in the left and single notes in the right.  The figures in the right hand follow those in the left after a long first note at the beginning of the measure that harmonizes both the left hand figures and the octaves.  After two measures, the figures in both hands come together in harmony.
5:11 [m. 84]--The “fate” octaves move up to D-sharp, and the variant of the episode just heard is played a fifth higher, in G-sharp minor.
5:21 [m. 88]--The key moves back to major, now again notated as D-flat.  The right hand begins a very quiet syncopated rhythm that will remain in force for some time.  At first, the note A-flat remains steady while a lower note is added and then moves to harmonies in seconds, thirds, and fourths.  The first of these is a dissonant adjacent half-step.  After three measures, beginning on an upbeat, a new and very soulful melody in D-flat major begins.  It is in the tenor range and played by the left hand, which also adds supporting bass notes that are often rolled up to the continuing melody.  The right hand continues with the syncopated pattern that had been established.  A prominent chromatic note (C-flat) colors the melody.
5:39 [m. 96]--A return to the dissonant half-step, or minor second harmony in the right hand syncopation coincides with the upward expansion and intensification of the tenor melody.  The melody soars up with a triplet rhythm, and then descends.  At the same time, the right hand syncopation expands to full chords.  Another upward triplet in the tenor melody, colored by more chromatic notes, also descends after a high note.  The right hand syncopation now leaps up into the very high register, still in full chords.  Becoming even warmer, the melody settles to a beautiful cadence in D-flat against the continuing high chords.
6:05 [m. 110]--The last notes of the warm D-flat cadence are repeated twice, inflected to minor.  The right hand chords become more chromatic, still in the same syncopated rhythm.  A third repetition seems to begin, but expands upward, and the right hand chords reach even higher.  A dramatic crescendo in a sustained tempo leads to a sudden outburst of the long-short-short rhythm in a passionate, cascading descent as the right hand syncopation finally breaks.  The key has moved to G-flat major, and after the descent, a descending triplet doubled in three octaves leads to a strong arrival in that key.
6:23 [m. 119]--A grand, triumphant statement of Theme 1 in G-flat major is expanded by full tolling chords.  In the left hand, these are rolled, enhancing the bell-like effect.  The meter is somewhat ambiguous here.  The placement of prominent chords and accents creates a subtle cross rhythm, so the four 3/4 measures can almost be heard as 6 measures in 2/4.
6:32 [m. 123]--Again, the music is suddenly hushed.  The syncopated pattern returns in the right hand, in high chords as it was before it broke.  The left hand plays with the long-short-short rhythm, this time cutting off the expected longer note or chord that follows.  The effect is somewhat disconcerting.  Four of these figures without the long note are heard.  The first three are in G-flat major.  The fourth makes a surprisingly smooth gesture toward F minor, a half-step lower.  Immediately confirming G-flat again, the pattern continues.  Four more figures are heard, this time with the long-short-short pattern leaping up a tenth to the expected longer note.  The fourth one, expanding the leap to an eleventh, makes the same disarmingly easy shift down to F minor, and this time it stays there, setting up the re-transition.
6:50 [m. 131]--Re-transition.  The opening is marked misterioso.  The “fate” triplets quietly return in high right hand chords while the left hand plays the pervasive long-short-short rhythm.  It is heard twice in each bar, leaping up an octave for the second statement.  The triplets are heard at the beginning of each measure, steadily moving upward.  In the fourth measure, a third long-short-short rhythm is added to the left hand and a crescendo begins.  The harmony also shifts to the “dominant” key, C major.  
7:00 [m. 135]--The triplets become constant beginning with the upbeat to the fifth measure of the re-transition.  Then both hands expand greatly in both texture and volume.  The long-short-short figures in the left hand make a grand arch, and the triplet chords in the right, now very high, are like tolling bells.  As the left hand arch concludes, the right hand chords leap down to a lower octave, emerging in a thick six-note texture with the top three notes doubling the bottom three an octave above.  The recapitulation is set up with a hanging and expectant, but very grand C-major chord in the preparatory “six-four” position.  Then the zigzag upbeat figure, in bass octaves, wrenches the music back to F minor.
RECAPITULATION
7:07 [m. 138]--Theme 1.  The first theme complex is greatly abbreviated.  The C-minor episode is cut, and this return, led into by the zigzagging upbeat octaves, resembles the second appearance in the exposition at 0:42 and 3:01 [m. 17].  The hands are reversed from that presentation, however.  The right hand takes the original long-short-short figures and the left follows them with the upward-shooting octaves.  The left hand makes things even more intense by adding a high rolled chord on the second beat of each measure.  The theme is expanded by one measure, the right hand again reaches high, and the emphatic cadence on the “dominant” is intensified beyond that in the exposition, tumbling down over left hand octave arpeggios.
7:22 [m. 145]--Transition.  Analogous to 0:56 and 3:15 [m. 23].  The march-like “fest und bestimmt” theme and the non-dotted long-short-short figure in the bass are heard in the home major key of F, which would be expected of a second theme.  But it follows the exposition exactly, being only transposed down a third.  Thus, it moves to G minor and then to D major, keys that have not yet been extensively used.
7:40 [m. 153]--Quieter transitional phrase, analogous to 1:14 and 3:33 [m. 31].  It begins in G major.  The low and high alternations of the long-short-short figures, the upward leaps, and the hand crossings follow as before.  The harmony moves through D minor to F major and the expected half-close.  The repetition two octaves higher follows as expected.
8:01 [m. 161]--Theme 2.  It proceeds as at 1:34 and 3:54 [m. 39].    The first phrase is in F major, the second in A-flat major (creating a connection to the use of that key in the exposition).  The building chords and widely-spaced left hand alternations lead to an arrival point on B-flat, analogous to the D-flat of the exposition.
8:18 [m. 173]--Grand arrival in B-flat major.  Analogous to 1:51 and 4:11 [m. 51].  A cadence in B-flat is avoided.
8:28 [m. 178]--Closing passage.  Material from the beginning of Theme 2 with chromatic motion.  Analogous to 4:20 and 2:00 [m. 56].  The left hand pedal point under the contracting alternations is on F, creating anticipation for a cadence on B-flat.  As in the exposition, the cadence is diverted by a repetition of the entire phrase an octave lower.  Unlike the exposition, where the cadence in D-flat arrived and was reiterated, the cadence in B-flat is completely avoided, never arriving.  It is instead broken off, led into a transition to the coda whose eventual goal is the home major key of F, where the movement will end.
8:43 [m. 190]--Transition to Coda.  The aborted cadence in B-flat is suppressed even more cruelly by a held note where it should come, creating mild syncopation.  The rocking pattern as the presumed cadence was approached then continues.  The bass pedal point gradually moves up to F-sharp, then to G, and the top notes of the alternations move up irregularly.  When G is reached in the bass, a huge crescendo begins.  The top notes of the left hand alternations expand upward as the rocking motion continues in the right hand.  The bass G implies C major, but C in turn serves as the preparatory “dominant” to F.  In the last two bars of the transition, solid chords in both hands point to a cadence on C, but C is immediately converted to the preparatory chord for an arrival on F.  The left hand pedal finally hits C and becomes an octave, leaping up to four-note chords.  This last measure slows down to add emphasis to the great arrival on F major.
CODA
8:56 [m. 200]--The definitive arrival on F major is indeed triumphant.  The four bars that follow are similar to the huge statement of Theme 1 material in G-flat from 6:23 [m. 119] in the development section.  The metric ambiguity is heightened even more by an addition of the long-short-short rhythm in powerful left hand octaves on the downbeat of each implied 2/4 measure.  Brahms tips his hat to this moment in the development by touching on G-flat halfway through the phrase.  Another arrival on F is expanded into an unexpected fifth bar with highly chromatic chords marked pesante.  This extra measure disrupts the meter even more.
9:07 [m. 205]--The disruptive fifth bar of the preceding phrase leads into a dissonant chord at the beginning of this measure, creating two more implied 2/4 measures that end on the downbeat.  Brahms marks the following passage “Più animato.”  Two loud chords, widely spaced, leap inward to quieter, clipped chords.  These chords are on the second beat of each measure, creating extreme syncopation and almost the sense of a restoration of 3/4 with the downbeat shifting to the second beat.  The pattern then intensifies.  The next chord, with a high right hand, acts as an upbeat to two more huge leaps inward that remain loud and forceful.  These also add new upbeats after them, creating the impression of two measures in a broad 3/2 rather than four in 3/4.  But the proper sense of the downbeat is restored as another cadence is approached.
9:20 [m. 214]--This cadence truly restores order.  Six full chords descend from on high in the right hand as six rising bass octaves oppose them in the left.  Brahms notates these as a 6/4 measure, presumably to add emphasis to the restoration of the metric pulse.  The right hand remains very high to the end.  The single 6/4 measure is followed by a third and final broad F-major cadence.  Low octaves in grace notes add emphasis and anticipation to the chords.  The final F-major chord, with the third (A) on top, is held two bars, then reiterated three times, the last also held two bars.  The rolled left hand moves lower in the reiterations, then adds a slower version of the “grace notes” in an upbeat arpeggio to the last two-bar chord.
9:53 (runoff after 9:43)--END OF MOVEMENT [222 mm.]

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2^nd Movement: Andante - Andante espressivo; Poco più lento; Andante molto; Adagio (Ternary form with extended coda).  A-FLAT MAJOR--D-FLAT MAJOR, 2/4, 4/16, 3/8, 3/4, and 4/4 time.
The movement is headed by the following poetic lines by Otto Inkermann under the pseudonym C.O. Sternau:

Der Abend dämmert, das Mondlicht scheint,
Da sind zwei Herzen in Liebe vereint
Und halten sich selig umfangen.

(The evening dims in twilight, the moonlight shines,
There are two hearts united in love
And they embrace each other in rapture.)

A Section--A-flat major, Andante espressivo, 2/4 time.
0:00 [m. 1]--Part 1 (a).  The theme is of exquisite beauty.  It begins with a descent in thirds, starting with an upbeat.  At the bottom, it turns around with an expressive trill.  The left hand accompaniment undulates, moving the bass line down with the melody.  The end of the first phrase is accompanied by a wide arpeggio under a half-close.  The second, complementary phrase is of the same shape, but makes a colorful turn to the “exotic” key of C-flat major.  The end of the phrase works easily back to A-flat major by way of A-flat minor, which is the “relative” key to C-flat.  The phrase ends in a similar way to the first one, but it is extended by two measures, with the arpeggios in the left hand leading to a cadence in A-flat.
0:29 [m. 1]--Part 1 (a) repeated.  The second ending (m. 10b) deviates at the end of the left hand arpeggio, which adds syncopation leading into Part 2 (b).
0:56 [m. 11]--Part 2 (b).  The top line is marked ben cantando, or songfully.  It begins with an upbeat followed by repeated notes in a dotted (long-short) rhythm which then descend.  Pulsing, detached chords accompany below the top line in both hands.  The chords and melody are mildly chromatic.  The top melodic line leaps up high before descending, and the first phrase turns to E-flat major without a cadence. 
1:07 [m. 15]--The second phrase, which has the same contour, begins with the left hand elegantly crossing the right with the upbeat and then continuing for a measure before the right hand takes over.  The left hand thus does not play the first pulses.  When the right hand takes over the melody, the left imitates the opening repeated notes in dotted rhythm below.  The leap up is now in a very high register and enhanced by rolled chords.  The phrase makes another motion on the circle of fifths and ends in B-flat, again with no cadence.
1:18 [m. 19]--The phrase is extended, including a new descent in triplet rhythm that is passed between the hands.  The closing gestures are reiterated.  The right hand, still very high, begins to circle around the closing figure as the pulsations stall on the note D-flat and the triplet descent is reiterated in the left hand.  The left hand uses the chromatic note F-flat (E) prominently.  The music slows down and becomes quieter, shifting back home to A-flat.  The pulses on the note D-flat help to re-establish that key, although it vacillates with its related key of F minor.  The extension ends on a half-close in A-flat.
1:34 [m. 25]--Part 3 (a’).  Both the melodic line and the undulating accompaniment are brought up an octave, and the right hand plays both, which requires dexterity.  The left hand holds a low octave pedal point E-flat under the first phrase and a C-flat under the second phrase.  It moves away from these long held octaves at the arrival back on A-flat, where it again takes over the arpeggios, which now reach much lower and are more widely spaced.  The right hand, meanwhile, much higher than the left, adds notes and rolled chords to the arrival on A-flat and the cadence.  The cadence itself is reiterated twice beyond what was heard in Part 1.  The third one is more final, and the music slows and quiets as the A section closes.
B Section--D-flat major, Poco più lento, 4/16 and 3/8 time.
2:08 [m. 37]--Part 1 (4/16 time).  The lovely upbeat figure repeats a steady note (A-flat) three times, adding a half-step, then a whole step (G-flat) below it to transition to D-flat major.  The choice of the highly unusual 4/16 time signature is probably to keep the sixteenth notes at roughly the same speed as in the A section while avoiding the faster tempo implied by 2/8.  Brahms marks the music “Äußerst leise und zart” (“Extremely quiet and tender”).  Over a throbbing pedal point D-flat, pairs of two-note harmonies alternate between the right and left hands, the hands moving in opposite directions.  After four measures, the left hand pauses.  After eight, it punctuates a cadence with a rolled chord.
2:24 [m. 45]--The next phrase is essentially a repetition of the first one, but the right hand adds a tolling A-flat above each pair of two-note harmonies.  The harmony is rolled up to this note.  After four bars, the upper “tolling” note moves to D-flat above the second harmony of each pair (rather than the first).  It then moves back to A-flat (and the downbeat) above the last chord.
2:39 [m. 53]--The next group of 15 bars is treated as a single unit.  The bass note is no longer a sustained pedal point, but the pattern of two-note harmonies in pairs alternating between the hands is maintained.  The first alternations of this phrase are exceedingly beautiful and evocative.  After four bars, a slow crescendo begins and the key shifts down a step to C-flat.  The bass notes become octaves and alternate between C-flat and F-flat.  After ten bars, forte is achieved and the harmony, through chromatic motion, moves back to D-flat.  The pattern is finally broken with a right-hand descent.  The last measure leading into Part 2 already establishes its new 3/8 meter.  It is a beautifully protracted approach to an arrival point.
3:04 [m. 68]--Part 2 (3/8 time).  The arrival point erupts into a heartfelt, ardent, and passionate melody in triple time.  The left hand is very active and moves in triplet rhythm.  It is a combination of octaves and trills on two notes, D-flat and E-flat.  The melody itself is richly harmonized, adding rolled chords and eventually its own triplet rhythm in the fifth measure.  The fifth, sixth, and seventh measures all repeat the same pattern beginning with that triplet rhythm.  The seventh measure slows and diminishes in volume, leading to an extended, gentle cadence as the left hand trills and octaves roll on to the reprise of Part 1.
3:27 [m. 77]--Part 3 (Part 1 partially repeated).  The 4/16 meter returns, and the second half of Part 1, the 15 bars from 2:39 [m. 53], is given a full reprise.   The crescendo and the forte are placed later (in the 11th and 14th measures, respectively), and Brahms indicates more freedom with the tempo than in the first playing, but the notes are the same. The first two phrases of part 1 do not return.
3:54 [m. 92]--Part 4 (Part 2 repeated and slightly varied).  The whole of Part 2 in 3/8 from 3:04 [m. 68] is also given a reprise, but Brahms does alter the harmony and melody slightly, replacing G-flats with G-naturals, anticipating the return of A-flat for the A’ section.  This is most notable in the first two of the repeated patterns beginning with the triplet rhythm.  There, the left hand also shifts from D-flat and E-flat to E-flat and F with added bass notes on A-flat, further increasing anticipation for the key of A-flat.  G-flat returns in the last of these, and the cadence is in D-flat as before.
4:15 [m. 101]--Re-transition.  The two-bar cadence is repeated, but inflected to D-flat minor, the left hand continuing its pattern on D-flat and E-flat.  The cadence is then further varied  and moved lower, still inflected to minor.  But this time it does not arrive on D-flat.  The bass shifts up to E-flat, which becomes the “dominant” of A-flat.  The last measure of the transition is in 2/4, preparing the return of the main melody from the A section, which begins on the upbeat into the next measure.  This measure also prepares the accompaniment for the first part of the A’ section, which maintains the triplet pattern established in the 3/8 music, but adds prominent upper notes.  These are colorful and chromatic in this preparatory measure.
A’ Section--A-flat major, 2/4 time.
4:27 [m. 106]--Part 1 (a).  Brahms indicates that the slowing into the opening tempo should happen very gradually.  The right hand is only very slightly adjusted from the presentation at the beginning, with notes added to cover harmonies not in the left hand.  The left hand accompaniment now incorporates the triplet rhythm from the 3/8 music of the B section and includes wide leaps.  There is a constantly reiterated high E-flat in this flowing triplet accompaniment.  A broken octave replaces the arpeggio at the end of the first phrase.  The high E-flats break during the phrase in C-flat.  The triplet rhythm is incorporated into the arpeggios under the extension of the last phrase and cadence, and they range rather widely.  In the second half of the last measure, the triplet rhythm finally breaks in anticipation of Part 2 (b).
4:55 [m. 116]--Part 2 (b).  The first phrase is presented without substantial alteration from 0:56 [m. 11].
5:07 [m. 120]--The second phrase is presented without substantial alteration from 1:07 [m. 15].
5:18 [m. 124]--The extended closing phrase is presented without substantial alteration from 1:18 [m. 19].
5:35 [m. 130]--Part 3 (a’).  Other than the fact that the accompaniment, now in the right hand, is again in triplet rhythm (which makes it even more difficult to negotiated under the melody, but Brahms does remove the trills), the passage is very close to 1:34 [m. 25].  The pedal point E-flat and C-flat are present in the left hand as before.  The wide arpeggios under the extension and cadence are also in the triplet rhythm.  At the cadence, the left hand triplets suddenly move to a droning trill on a low G and A-flat.  Brahms explicitly places the trill in slurred two-note groups, which conflict with the triplet rhythm and create great ambiguity.  The extension of the cadence, described below, is greatly expanded from the one in the first A section.
6:04 [m. 140]--The reiterations of the cadence make an early turn to D-flat, a turn that is totally unexpected in a ternary form.  The first reiteration uses the harmony of D-flat minor, not major, while the droning trill, still in triplet rhythm but in two-note groups, continues below.  The second reiteration returns to A-flat.  A third, moving lower, is again over D-flat-minor harmony.  Finally, a fourth reiteration, even lower and in the tenor range, is on the “dominant” chord of D-flat, anticipating its firm arrival.  The entire passage diminishes greatly in volume, reaching ppp on the “dominant” chord.  Under this chord, the first note of each left hand triplet is replaced by a rest, bringing the two-note slurs in alignment with the rhythm.
Coda--D-flat major, Andante molto/Adagio, 3/4 and 4/4 time.
6:21 [m. 144]--The gigantic coda takes on the life of a second B section, and indeed it is in the B section’s key of D-flat.  It has a certain thematic affinity with the 3/8 music of the earlier section as well, which becomes more pronounced as it progresses.  The marking “Andante molto” and the 3/4 meter indicate a broader presentation.  It begins very quietly, ppp.  A low throbbing pedal-point A-flat is established that remains in force  for the first two phrases.  The melody itself is heavily upbeat-driven, with rich harmonies and an ardently passionate character similar to that of the B section.  The first phrase works upward, reaching a half-close.
6:46 [m. 151]--The first phrase is repeated an octave lower, with slightly varied harmonies.  A lower line, beginning with long tolling D-flats, is added below the throbbing A-flat pedal point.  The end of the phrase is altered to reach a full close instead of a half-close.
7:09 [m. 157]--Still very quiet and in the original higher register, the next phrase offers contrast, with more chromatic inflections to the melody and harmony.  The throbbing pedal-point wanders narrowly away from A-flat in the bass, and the lower line below it is also more chromatic.  After four bars, the pedal point settles on A-natural and the harmony moves briefly, but unexpectedly, to the key of F major, which then shifts to F minor.  At this point, a powerful crescendo begins and the melody begins to work up to its first climax.  A triplet is added to the last two upbeat figures, including a final bass descent, and the coming climax is indicated pesante.  The F-minor harmonies quickly move back toward D-flat for the arrival point.
7:36 [m. 164]--The arrival is marked molto pesante and fortissimo.  In very high chords, the original phrase is stated in full harmonies and extended to eight measures.  The pedal point in the bass is now in octaves on D-flat and, significantly, in triplet rhythm.  After four bars, the octave triplets move away from D-flat and chromatic harmonies are introduced.  The presentation is very grand and triumphant.  There is imitation of the upbeat figures in the left hand, which plays these imitations along with the continuing triplets.  The cadence of the extended phrase does not settle, but pushes forward, the octave triplets in the left hand returning to D-flat, the home keynote.
7:55 [m. 171]--The driving, passionate music presses forward, extending higher.  The pedal point is maintained in the left hand, but is decorated by wide leaps to other notes.  A second, even more powerful climax is approached.  It arrives with great intensity as the left hand triplets change to straight sixteenth notes on a thick “dominant” chord in its unstable third inversion.  The climax, intense as it is, only lasts for one measure, and the music rapidly settles down in pitch and volume.  The left hand chords return to triplet rhythm and then settle on D-flat octaves.  The cadence is extended over greatly diminishing volume.  In the last measure, the octave D-flats slow to straight rhythm and introduce halting rests on the last two 3/4 beats.
8:22 [m. 179]--The tempo is now “Adagio.”  The volume is indicated as ppp.  The bass octaves move down in a true chromatic line with full harmonies.  Over this, the right hand, in the tenor range, plays what sounds like a statement of benediction.  Its last chords are extended with breathless anticipation.  The “benediction” even ends with a “plagal,” or “Amen” cadence.  The last bar of the “benediction” changes to 4/4 meter (marked as common time).  The chord is held for a full three beats, but an upbeat is added for the final return of the theme from the A section, which is in 4/4 time.
9:00 [m. 187]--The opening figure from the A section, marked con molto espressione, returns, complete with its typical accompaniment pattern in the left hand.  But it is in the D-flat major of the coda, where the movement remarkably ends.  For a movement to unambiguously begin and end on different key centers is extraordinarily unusual, and this example is almost unique in Brahms (the Schicksalslied, Op. 54, is another example).  The figure works its way upward, very gently, but it suddenly erupts in a final outburst of forte rolled chords that quickly settle down to four reiterated rolled D-flat chords with the third, F, on top.  They are approached by another somewhat altered “plagal” cadence.  The last chord is held until it fades.
9:49--END OF MOVEMENT [191 mm.]

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3^rd Movement: Scherzo - Allegro energico  (Scherzo with Trio).  F MINOR, 3/4 time.
SCHERZO
0:00 [m. 1]--Part 1a.  The opening approach is a huge arpeggio on a dissonant “diminished seventh” chord notated as grace notes before the downbeat.  The first section of Part 1 has two phrases.  They establish the rollicking, swaggering rhythmic sweep that characterizes the scherzo.  The right hand octaves are supported by a left hand that treacherously leaps from low octaves on the downbeats up to mid-range chords on the second and third beats.  The first phrase moves from F minor to the “subdominant” key of B-flat minor in an incomplete close.  The long-short rhythm broken by rests is characteristic of the scherzo theme.
0:07 [m. 9]--The second phrase is similar to the first, also beginning with the “diminished seventh” grace-note arpeggio.  It also ends on B-flat minor, but begins in E-flat minor, approaching from the other direction.  The second half of the phrase becomes suddenly quieter and light.  It reaches a full close with a rolled chord and descending arpeggio.
0:13 [m. 17]--Part 1b.  In the next section, which begins back in F minor and also has two phrases, the long-short octaves move to the left hand, establishing a strong, marching bass line.  The right hand plays loud descending chords against them.  The second half of the phrase again becomes quiet and light, with smooth two-part writing in the right hand and single detached notes, still in the prevailing rhythm, in the left.  Again, the goal is B-flat.
0:19 [m. 25]--Mirroring Part 1a, the second phrase begins in E-flat minor and ends in B-flat minor.  The first four bars are similar to those of the first phrase.  The second half again becomes quiet and light, but it is extended and based on leaps of a fourth in the top voice.  After four bars of the smooth leaps, the extension leaps down an octave and reaches another full cadence in B-flat minor with a descending arpeggio in the higher register.
0:28 [m. 37]--Part 2.  The bass line moves up by half-step in octaves, still at a quiet level.  Two half-step shifts are each followed by a high descending right hand arpeggio similar to the cadences in Part 1.  When the bass octaves reach D-flat, a sequence of arpeggios begins based on motion in both directions along the circle of fifths.  The left hand plays longer rising arpeggios in a slower long-short rhythm across two bars.  The right hand continues to play the high, short, descending leggiero arpeggios derived from the Part 1 cadences.  The first harmonies remain on the “flat” side: D-flat major, A-flat minor and major, E-flat minor.
0:34 [m. 46]--A chromatic alteration moves the arpeggios to the “sharp” side: E major, B major and minor, F-sharp minor.  The note “D” is used as a pivot from B minor to G.  The bass stalls on G under four widening leaps.  It begins to function as a preparatory “dominant” note.  At the arrival on G, the volume also begins to build.  It eventually reaches forte, and the left hand moves from its broad arpeggios to sharply syncopated dissonances that resolve downward by half step.  The volume diminishes again as the right hand arpeggios move lower and begin to trail away, the bass remaining anchored to the note G.  The last left hand syncopation abandons the half-step descent in favor of a more solid establishment of G.
0:46 [m. 63]--Re-transition.  The bass on G suddenly merges into the head rhythm of Part 1, the long-short figure broken by a rest.  This rhythm is interrupted once by a final descending right hand arpeggio, also on G.  It is then heard again.  Finally, the first note is cut off, and only the clipped “short-long” figure is heard.  Three of these raise expectations for an arrival on C minor.  These expectations are thwarted by a sudden jarring descent, with right hand octaves following the left hand notes.  The descent, swelling in volume, leads not to C, but a level beyond that, the home key of F minor and the return of the Part 1 material.
0:51 [m. 70]--Part 3 (Varied return of Part 1).  The first phrase of Part 1a is played with some alterations. The grace-note arpeggio, which would be impractical after the descending approach, is replaced by a full “diminished seventh” chord harmonizing the first beat.  The first descending right hand octaves are imitated by the left hand in the third measure.  There are other subtle alterations to the left hand, especially its low bass octaves.  The last four of these descend, rather than ascend as they did before.
0:56 [m. 78]--The second phrase of Part 1a appears to begin in E-flat minor as expected, even beginning with the grace-note arpeggio.  But the left hand is changed to an arching pattern in octaves.  The phrase stalls after two measures.  The opening gesture is again heard in F minor, as at the beginning of the first phrase, but with the arching octaves in the left hand.  A third gesture reaches very high and begins a long, loud, and treacherous octave descent in both hands outlining another “diminished seventh” chord, one that seems to move away from F minor.  The right hand follows the left after the beat, and the descending arpeggio plunges for four bars before moving to a stepwise descent in a fifth.
1:02 [m. 87]--The passionate descent lands on a note, D-natural, that does not belong to F minor.  But it begins a sequence that will firmly establish that key.  Loud octaves on the downbeats descend, then ascend, eventually landing on C, which acts as the “dominant” to F minor.  Each of these octaves leaps up to a higher chord on the last beat of the bar.  In the left hand, this chord is rolled.  After this eight-bar sequence, an F-minor cadence is reiterated in the same rhythm, leaping down before the two last chords, which are supported by solid F octaves in the bass.  The scherzo portion ends with a two-measure pause.
TRIO (D-flat Major)
1:12 [m. 101]--Part 1.  In stark contrast to the main scherzo, the trio section is smooth and hymn-like, played entirely in warm chords and bass octaves.  The first two phrases support an arching melody with these chords, the second phrase rising slightly higher.  Both phrases hold the second chord for two measures, then become more active.  Both phrases end on the same half-close.
1:25 [m. 117]--The last phrase of Part 1 is extended.  It immediately takes on a darker color, turning to E-flat minor and establishing a pedal point low bass octave on E-flat.  The swaying motion of the first two phrases and the chordal support are maintained.  The passage gently rises and falls.  At the extension of the phrase, both hands become chromatic, and the bass octaves rise by half-steps from E-flat until they reach A-flat, the “dominant” of D-flat.  The right hand becomes more active, chromatically winding downward.  The first ending (mm. 129a-132a) prolongs two dissonant chords before moving to D-flat for the repeat.
1:37 [m.101]--Part 1 repeated.  Restatement of the first two phrases.
1:50 [m. 117]--Restatement of the extended phrase beginning in E-flat minor.  The second ending (mm. 129b-132b) is subtly altered so that A-flat does not act as a strong “dominant” pulling toward D-flat.  In fact, the beginning of Part 2 is in E-flat minor, the key of the extended phrase.
2:02 [m. 133]--Part 2.  The opening music is very similar to the first phrases of Part 1, but the key is E-flat minor and the phrase structure is irregular.  A six-bar unit merges prematurely into a longer unit of eight bars, creating an unsettled feeling.  The end of the eight-bar unit then itself merges into an extension of oscillating chords using the unstable note F-flat, but otherwise suggesting the preparatory “dominant” of D-flat.  A dissonant chord is held for four measures in the right hand as the left hand octaves slowly inch upward chromatically until they again reach the pivotal note A-flat.
2:18 [m. 154]--The first phrase of Part 1 returns in D-flat major, with the right hand an octave higher.
2:24 [m. 162]--The second phrase from Part 1 is expected, but it turns to the minor key.  Instead of arching down where expected, it continues to work up to the very high register over held bass octaves.  These high chords are breathlessly held over bar lines, and they approach a cadence in C-flat major.
2:31 [m. 172]--The arrival on the rather remote C-flat is curiously satisfying, but the bass immediately disrupts things by bringing back, most unexpectedly, the long-short rhythm of the main scherzo section.  This rhythm works downward chromatically as the high C-flat chord is reiterated on the weak third beat of the bar, then held.  At the same time, a powerful crescendo begins.  When the bass again reaches the crucial note A-flat on the scherzo rhythm, the right hand chord replaces C-flat with C-natural and the harmony is once again on the preparatory “dominant” chord of D-flat major.
2:36 [m. 180]--The climax of the trio section makes a glorious arrival.  The chords and bass octaves ring out like bells in a joyously arching motion.  After eight bars, the music breaks into a descending arpeggio with the right hand following the left after the beat, similar to the descent toward the end of the main scherzo before 1:02 [m. 87].
2:45 [m. 192]--The climax continues and becomes slightly more chromatic.  The bass assumes the shape, but not the rhythm of the main idea from the scherzo section.  The right hand chords again reach very high, the intensity builds, and a huge cadence in D-flat is expected.  It is prepared, but never arrives, being cruelly cut off by a pause.
2:52 [m. 203]--Transition to reprise of scherzo.  The rhythm and shape of the main scherzo idea has become pervasive, and now it is used as a transition to the reprise and to its key of F minor.  The preparatory arpeggio, heard in grace notes in the main section, is written out and takes up a measure of its own.  The first transitional phrase, clearly based on the main scherzo idea, is still in the trio section’s key of D-flat.  The second, also preceded by a measured arpeggio, is in E-flat minor, the trio section’s secondary key.
SCHERZO REPRISE
2:59 [mm. 211-212 (1)]--The reprise itself arrives by way of another measured arpeggio that takes the place of the unmeasured one in the first bar of the scherzo.  It is not a “diminished seventh,” but a tamer B-flat-minor chord.  The last notated measure, m. 212, is equivalent to m. 1 except for the missing grace note arpeggio and the first right hand harmony.  The reprise is indicated with a sign leading back to m. 2.  From that point, Part 1a follows as at the beginning with the first phrase moving from F minor to B-flat minor.
3:05 [m. 9]--Second phrase moving from E-flat minor to B-flat minor, as at 0:07.
3:10 [m. 17]--Part 1b.  Long-short octaves in left hand and loud octaves in right hand, as at 0:13.
3:16 [m. 25]--Second phrase with ending with smooth leaps and full cadence in B-flat minor, as at 0:19.
3:25 [m. 37]--Part 2.  Bass line moving by half-steps, then circle-of-fifths sequence of descending arpeggios, as at 0:28.
3:31 [m. 46]--Arpeggios in “sharp” keys, buildup, and establishment of pedal point on G, as at 0:34.
3:42 [m. 63]--Re-transition.  Establishment of prevailing rhythm in bass, then motion back to F minor, as at 0:46.
3:47 [m. 70]--Part 3 (Varied return of Part 1).  First phrase of Part 1a with added imitation in the left hand, as at 0:51.
3:53 [m. 78]--Stalled second phrase leading to treacherous descending “diminished seventh” arpeggio, as at 0:56.
3:59 [m. 87]--Final sequence with loud octaves leaping to chords, then final chords and pause, as at 1:02.
4:18--END OF MOVEMENT [211 (+100) mm.; m. 212 is equivalent to the second m. 1]

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4^th Movement: Intermezzo (Rückblick) - Andante molto (Binary form).  B-FLAT MINOR, 2/4 time.
Part 1--First Statement
0:00 [m. 1]--The subtitle “Rückblick” means “Backward Glance” or perhaps more appropriately, “Reminiscence.”  The look back is toward the second movement, whose main theme is transformed from a love song into a ghostly funeral march.  The identity of the theme is unmistakable, although it is changed to minor and placed a step higher, on B-flat instead of its original A-flat.  The descending line begins with an upbeat, as expected, but instead of a flowing accompaniment, it is harmonized in rather bare “horn fifth” style.  The left hand bass adds another new element, a drum roll-like triplet figure that also evokes the Beethovenian “fate” rhythm and helps establish the key.  The first two gestures begin similarly.  The first is a closed statement in B-flat minor.  The second is subtly shifted down to A-flat major at the end, as confirmed by the “fate” triplets.
0:21 [m. 5]--The second movement theme had descended and arched back upward.  The upward motion is now developed in the funeral march.  Two such gestures are played over a powerful crescendo and increasingly full harmony.  The first closes at home on B-flat after working back from A-flat, but changes it to major.  The second begins forcefully, pesante, and with an upbeat triplet.  It reaches higher and comes to a powerful close on F minor, making a nod to the sonata’s principal key.  The minor to major pathway of the descents is thus mirrored in the ascents.  The “fate” triplets confirm the cadences.
0:40 [m. 9]--The cadence on F is reiterated forcefully in a powerful chordal descent, with pounding “fate” triplets in the low bass.  It first lands on F minor, as before.  Then, in a second gesture of confirmation that reaches higher for a full cadence, it is changed to F major, still punctuated by the “fate” triplets, which leap up an octave.  The arrival on F major is a climactic moment.
0:58 [m. 13]--Everything becomes suddenly quiet again after the huge arrival.  The main descending gesture of the theme begins again, this time harmonized as an eerie “diminished seventh.”  The “fate” triplets remain on F, which now appears to function as the “dominant” of the home key, B-flat minor.  This is confirmed by the second descending gesture.  The triplet drum roll alternates between the low bass and the tenor register three octaves higher.
1:16 [m. 17]--The descending gestures are reduced to two-note groups on the upbeats, widely harmonized in sixths and sevenths over the “fate” triplets in the tenor range.  Two of these reach higher.  A third begins, but it continues beyond the two-note group for a full descent.  This descent has a “deceptive” arrival on G-flat major where B-flat minor is expected. 
1:27 [m. 19]--The volume is now very quiet and subdued.  What follows the “deceptive” motion is a highly strange and evocative passage of open fifths in both hands, alternating steadily up and down, with every voice forming a three-note arpeggio and the hands constantly in contrary motion.  The combination of the fifths in both hands results in two alternating chords, both of which feature the foreign note F-flat.  One chord is a “diminished seventh,” the other is the “dominant” of C-flat, a key that is suggested, but which never arrives.  The resulting oscillation speeds up and then slows back down, always remaining quiet and spectral.  The last chord is re-notated so that it can function in B-flat minor (as a so-called “augmented sixth chord”) instead of the “dominant” of C-flat, which is never established.  A reiteration is followed by a full-measure pause.  This pause, which breaks things off without resolution, ends the first section or statement.
Part 2--Counterstatement
1:48 [m. 25]--A very quiet and ominous left hand tremolo begins on low octave F’s.  It occupies the measure before the upbeat of the theme.  Against the tremolo, the right hand begins the main funeral march theme (the transformed second movement theme), and plays the first two phrases as at the beginning, ending on B-flat minor and A-flat major.  The right hand has no changes.  The left hand continues the octave tremolo through the first descent, including where the first “fate” triplets were heard.  From there, the remaining “fate” triplets are replaced with tremolo-like groups of five notes in octaves.
2:10 [m. 30]--The tremolo and its derivatives end.  The left hand returns to the notes used in the first statement.  The upward gestures against the crescendo are heard as at 0:21 [m. 5], and the “fate” triplets return in their proper places.  The first phrase ends on B-flat as before.  The second begins as before, with the upbeat triplet and the marking pesante, but Brahms makes a sudden harmonic turn at the end.  The powerful close still has the same high top note (F), but the harmony under it is changed to another bright B-flat-major chord, confirmed by “fate” triplets, indicating that the second half will remain in B-flat.
2:29 [m. 34]--The reiteration of the cadence follows, analogous to 0:40 [m. 9], with the pounding “fate” triplets, but both climactic arrivals remain firmly anchored not only on B-flat, but on B-flat major.  The second, very high arrival is almost triumphantly confirmed by the “fate” triplets.
2:47 [m. 38]--The climax of the movement arrives.  As the “fate” triplets continue to hammer on the B-flat cadence, the right hand immediately turns back to minor.  An octave on the dissonant note C-flat in the tenor range hints at E-flat minor, but the “fate” triplets will not allow the right hand to assert a new key despite the valiant attempt.  Extremely agitated, passionate chords, still featuring the dissonant C-flat, work upward, then back down.  Brahms indicates that the speed should increase.  The volume and the speed then both settle back down.  An extended cadence in B-flat-minor, still tinged by the persistent C-flat, is suddenly cut off in both the right hand and the triplets.
3:12 [m. 44]--The opening descending gesture of the movement, at a very quiet level, is played an octave higher than its original statement.  The left hand and its “fate” triplets do not accompany, so the “horn fifth” harmonies are bare.  It turns toward a half-close on the “dominant” note F.  The left hand, sounding almost desolate and with no harmony, then plays a new version of the main descending idea that comes to a full close on a low B-flat.
3:40 [m. 50]--The “fate” triplets close the movement in a defeated manner, with both hands in the bass.  Two motions to the “subdominant” chord of E-flat minor are followed by the final full cadence and held B-flat-minor chord.
4:09--END OF MOVEMENT [53 mm.]

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5^th Movement: Finale - Allegro moderato ma rubato; Più mosso; Presto; Tempo primo (Rondo form with large triple coda).  F MINOR/MAJOR, 6/8 time (with numerous passages in implied 2/2 or 4/4).
FIRST STATEMENT OF RONDO THEME (A)
0:00 [m. 1]--The galloping F-minor theme has a somewhat ominous quality.  It begins in the low range, in full chords with low bass notes.  It has a typical 6/8 long-short swing at the outset, then it adds a clipped dotted rhythm.  The response, which is much quieter (pianissimo) leaps up to the high register and adds syncopation (entry on the weakest parts of the measure).  After the response, the music moves back to the low range for a slower, cautiously questioning rising gesture.
0:11 [m. 7]--Another high syncopated response follows the questioning gesture, but this time it is supported by very low bass octaves.  Another rising, questioning gesture comes next, this one in the upper range.  The response this time is a suddenly loud, cascading pattern using the swinging rhythm of the theme.  The pattern is closed off by the left hand leaping up to two prominent syncopated octaves.  These are dissonant, craving a resolution toward the “dominant” chord on C.
0:21 [m. 15]--The “dominant” chord arrives forcefully and immediately moves into two statements of the syncopated response, first high and harmonized in thirds, then lower, with bass octave support and in full harmony.  The response is then developed in a large chromatic sequence marked sempre più agitato.  This steadily rises with ever more colorful chords over left hand octaves moving up and down by half-step, becoming more and more unsettled and syncopated until it arrives on a loud, but uneasy F-minor chord in the preparatory “six-four” position.
0:33 [m. 25]--Transition.  The left hand moves to a low bass octave on the “dominant” note, C.  The right hand breaks into a rapid series of jagged descending arpeggios.  The left hand then enters again with rising gestures against these arpeggios,  first in thirds before landing on a low F octave, then rising up from that octave and leaping back down to G-flat, strongly suggesting B-flat minor.  It finally rises to the “dominant” C again.  At this arrival point, the arpeggios become softer, then actually slower as Brahms indicates that four “straight” notes are to be played where six notes in 6/8 would normally be heard.  The “dominant” now has another strong pull toward the home key.
0:43 [m. 33]--Transition, cont.  The right hand quietly hammers an octave on F.  Against it, the left hand plays descending octaves in the rhythm of the syncopated response.  The first group of octaves suggests B-flat minor/major, but the second, whose final notes are repeated, is clearly in F again.  It makes a late turn from minor to major.  The “hammering” octave is reduced to a single bare note leading into the contrasting theme.
FIRST CONTRASTING THEME (B) – F major
0:50 [m. 39]--The theme is long and heartfelt, played in pure and rich F-major chords against murmuring thirds (sometimes briefly turning to fourths or seconds) in the left hand.  These thirds are approached by a wide arpeggio in each measure that begins with a punctuating bass note.  Some measures also place a bass note in the middle.  The first phrase is has a wide breadth.  Where it might be expected to close, it is extended, briefly turning to “dominant” C-major harmony over steadily rising bass notes, and adding overlapping voices.  It is extended by another five bars in F major, settling down to an extended half-close for an irregular total of thirteen measures.
1:08 [m. 52]--The second phrase begins like the first, but its second gesture rises higher.  The turn to the “dominant” happens a couple of measures earlier.  The “murmuring” pattern widens as far as a fifth.  It is followed by another digression to A minor/major.  This happens in eight bars.  Three more bars meander back toward F over the same basic pattern in the left hand.
1:23 [m. 63]--The preceding 11-bar phrase is extended by a drawn-out meditation in a flowing rhythm.  It is harmonically active, moving from F major to the unexpected key of A-flat major.  It also swells slightly in volume.  A drawn-out, expected cadence in A-flat is rather brusquely aborted and pushed aside by the preparatory “dominant” chord in F major or minor.
RE-TRANSITION (Parenthesis in D-flat)
1:34 [m. 71]--A light, rapid arching figure is followed by the opening gesture of the rondo theme in bass octaves.  These move the music back to minor.  The light figure is repeated an octave lower, followed by the bass octaves.  The opening of the rondo theme is then transferred to its original right-hand chords in the tenor range.  These alternate twice with the bass octaves, not quite able to continue with the theme.
1:42 [m. 78]--A completely unexpected diversion based on the rondo theme, almost like a parenthesis, extends the re-transition.  The key very smoothly shifts to D-flat major, where a thumping bass pedal point is established with two in each measure.  A transformed, serene version of the rondo theme is played in the upper register, pianissimo.  The thumping D-flat pedal continues through a harmonic diversion suggesting F-sharp minor (notated as G-flat).  The bouncing chords then stall on a pattern of “seventh” chords.  These begin far removed from the D-flat pedal and clashing with it (suggesting D, a half-step above), but are steadily altered to reach the “dominant” chord.
1: 56 [m. 90]--The D-flat pedal continues in the bass, as do the bouncing chords.  These do not arrive on D-flat, but continue to wander.  A prominent four-note chromatic descent begins in an inner voice, moving down by one note every two measures as the harmony changes above it.  The key begins to veer toward the “relative” minor key of D-flat, B-flat minor.  Finally, the bouncing right hand harmonies reach D-flat, agreeing with the pedal point.  At this point, the thumping bass D-flat decelerates to one per measure, the bouncing right hand is reduced to a third, then it is also stretched out.
2:07 [m. 100]--The bass octaves heard at 1:34 [m. 71] enter in a sudden turn back to F minor.  This time they continue with the rondo theme a few notes beyond where they did there.  They are interrupted by the opening rondo theme chords in the right hand, but these are cut off by the octaves as they were before the D-flat digression.  The octaves slide surreptitiously into the full statement of the rondo theme
SECOND STATEMENT OF RONDO THEME (A’)
2:11 [m. 104]--The theme begins, adding stronger bass octave support.  But after the opening statement of the rhythm, it skips the syncopated response and moves straight to the cautiously questioning gesture, specifically the C harmony immediately preceding 0:11 [m. 7].  It is given in minor, then repeated in major, slightly thicker, before the theme continues.  Everything remains at the quiet pianissimo level established in the “parenthesis,” and the “questioning” gestures slow down as expected.
2:17 [m. 108]--The syncopated response, questioning gestures, loud cascading descent, and syncopated octave leaps in the left hand are played as at 0:11 [m. 7].
2:27 [m. 116]--The syncopated response and agitato chromatic sequence, leading to the F-minor chord in six-four position follow as at 0:21 [m. 15].
2:39 [m. 126]--Transition with “dominant” octave, jagged descending arpeggios, rising left hand figures, and slower, softer arpeggios with “straight” notes, as at 0:33 [m. 25].
2:48 [m. 134]--Rhythm of the syncopated response with “hammering” octave, as at 0:43 [m. 33].  The bare note F in the last measure is replaced very subtly by a broad octave descent in the bass from F to E-flat.  It will continue to move down to D-flat for the second contrasting theme (whose key was foreshadowed in the “parenthesis”).
SECOND CONTRASTING THEME (C) – D-flat major
2:56 [m. 140]--The theme is noble and filled with potential for future grandeur, although it is presented in a subdued way.  Full descending chords in pure major are played against bass octaves.  Three descending “waves,” each one higher, are followed by a “rounding” figure.  The whole phrase is then played an octave higher and at a stronger volume level, with the left hand doubling the chords below on the original octave, after low bass grace notes, in the first two “waves.”
3:15 [m. 156]--A closing phrase is added, creating an “aab” structure similar to a chorale.  This closing phrase is played forte.  It begins with a metric cross-rhythm.  The first four bars are played in a “straight” rhythm that has the feel of 2/2 (alla breve) meter rather than the 6/8 flow with its triple grouping.  Quarter notes are grouped explicitly with indications of “2” or “4” (“duplets” and “quadruplets”) where there would normally be three or six eighth notes.  The effect is essentially “two in the space of three,” or the opposite of a triplet rhythm in a “straight” meter.  There are two swelling “waves” in this cross-meter with the left hand doubling the right.  They are followed by jubilant fortissimo chords that descend to a triumphant cadence.  It is extended by a measure, creating a nine-bar phrase that overlaps with the following canon.
3:26 [m. 164]--A canon (imitation) begins on the first phrase of the theme, with the three “waves” and the “rounding” figure.  It returns to a more moderate volume level.  The left hand plays it in bass octaves, beginning in overlap with the extended cadence.  The right hand follows a measure later in full chords, with the top voice imitating the melodic line in the left hand octaves.  As the right hand plays the last measure of the “rounding” gesture, the left hand, having completed the phrase but still in octaves, plays a brief preview of the closing phrase with its “duple” grouping.
3:37 [m. 173]--A variant of the closing phrase begins.  In the right hand, the phrase, still including the “2” and “4” groupings, turns to the minor key in the first “wave,” then abruptly shifts up a half-step in the second “wave,” suggesting a motion to D major.  The left hand no longer doubles the right, but adds a low accompaniment in octaves.  It is in the regular 6/8 grouping and includes ominous “neighbor note” figures on the upbeats as the bass descends by half-steps.  Thus, the hands clash rhythmically with one another.
RE-TRANSITION
3:42 [m. 177]--All of a sudden, the music becomes very quiet  The right hand has the “4” grouping all the way through the re-transition.  It plays off-beat chords on the second and fourth “beats.”  The left hand plays the ominous neighbor-note figures on the upbeats, still in regular 6/8 grouping.  The off-beat right hand chords are dissonant “diminished” triads.  They are in two descending groups of four, and seem derived from the jubilant chords  that previously ended the closing phrase and were here cut off.  The upbeat figures in the left hand remain anchored like an ostinato around the note G-flat.
3:46 [m. 181]--The pattern continues, but the bass neighbor-note figures shift up to G-natural, then A-flat, the “dominant” of D-flat.  The right hand still plays off-beat chords in its quadruple grouping, but it now becomes stuck on the “dominant seventh” chord of A-flat major (on E-flat), suggesting a motion to that key.  The bass, however, is now no longer an ostinato, and it continues to wander to A-natural, then back to A-flat.  The last measure of the pattern suddenly returns back home to D-flat through the “dominant seventh” chord on A-flat.
3:52 [m. 185]--A satisfying cadence on D-flat leads to a canon based on the first descending figure of the theme, but both the left and right hands are now in the “straight” quadruple (“4”) grouping.  The left hand leads, and the right hand follows two beats later.  The right hand, however, alternates between following an octave higher and an octave lower, leaping up and down the keyboard for each four-note descent and crossing over the static left hand.  After four measures, the lower right hand imitation moves to a dissonant, wide descent to D-flat instead of imitating the left hand below.  The left hand moves up to a more “final,” narrower descent to D-flat after this, where it stays.  The upper right hand imitations remain precise, but the next lower imitation is the more dissonant version.  Finally, in a last alternation, the lower right hand imitation changes to the more “final” version.  The left hand then has a closing descent, two octaves lower (and below the last lower right hand imitation), that is stretched to two measures and restores the 6/8 flow.
THIRD STATEMENT OF RONDO THEME (A”)
4:04 [m. 195]--The upbeat of the theme easily moves back to F minor from the final D-flat-major descent.  The return is similar to that at 2:11 [m. 104], where the syncopated response is skipped and the first motion is to the questioning gesture on the C harmony.  The left hand, however, is different.  It takes the pattern of the descents in the previous canon (albeit in the regular 6/8 meter).  These two descents are somewhat chromatic, but end with a leap down to the “dominant” note, C.  There is a hold (fermata) on the last chord of the questioning gesture, which has slowed down.
4:12 [m. 199]--Unexpectedly, the music returns to another canon like the one at 3:52 [m. 185] in the quadruple (“4”) grouping.  This one is more regular.  The left hand still remains static while the right hand imitates first above, then below.  The first descents are down to C, but the left hand holds long, mildly dissonant notes below all of its descents.  These long notes add harmonic character.  After one high-low alternation, the left hand pattern changes slightly, moving up and descending to E.  The right hand again imitates this twice, higher and lower.  Then the left hand moves up again and descends to G, followed by the right hand imitating above and below.  This time, there are two alternations, with the long left hand note (E) moving down a half-step under the second one.  Then the left hand leaps down two octaves for a final descent in regular 6/8 meter, similar to the end of the previous canon.  The volume becomes very quiet.
4:25 [m. 209]--A completely new version of the theme’s opening gesture adds more variety.  It is in A-flat, the “relative” key to F minor, and still uses the descending octaves from the canons (and ultimately from the second contrasting theme) in the bass.  It is followed by the questioning gesture in a new, highly chromatic version that moves toward the C harmony that is expected on this pause.  That harmony arrives with the loud cascading descent familiar from 0:11 [m. 7] and 2:17 [m. 108].  This is also a new version, in C minor, but it ends on the C-major harmony that is expected at this point in the rondo statement.
4:37 [m. 216]--A new upbeat, a rushing scale, leads to the agitato syncopated responses from 0:21 [m. 15] and 2:27 [m. 116].  The first two statements, the one in thirds and the lower one with bass octave support, are as before, but the rising and falling chromatic sequence is replaced by an extension and diversion.  This passes through keys that have been seen before, D-flat and A-flat major and B-flat minor.  It is somewhat less intense than the chromatic sequence.  Like that sequence, however, it has a rising bass, which moves to chromatic half-step motion at the end, and its goal is the same: the F-minor chord in six-four position.
4:50 [m. 226]--Transition.  It begins like 0:33 [m. 25] and 2:39 [m. 126], but it adds upper third harmonies to many of the notes in the jagged arpeggios, making them even more exciting and virtuosic.  The bass is similar at first, beginning with the rising thirds and motion toward B-flat minor, but the following harmonies are changed.  The bass octaves continue to focus on B-flat-minor harmony.  Then they alternate with more rising thirds, but these move to the high register, with the left hand leaping and crossing over the right.  This alternation happens twice, with the “crossover” left hand thirds moving even higher.
4:57 [m. 232]--The harmony abruptly changes to another familiar home, C, and the thirds stall on an oscillating motion.  The C harmony is colored by a lingering note from F minor, A-flat.  The right hand slows to the “straight” notes, but now the left hand, crossing back below, also changes to “straight” rhythm,” the quadruple “4” groups familiar from the second contrasting theme and the canons.  A measure is added with the right hand moving from the “straight” notes to a slow 6/8, and the C harmony is altered to function as the “dominant” of F, suggesting a final motion back home, though the disruptive A-flat persists.
5:04 [m. 236]--The motion to F indeed arrives, but it is explicitly F major, and the remainder of the movement is primarily in the major key.  The presence of A-flat in the preceding transition, with its strong implication of F minor, makes this rather surprising.  What follows is yet another (the last) version of the canon in quadruple “4” metric grouping with hand crossing.  This time, it is the right hand that leads and remains static while the left hand follows above (crossing over the right hand) and then below.  There are three sequences of this pattern, each a third higher.  The higher left hand imitations, which cross over, are as expected, but the lower ones replace the actual imitation with a stepwise descent followed by a downward octave leap.  The first of these definitively establishes F major, as the C-major flavor was still present in the first imitative descent.  In the last sequence, a long dissonant C-sharp is added below the leading right hand.  The last lower left hand “imitation” is a stepwise octave descent to F.
5:11 [m. 242]--The rhythm moves back to the regular 6/8 flow, although the right hand still retains some descending groups of four in that rhythm.  The left hand moves to two note upbeat/downbeat groups that leap up, crossing over the right hand for a rising step, then back down to the bass for falling octaves.  F major seems to be in conflict with its relative key, D minor, for two bars.  Then the C-sharp is banished and F major reigns for now.  Brahms indicates an acceleration at this point.  The left hand upbeat/downbeat figures are now wide leaps.  They briefly move closer together and break off as the right hand reaches ecstatically high, then plunges downward.  This plunge is the approach to the first part of the coda.
FIRST SECTION OF CODA – F major, Più mosso
5:17 [m. 249]--The left hand suddenly erupts into a steadily running series of light, but distinct notes that will continue (occasionally moving to the high register and shifting to the right hand) throughout this section.  Everything remains in the basic 6/8 pulse throughout, but the first notes in the left hand runs are three descending groups of four (again derived from the second contrasting theme) that go against the 6/8 flow for two measures.  After four measures, the right hand enters with the second contrasting theme itself, its appearance in the home key of F confirming its significance.  Against the first four-note descent, the left hand runs again break into two measures of meter-defying four-note groups, but the longer right hand notes fit into the 6/8 rhythmic flow.  After this, the left hand returns to regular metric grouping.
5:25 [m. 261]--The repetition of the first phrase is omitted, and the closing phrase originally heard at 3:15 [m. 156] follows at a louder level.  It is no longer compressed into duplet and quadruplet groupings of notes with altered values, as it was there.  Its notes are actually lengthened to fit into the regular 6/8 flow, and this lengthening is compensated by the faster tempo.  Against it, the running left hand notes break into long rising scales that turn around into descending arpeggios.  These sweep up the keyboard and are passed to the right hand as they approach the top, at which point the thematic melody is taken by the left hand.  This happens halfway through each of the two “waves.”
5:31 [m. 269]--The jubilant closing chords are also doubled in length from their original appearance, again compensated by the faster speed.  They are played by the right hand, the running notes leaping back to the bass register.  These running notes include significant leaps up at the end of the first three measures, followed by two long descents in the next ones.  The cadence is abruptly and unexpectedly broken off.
5:35 [m. 275]--In a brief return to F minor, the running notes are again passed to the right hand, which plays mainly arching arpeggios.  The left hand returns, most effectively, to material from the main rondo theme, specifically the syncopated response in thirds heard at 0:21 [m. 15] and 2:27 [m. 116], and 4:37 [m. 216].  These begin at their original level, and are repeated there, but then they work upward twice, moving briefly to B-flat minor and D-flat major, but remaining in harmonized thirds.  The right hand also works upward to the high register.  All of this swells in volume.
5:41 [m. 283]--F major arrives again, more triumphantly than ever, and under the continuing rapid figuration in the right hand, the left hand plays a joyous series of chords.  These incorporate a brief duplet grouping of two quarter notes in the space of three eighth notes, harking back to the earlier frequent use of this alteration.  All of these chords prolong the “dominant” harmony, increasing greatly the anticipation of a new arrival on F.  A half close is stated three times, each one moving lower down the keyboard, as the right hand cascades downward in an arpeggio.  The last measure of this arpeggio groups ten notes in the space of six, then leaps down to a low C in the left hand, prolonging the anticipation.
SECOND SECTION OF CODA – F major, Presto
5:47 [m. 293]--A rapid scale figure on an upbeat, notated to anticipate the even faster coming tempo, leads to the confirming arrival on F and once again to the original series of notes heard in the left hand at 5:17 [m. 249], still retaining the clashing groups of four, but transferred upward to the right hand in its high register.  The speed is also faster and the volume level quieter.  Against them, the left hand plays wide, treacherous rolled chords.  The expected arrival of the second contrasting theme does not happen, however.  Instead, the dizzying figuration in the right hand and the treacherous rolled chords in the left continue unabated, becoming mildly chromatic and steadily building in volume.  The right hand adds accents to the strong beats.  Finally, the left hand abandons its chords and joins it an octave below.  The key shifts to B-flat major.  The climax, which briefly halts the torrent, is another sudden duplet disruption, this time syncopated and on the note E-flat in a high octave.
5:57 [m. 309]--E-flat is used to pivot to a totally unexpected and remote key, C-flat major.  A series of upward-striving right hand notes, again grouped in clashing four-note descents, reaches to the very high register of the keyboard over four measures.  The left hand plays longer chords and low punctuating octaves to confirm the new key.  Both hands then plunge downward, the right hand from on high in its faster notes, and the left hand in a slower descent based on the second contrasting theme.  The descent restores the 6/8 flow after the four-note groups.  The passage is quite wild, and is marked con fuoco.
6:02 [m. 317]--Still in C-flat major, the right hand breaks into a climactic and jubilantly victorious new theme, which arches upward twice, supported by descending arpeggios under it and chord progressions, often syncopated, in the left hand.  It is marked appassionato.  The melody stalls somewhat as the left hand again introduces forceful four-note octave descents derived from the second contrasting theme.  There are four of these.  The last of them finally starts to move away from the remote C-flat key.
6:12 [m. 333]--The pattern breaks, and the key shifts to B-flat.  The right hand plays thick chords that lead from B-flat back to F, using several dissonant “suspensions” in its gradual descent.  Brahms indicates that these chords should be somewhat sustained.  The left hand plays sweeping arpeggios, first in B-flat major and G minor, then on “diminished” chords as F major is finally approached.  When it finally does arrive, it is confirmed by a huge series of arpeggios in both hands, again briefly using the ubiquitous four-note descents.  These begin at different points in each hand, creating more metric confusion.  Finally, the left hand breaks off into rolled chords while the right hand sweeps down and back up in two huge anticipatory arches.  The upward motion in these groups seven notes into the space of six (or six in the space of five).
THIRD SECTION OF CODA – B-flat and F major, Tempo primo
6:23 [m. 349]--The second contrasting theme has dominated the coda.  At the close, the main rondo theme returns, as if to make sure it is not forgotten.  The original tempo suddenly arrives.  The return is based on the syncopated responses originally heard at 0:11 [m. 7].  There are two of them, marked grandioso and supported by thick harmonies in both hands.  They are not in F, but B-flat, and are followed by four off-beat chords with the left hand rolled, again using dissonant suspensions.  Two more on-beat chords, preceded by bass octaves, anticipate a cadence in B-flat.
6:34 [m. 356]--The arrival on B-flat is unstable, and the following descent reinterprets it as the “subdominant” chord in F major.  This last descent is essentially a gigantic cadence and ultimate arrival on F major.  The huge chords are supported by the grace-note arpeggios in the bass that have been so prominent in this wild movement and the sonata as a whole.  The arrival on F is then reiterated by two “plagal” (or “Amen”) cadences from B-flat to F.  All of these last chords have a rolled left hand.  This closing is vaguely reminiscent of the first movement’s ending, with the final descent, bass grace notes, multiple chords and rolled left hand, but the arrival from B-flat and the plagal cadences are quite different from that ending, as is the presence of F as the top note of all these final chords.
7:10 (runoff after 7:00)--END OF MOVEMENT [365 mm.]
END OF SONATA


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