Brahms’s first truly “major” work is also the most “symphonic” piano concerto that had been written up to that point in music history.  It is also the composition where he developed and established his personal orchestral technique.  The First Serenade was published with an earlier opus number, but the concerto was conceived first, its genesis protracted and complex, stretching from the first ideas in 1854 to the infamously unsuccessful first performances in 1859.  Beethoven’s last concerto, the “Emperor,” Op. 73, is the most obvious model.  Laid out on a broader scale than that composer had used in his previous piano concerti, he also dispensed with tradition by avoiding the improvised cadenza in the first movement.  Other great piano concertos had of course been written between Beethoven and Brahms, most notably the masterpiece by his mentor Robert Schumann (whose spirit pervades this work), but the Beethoven line is more direct.  Given the concerto’s power and significance, its early opus number is astonishing.  Initially sketched as a sonata for two pianos, it then expanded into what would have been his first symphony (an attempt to fulfill Schumann’s predictions of what he would do with that genre).  He received advice from friends such as Joseph Joachim on the craft of orchestration, but ultimately, the piece could not escape the pianistic textures with which it was conceived.  Thus, he compromised with the “symphonic concerto,” a colossal work of intense tragedy leading to ultimate triumph, colored deeply by Schumann’s final illness in 1854 and death in 1856.  The writing for piano is titanic and fiendishly difficult, but never composed for obviously showy display, as in most romantic-era concertos.  The orchestral scoring is assured, sounding like the mature Brahms.  The ensemble is severely classical, with double woodwinds, four horns, two trumpets, and timpani.  There are no trombones or tuba.  It is often astounding how he achieves such strong sonorities with such limited means, although he does indulge the timpani to great effect.  Ultimately, the First Symphony would not appear for another 18 years, his next concerto (for violin) not for another 20, and his Second Piano Concerto not for another 23.  The later, more epically serene concerto is different from this one in many ways, at times grander with its extra movement, and at times more modest, as in its finale, but the symphonic conception is similar.  Indeed, its success helped the First Concerto to gain broader acceptance.  In terms of performance time, this first movement is the longest instrumental piece Brahms ever wrote (and besides Rinaldo, the longest stretch of continuous music), almost always lasting over 22 minutes.  The first movement of his Violin Concerto with the Joachim cadenza comes very close.  That of the Second Piano Concerto never exceeds 20.  That of the Second Symphony--even with its long exposition repeat--is still generally a minute or two shorter.  This is on the scale of Beethoven’s “Emperor” and Violin Concertos.  Because of the long 6/4 measures and the rather broad tempo, it does not come close to having the highest measure count (even the work’s own finale, a little over half the length, has more).  It is a monstrous structure, heralded by its awesome opening.  The first orchestral statement proclaims the movement’s monumentality with its long-held bass pedal point under the dramatic presentation of the angular main theme.  Although the orchestral exposition is full, Brahms holds off on his main subsidiary theme, allowing the piano to present it well into the solo exposition and six minutes into the movement.  The rising shape of this theme, whose analogous restatement in the recapitulation is very literal, becomes the source of all the themes for the rondo finale.  The long solo presentation of the theme may compensate for the lack of a cadenza, but the piano has enough exceptionally difficult material, including a brutally hard series of cascading octaves at the outset of the development section.  The striking new harmonization of the main theme upon its return is justly famous, and the powerful conclusion is unremittingly tragic, thwarting a trajectory that seemed to be heading for a major-key fulfillment.  The slow movement is a complete contrast in mood and presentation.  The extremely subdued dynamic level and intimate scoring seem as if the energy has been sapped.  Brahms creates a connection by unusually retaining the long measures of 6/4 meter and the key center on D.  A reference to the opening lines of the Benedictus from the Latin mass, written under the notes of the opening, seems to be an explicit memorial to Schumann (whom Brahms often addressed as “Mynheer Domini”), but Brahms also once described the movement as a portrait of Schumann’s wife Clara.  The whole piece is hymn-like, with a couple of brief forceful outbursts.  Unlike the first movement, it contains a cadenza, albeit a meditative quasi-improvisatory one.  Like Mozart and Beethoven, Brahms gives the initial presentation of the main theme in his rondo finale to the soloist.  The movement’s structure resembles that of Beethoven’s only minor-key concerto, his Third (Op. 37).  The theme is as passionate and intense as that of the first movement, but more compact and breathless.  The buildup to the orchestral takeover is natural and exhilarating.  The succeeding themes are more heroic and jubilant in nature, all with the same rising shape.  Tragedy gives way to triumph, but not without a battle, including a remarkable developmental fugato episode.  Leading to the grand and triumphant major-key conclusion, Brahms gives the soloist not one, but two cadenzas (both short, the first more substantial), and there is even a pastoral bagpipe-like episode.  The major key completely takes root, and the windup to the conclusion is one of the most famously exciting and satisfying in the concerto literature.

IMSLP WORK PAGE
ONLINE SCORE FROM IMSLP (First Edition from Brahms-Institut Lübeck--solo part with orchestral cues)
ONLINE SCORE FROM IMSLP (First Edition of full score from Rieter-Biedermann, 1875)
ONLINE SCORE FROM IMSLP (from Breitkopf & Härtel Sämtliche Werke)
ONLINE SCORE FROM IMSLP (Two-piano score, orchestral reduction by Brahms; first edition from Sibley Music Library [University of Rochester])

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1^st Movement: Maestoso (First movement concerto [Double exposition sonata] form). D MINOR, 6/4 time, with two measures of 9/4.
ORCHESTRAL EXPOSITION
0:00 [m. 1]--Theme 1.  Timpani, horns, violas, and string basses establish the thunderous, heavy “pedal point” on the keynote D.  In the second measure, the first violins and cellos intone the severe, angular downward-arching theme.  The opening outlines the chord not of D minor, but of B-flat major.  Clarinets and bassoons support this.   The continuation includes two trills on a highly dissonant A-flat followed by upward leaps and descents, the second leap a third higher.  The timpani roll swells between the two trills. 
0:18 [m. 8]--As horns re-enter, the violins and cellos sweep up to an even longer A-flat trill followed by a descent, with connecting grace notes leading to two more shorter trills.  The final element is a jagged up-down motion on the B-flat harmony whose overall motion on both the lower and upper notes is downward.  This ends with another A-flat, descending to G, leading to the next presentation.
0:26 [m. 11]--The pedal point moves down a half-step, to C-sharp, but the timpani roll is on A.  Prepared by a new chord halfway through the opening measure, the thematic statement begins anew, now incorporating second violins and with full woodwind harmonic support.  It begins on the chord of A major, which is the “dominant” key and therefore less harmonically ambiguous.  The trills are now a half-step higher than the chord (on B-flat) rather than a whole step lower as before, but they are still dissonant with the pedal point.  The violins are now offset from the cellos, who play their trills and upward leaps in imitation of and overlapping with the violins.  The woodwinds thin to oboes and clarinets against the trills.
0:41 [m. 18]--Winds and horns enter again for the sweep up to the longer trill and descent, again with grace notes leading down to two more trills.  This time, the violas enter in imitation of the violins, harmonizing on the shorter trills, while the cellos join the pedal point.  The violins play the jagged up-down motion, and as they conclude it, the woodwinds (flutes, oboes, and bassoons) imitate the sweep up to the long trill and descent, playing the long trill on E-flat.  The cellos and basses move down a half-step to C.  The violas also imitate this and again harmonize the short trills.
0:52 [m. 23]--The violins, with clarinets, sweep up to another long trill on A-flat as the cellos and basses move down to B.  The oboes, bassoons, and violas (the latter adding shorter reiterations) play the jagged up-down motion, which now forms a colorful “diminished seventh” with the bass pedal on B.  The timpani roll moves up to D.  After the jagged descent, the “diminished seventh” harmony is extended through the first descending trill, now harmonized by the full orchestra.  The second descending trill is on B-flat harmony.  Horns and trumpets punctuate both.  Finally, the bass moves down to A and two short chords, the first one dissonant, at last lead to a full arrival on D minor, where the cellos begin a quiet undulation.
1:01 [m. 27]--Transition.  The cello undulation on the broken D-minor chord, which began under the previous chords, continues for a measure before the first violins, doubled by clarinet, play an expressive new melody in D minor.  It consists of long-held notes, upward-leaping sighs, and short descents, with a swaying character.  The horns play long background notes and the cello undulation shifts.  The melody shoots up an octave, briefly turning to major, as flutes join the presentation.  Moving down in long notes by half-step, the melody settles over “dominant” harmony on A, transformed to minor by cellos and bassoon.
1:23 [m. 36]--The same melody, beginning with its second measure, is now stated in A minor, with the violas joining first violins and without wind doubling.  It is very quiet, with the violins using mutes.  The cellos, having earlier been joined by basses, continue to undulate.  After the brief turn to major and one downward half-step, with the oboes joining, the melody is diverted, twice reaching very high over evocative new “diminished seventh” harmony in the undulating cellos and basses.  The violins and violas cut off, along with their backing winds, and the cellos and basses alone play an upward arpeggio on F.  This key, the “relative” major, is also the “dominant” in B-flat minor, where the next theme will be heard
1:48 [m. 46]--Theme 2a (B-flat minor).  The more substantial Theme 2b will not be heard until the solo exposition.  This one, with its characteristic and melancholy downward swing, is played here by pulsating tremolo violins, accompanied by clarinets, bassoons, and tremolo violas over a held F in the low strings.  The oboe joins as the melody turns upward, a point also marked by a rising arpeggio in the low strings, and the flutes join as it surges up and down toward the half-close marking the end of the phrase.
2:03 [m. 52]--The oboe now has a solo presentation, stating the theme’s first descent against tremolo violins and a low string arpeggio.  When not playing the arpeggio, the low strings hold the “dominant” note F.  The flutes take up the arpeggio from the low strings.  The oboe plays the phrase again, with the low string arpeggio, but the flute response is a step lower.  The oboe drops out, but the flute arpeggios continue, moving down two more steps.  The bassoons and clarinets, emerging from the background, mark the flute arpeggios with their own slow three-note descents in alternation, as do the tremolo violins.
2:17 [m. 58]--The violas suddenly emerge as prominent descending instruments, moving down three notes as the last flute arpeggio is repeated.  Then the low strings, with a syncopated entry from flutes and oboes, suddenly wrench away from B-flat minor toward A minor, a half-step lower.  The low strings move away from their held F.  The violas have another three-note descent, a half-step lower than the previous one.  The low strings and winds make another motion, apparently back to the home key of D minor, and the five-flat key signature, which has been in force since m. 46, now changes back to one-flat.  Meanwhile, the tremolo violins drop out, and a solo clarinet joins the now tremolo violas for a last low, hushed three-note descent.
2:32 [m. 64]--With violent force, beginning on the upbeat, the cellos, violas, and bassoons rise forcefully against chords and a timpani roll from the rest of the orchestra, the violins having removed their mutes.  The rising scale figure turns back down in an arpeggio.  The full orchestra asserts itself with a massive D-minor cadence beginning with three short, loud, fully isolated chords.  Brahms changes the time signature to 9/4 for these chords (three beats, the chord and two rests, for each) to broaden the cadence.  The emphatic arrival on a unison D is given a second 9/4 bar to prepare the grand restatement of Theme 1.
2:43 [m. 67]--With violas supplying a tremolo background, the violins begin Theme 1 on its original notes, but now it is played in full three-part imitation.  The horns loudly imitate the downward-arching figure at a half-measure distance, and the low strings follow that, on the next full measure.  The thunderous timpani roll begins with the low string entrance.  The continuation, with dissonant A-flat trills, leaps, and descents, begins in the violins before the low strings finish their statement of the opening figure.  The three-part imitation continues for the two statements of this figure, the horns limited to an arrival on the A-flat.  Clarinets and bassoons, along with the other pair of horns, provide a background in long-held notes.
2:56 [m. 73]--The sweep to the longer trill follows as at 0:18 [m. 8], but now with the low strings continuing to imitate the violins.  The horn imitation breaks, but there is a loud horn blast that echoes the last two notes of the Theme’s opening figure.  The connecting grace notes and two shorter trills happen in both the violins and the imitating low strings.  Oboes, then flutes enter at this point.  The jagged up-down motion on B-flat harmony follows as expected, and the low string imitation breaks.  It will land on G as before, but now the motion of the “pedal point” to C-sharp does not happen.
3:03 [m. 76]--Closing material.  The orchestra erupts into a new and passionate idea.  Powerful downward motion, led by the violins and incorporating repeated notes, breaks into shorter figures with rising half-steps, each figure a step lower than the last.  The timpani and bass instruments emphasize the secondary harmonies of G minor and A major.  As the violins and high winds move to a jagged, upward-striving line, the powerful downward motion moves to the lower instruments while the trumpets enter.  The jagged motion breaks into hammer-like descending first violin octaves over the shorter figures in the low strings.
3:16 [m. 82]--A new fanfare-like idea suddenly erupts in D major, leaping up and down in the violins and upper winds, supported by march-like figures in the bass reminiscent of Theme 1.  The leaping fanfare is interrupted by longer notes.  This fanfare will be much used and transformed over the course of the movement.  The fanfare figures gradually subside as the clarinets and bassoons, then bassoons alone, trail downward in thirds.  Throughout the fanfare, the bassoons and violas have continued the shorter figures with rising half-steps.  The violas still do so as the bassoons trail away.  The cellos, meanwhile, settle on a three-note octave descent (D-A-D) and everything thins to a murmur in preparation for solo piano entry.
SOLO EXPOSITION
3:38 [m. 91]--Introduction.  The piano’s subdued entry is on new material superficially related to the figures with repeated notes from the closing material just heard.  At first, it is only accompanied by interjections from trumpets and timpani.  Its left-hand bass takes up the D-A-D cello descent.  The right hand quietly surges forth, with longer harmonies emerging into shorter continuations mostly harmonized in thirds and sixths.  The bass descents begin to incorporate G in addition to A as an arching motion concludes the first phrase.
3:48 [m. 95]--The second phrase begins like the first, but it deviates in the second measure.  Plucked low strings join the minimal accompaniment from trumpets and timpani.  The bass descents remain consistent in shape, but the passage makes a detour toward the “relative” major key of F.  The right-hand reaches higher in its arching motion, then extends its descent as the harmonies thicken to full three-note chords.  These chords extend the phrase for two measures and settle on the “dominant” harmony.
4:03 [m. 101]--All strings except basses enter on a quietly held A with their bows.  The piano’s right hand begins a long passage in sixths, beginning with four successive upward surges.  Under these, the left-hand descents first remain on A, then move to C and finally E, along with the held string notes.  The volume steadily builds.  That E indicates a motion toward the “dominant” key that never really arrives.  Instead, the piano continues to surge forth in its sixths, now without breaks, and shortly doubled by the left hand an octave below as it abandons its descents, leaving these to the violas and cellos.
4:17 [m. 107]--The piano sixths begin to be played in groups of two, with repetition between the groups.  Under this, the violins play a rising line suggesting an arrival on A as the violas and cellos continue to play octave descents on E.  When they do reach the A, the violins play an A-minor arpeggio with three notes in the measure, disrupting the 6/4 flow in an implied 3/2 for that measure.  This is supported by the violas and cellos.  The piano, meanwhile, also supports this grouping as it moves from sixths to full chords implying a full arrival back on D minor.  Finally, after a tremendous crescendo, both hands play a huge arpeggio in triplet rhythm (nine-note groups) on a “diminished” chord as the low strings continue the 3/2 grouping.
4:24 [m. 110]--Theme 1.  It arrives mid-stream at a point analogous to 0:41 [m. 18], the “diminished” arpeggio taking the place of the preceding upward sweep.  The piano, in an unusual texture, plays the trill in octaves including the descents with grace notes as the low strings establish the “pedal point” on C-sharp.  Meanwhile, the horns and timpani enter, the latter on another continuous roll.  The piano plays the jagged descent in octaves.  The sweep up to the long trill and descent beginning on E-flat is in the violins, with the low strings moving the “pedal point” down to C.  The woodwinds enter to harmonize the short trills.
4:35 [m. 115]--This is analogous to 0:52 [m. 23].  The long trill on A-flat and the descents following it are again in the piano octaves, with the jagged descent in violins and viola, the low strings moving to B as part of the “diminished” harmony.  The slide down to B-flat in the bass and the timpani roll motion to D occur as expected.  The arrival on D minor, however, deviates from the previous model.  The two short chords are played as expected, by the piano with some support.  The bass instruments, however, while they do move to A, do not settle on the quiet undulation, but begin a lead-in to a new transition based on Theme 1.
4:42 [m. 118]--Transition.  The piano drops out.  After the lead-in from the bass instruments, the upper strings, supported by horns, play the opening of Theme 1 on the chord of B-flat, reminiscent of the beginning.  Meanwhile, the bass instruments continue and play the trill on A-flat.  The violins and the low strings alternate with the opening gesture of Theme 1, directly followed by the trill without a pause, creating an accelerated effect.  There is continuous upward motion as B-flat gives way to G.  The violins reach very high for their second statement and trill.  This all occurs against held woodwind chords and brass/timpani interjections.  A third lead-in from the bass is thwarted by a sudden shift to the “dominant.”
4:53 [m. 123]--At this point, the piano enters and plays a variant of the original transition from 1:23 [m. 36].  Continuous angular chromatic motion in the left hand, winding down before reaching up, takes the place of the previous cello undulation.  The right hand plays the original transition melody, with D minor changed to A major.  The orchestra cuts off before supporting the piano presentation with plucked strings and quiet brass/timpani interjections.  The melody, already in major, continues with the upward reach, including the downward half-step, but the high upward reaches over diminished harmony do not happen, and instead the piano moves down another half-step over the continuing left-hand figuration.
5:11 [m. 131]--The last descent resembles the end of the passage from 1:01 [m. 27], where it was in D minor.  Thus, the young composer has conflated the key of 1:23 [m. 36] with the function of the music before it.  Following the same harmonic implication, the transition theme is stated by the piano in E minor, now with the left hand on the original undulating arpeggios.  Plucked strings and winds (clarinets and horns, later flutes) provide a background.  The high upward reaches over diminished harmony that had been expected now do occur in the right hand with wind doubling, making this statement truly analogous to 1:23 [m. 36], leading to F instead of B-flat.  Bowed low strings and piano left hand play the lead-in arpeggio.
5:39 [m. 142]--Theme 2a (F minor), corresponding to 1:48 [m. 46].  The theme had been played by tremolo strings.  Now it is in triplet arpeggios from the piano, doubled in both hands, with the melody following the upper notes of these arpeggios.  At first, bass strings and horns hold a low note.  Flute and oboe, with harmonic clarinet support, enter to double the melody on the upward reach, as expected, and the rising arpeggio in the low strings also happens as expected.  The piano triplets provide reiterated melodic notes that have some of the same character as the previous string tremolo.
5:54 [m. 148]--The piano cuts off, and the winds and strings seem to follow the pattern from 2:03 [m. 52].  The tremolo violins and low string arpeggio are present, but the melodic statement is from the clarinet instead of the oboe.  The flute does take over the arpeggio from the low strings, as it had done before.  The continuation from here deviates greatly.  The piano enters with trill-like motion in both hands.  The key signature changes to F major.  The first violins then take up the melody in major, repeating its opening gesture over second violin and viola tremolos.  The gesture is doubled by horn, then oboe.  The piano emerges into a full trill, gradually moving up against the melodic gestures.
6:04 [m. 152]--The melody continues down in the first violins, with bassoon joining the oboe on the doubling.  The piano breaks its trill and reaches up in two-note groups, the hands still in octave doubling.  The piano and orchestra then emerge into an implied 3/2 measure (a “hemiola”), with the piano, now in a very high register, reaching down and back up in its two-note groups.  It then moves to trill-like motion in triplet rhythm (nine-note groups), which breaks to become more decorative and then tumbles down.  The woodwinds and violins drop out, leaving only a backdrop of horns and low strings.  The fast piano triplets reach lower, where they trill and turn, slowing to straight rhythm, settling down to lead into the new theme.
6:19 [m. 157]--Theme 2b (F major, Poco più moderato).  This theme has been long awaited, and it is both memorable and noble.  The piano gets to present it by itself in its first true solo passage as the orchestra takes a long break.  The right hand reaches up in rich chords, the left responding with octaves.  Two rising gestures are followed by a descent with some chromatic harmony and an active inner voice in the left hand.  The theme begins again, but the second gesture reaches higher and is followed by a third that moves higher than that.  The right hand then moves down in mildly syncopated figures against marching octaves in the left hand.  These finally emerge into a cadence-like turning figure. 
6:56 [m. 166]--In a most unexpected turn, the piano emerges into the fanfare idea originally heard at the end of the orchestral exposition at 3:16 [m. 82].  Where that had been forceful and dramatic, it is now dolce.  The right hand plays the fanfare figures over undulating triplet motion while the left hand plays wide arpeggios in straight rhythm.  After two measures that resemble the original statement, the fanfare figures rise over three long measures, the volume building, and the harmony favoring the “subdominant” B-flat major.  The second of these measures includes a colorful “diminished seventh” harmony.
7:13 [m. 171]--At the climax, the fanfare figures break, and the piano has a long series of right hand triplets against harmonic thirds in the left hand.  These begin very high and outline an angular melody with the first note of each triplet.  The two remaining notes reach down and scoop back up.  The left-hand thirds, twice supported by a lower C, begin in the treble range, then gradually work down with the right hand.  The harmony strongly suggests the “dominant” C major, but there is a persistent A-flat borrowed from the minor.  Both hands stagnate and reiterate the same figures, then move to an up-down alternation.  The note D-flat is introduced at the very end, with crunching dissonances (seconds) in the left hand.
7:30 [m. 176]--The piano solo ends as the flute enters on an upbeat, leading to an arrival on a D-flat chord.  The piano drops out, and D-flat is revealed as the “dominant” in the very remote G-flat major.  This is confirmed by the clarinets, who play flowing sixths against the flute’s upbeat figure, which is repeated.  The bassoon reiterates the D-flat.  The strings are completely absent here.  The oboe takes over from the flute, narrowing the leap to a third against the continuing clarinets.  It then seems to want to descend to an arrival on G-flat, but this is suddenly thwarted by a striking shift down to C (the “dominant” in F) as the horns enter.  Back in F, the woodwinds, led by the oboe, play the rising gesture and descent from Theme 2b.
8:00 [m. 184]--The strings now get their turn at Theme 2b.  They expressively play the first measure in full harmony, the first violins carrying the melody.  With the second measure, the piano surreptitiously enters on a rising, partly chromatic line in both hands that then breaks into a trill-like downward zigzag.  In the fourth measure, the decorative piano figuration speeds up to triplet rhythm, the hands tumbling down in wide leaps, still doubled in upper notes but not on lower pedal-like notes.  Under this decoration, the string presentation of the theme in these first four measures closely follows the original piano solo statement.
8:15 [m. 188]--The string presentation seems to continue as expected with this second phrase.  The piano decorations, still in triplet rhythm and again fully doubled between the hands, work back up and then stop on a C-F alternation in both hands.  With the second gesture, however, there is a deviation in the strings, which do not reach higher as the piano had done, and briefly turn toward B-flat, also building in volume.  The piano decorations now wind their way upward, reaching very high against the third gesture.  Finally, the woodwinds enter, and with the strings emerge into powerful long-short (half-quarter) punctuations.  The joyous piano figures leap down and back up, adding short breaks in what had been continuous motion.
8:28 [m. 192]--The loud punctuations land on A major.  The piano, still in triplet rhythm, breaks into a series of upward-winding doubled thirds in the right hand against wide-ranging leaps in the left.  The horns, making a dramatic entry, blast out the fanfare idea.  With a forceful shift, punctuated by wind and bass chords, the piano restarts its doubled third idea, and now the violas have the fanfare, back on D.  A third statement of the fanfare is in the second violins on G, the piano figuration beginning yet again after a chord-punctuated shift.  Finally, a fourth statement of the fanfare in first violins continues the pattern on C, briefly imitated an octave below in second violins, the piano figuration continuing without a break.
8:38 [m. 196]--The piano, continuing in triplet rhythm, breaks into a new pattern, gradually tumbling down.  The right hand now plays in double fourths.  The left hand initially has wide descending arpeggios, then briefly moves to downward leaps in “straight” rhythm.  The strings and horn quietly drop out after a violin descent.  The piano, left alone and rapidly quieting down, continues with the fourths in the right hand and wide alternations in the left hand (which is back in triplets).  As it moves down, the left hand adds some harmonies.  Finally, both hands slow to “straight” rhythm before gently descending onto an F-major chord.
8:49 [m. 199]--Closing material.  As the piano makes its arrival, the strings re-enter on a murmuring oscillation of trill and tremolo-like figuration in triplet rhythm.  A horn sneaks in with an extremely sweet version of the fanfare idea, supported by a low note from its companion and harmonies from clarinets and bassoon.  The fanfare is presented in its usual twofold version.  As it is completed, the horn reaching high, the piano bass, supported by the low strings, surreptitiously enters. 
8:57 [m. 201]--The horns and winds drop out as the piano breaks into a rhapsodic solo passage beginning with rising triplet arpeggios.  A decorative melody then develops in the right hand in “straight” rhythm against arching triplet arpeggios in the left.  Only plucked low strings accompany.  The melody in the right hand develops a lower imitative counterpoint before bowed strings quietly re-enter and the horn unobtrusively inserts a reiteration of the second fanfare gesture.  This ends the first melodic statement of the piano’s heartfelt reverie.
9:09 [m. 204]--The piano begins another statement of its melody, making a striking shift to D-flat major, now only against a low A-flat in the cellos.  When the counterpoint enters in the right hand, it adds some triplet figures, creating a tension between groups of three and two.  The left-hand arpeggios become even wider and more sweeping.  The phrase is extended, and the piano slides back to F, but now F minor, supported by a motion in the cellos and plucked basses.  A few first violins unobtrusively enter with falling octaves that gradually move down, and a low horn also comes in.  The piano figures change to F major, slowing to another arrival, the left hand settling on an octave oscillation on the “dominant” note C.
9:35 [m. 210]--The piano moves to quietly rippling, melodically and harmonically active triplet arpeggios in both hands over a reiterated bass F.  The horns alone now join it.  The upper one has an extended solo on the fanfare figure.  After the twofold statement, it extends the solo with three more reiterations of the opening leap, the first note of each moving gradually down against the continuing piano arpeggios, which briefly hint at B-flat.  Joined by its companion, it now slowly descends two octaves to a very low, resonant F, which is held as the piano arpeggios move up steadily on the F-major chord.  The left hand, which has worked up to the treble register, finally changes to “straight” octaves against triplets in the right.  The upper left-hand notes interlock with the right-hand triplets, creating a 1-2-and-3 bell-like effect over one measure.
10:01 [m. 216]--The conclusion and transition to the development is taken by the orchestra as the piano drops out.  The violas provide a shimmering tremolo background.  The oboe leads a wistful reminiscence of Theme 2a in B-flat against clarinet/bassoon chords and the continuing low horn note.  Before its upward turn, the violins imitate the tune in F.  They pass the upward turn to the entering flute and the oboe, which has just finished the first one.  But another imitation now follows, in the cellos, again in B-flat as the horn note fades out.  A final imitation, again on F, is in the string basses and bassoon, but it does not turn up.  Instead, the upward turn in the cellos leads to a mild dissonance, then a quiet, reverential cadence.
DEVELOPMENT
10:49 [m. 226]--The exposition has ended in a hazy state of suspended, dreamlike stillness as the orchestra fades out.  The extreme contrast of the abrupt fortissimo entry of the piano, playing doubled octaves in both hands in a massive unison eruption, shocks the listener out of that haze.  The material is the fanfare idea, but this devolves into a series of incredibly difficult four-note descents, still in fourfold doubled octaves.  Finally, they stall on a turning figure, moving from F back to the home key of D minor.  A timpani roll begins on D and builds.  Horns and trumpets also enter and swell on that note.  Middle strings, bassoon, and clarinet sneak in.  The piano octaves now shoot up in a detached zigzag pattern, arriving on B-flat.
11:00 [m. 231]--The pedal point is established on D by the timpani roll and the basses.  The strings and horns intone the first gesture of Theme 1 in its original orientation on the B-flat chord against clarinets and bassoons in the background.  But instead of moving to the expected trill, the orchestra cuts off, including the timpani, leaving only the background instruments and bass.  The piano enters with another passage of octaves, now much quieter and doubled threefold (the left hand playing only one line).  They wander up and down, gradually spreading out and then shooting up, building strongly.  They suggest the key of E-flat.  At the top, both hands tumble down in an angular pattern, the right adding lower harmonies.
11:13 [m. 237]--The orchestra, which has gradually entered and swelled with the piano, enters again with the Theme 1 gesture, wrenching it down a half-step on the chord of A major with C-sharp in the bass.  The piano responds with the same triple-octave pattern, now suggesting D major.  It reaches a high point and tumbles down in the angular pattern, as before.  This time, the orchestra does not interrupt with the Theme 1 gesture, but the piano itself shifts down another half-step (C-natural in the bass strings), repeating the tumbling angular pattern.
11:29 [m. 244]--A pattern of exchanges begins between the unison strings (supported by winds) and the piano on the angular pattern.  The strings, rapidly repeating each note, work up while the piano, adding harmonies on alternating notes, moves down.  At first the bass continues to descend to B and then A, but then each exchange moves down the circle of fifths, from A to D to G to C.  The mood is extremely agitated.  After two exchanges, they are shortened by half for three more, and the bass motion again descends, from C to B to A.  The energy spills into a powerful “diminished seventh” harmony on G-sharp.
11:43 [m. 251]--After the arrival on the “diminished seventh,” the piano sweeps up in a rapid arpeggio and emerges into the familiar descending trills beginning on F.  Because of the arrival point and arpeggio, the initial trill, usually long, is as short as the others, but the pattern continues through a second statement with the expected long trill moving to the short ones.  Against these trills, the cellos and basses play an upward line suggesting the undulations that typically underpin the transition theme.  The winds, with pulsing horns, provide the background.
11:52 [m. 255]--The piano drops out, and the orchestra suddenly quiets down.  The violas, intermittently doubled by bassoon and clarinet, play the undulation previously taken by the cellos.  The “diminished seventh” on G-sharp is still the prevailing harmony, and the undulations outline the upper notes of that chord above the persistent G-sharp bass in the cellos.  Horns provide harmonic support.  The viola undulations continue for four measures before the actual beginning of the transition theme.  The last two measures change from the “diminished seventh” to an E-major chord, still with G-sharp in the bass.
12:00 [m. 259]--The cellos and basses now play the transition theme, in the form as at 1:01 [m. 27] but in the A-minor key as at 1:23 [m. 36] and 4:53 [m. 123].  The violas continue the undulation, along with the bassoon and clarinet doubling.  At the upward octave leap with its turn to major, there is no descending half-step.  Instead, the piano enters against it and begins to play the theme in C-sharp minor, in simple octaves divided between the hands.  The low strings add another varied upward turn underneath this against the continuing undulation.  The violas are now doubled by clarinet and flute.
12:20 [m. 267]--As the piano statement turns to major with its upward turn, it dovetails with yet another statement of the theme in the low strings.  Transforming C-sharp into D-flat, it is in the key of B-flat minor.  After two measures, the doubling woodwind instruments (now two clarinets) drop out, and first violins join the violas on the undulation.  The piano shifts its second upward turn up a half-step.  As the low strings make the turn to B-flat major on the upward turn, there is one last dovetailing statement, again in piano octaves in the key of E-flat minor.  Instead of another upward turn, the low strings finally make the familiar half-step drop.
12:35 [m. 273]--The dialogue breaks off, and finally, the familiar upward reaches and descending half-steps over diminished harmony alternate between the cellos and the piano octaves.  Oboe and bassoon join the cellos.  The first violins and violas continue their undulation.  The piano notes are on the downbeats and the cellos, with their accompanying winds, play halfway through the measure.  Two such exchanges of the upward leap and half-step descent gradually fade away.  Finally, the first violins and violas play the “lead-in” arpeggio on the “dominant” of B minor, in preparation for the suddenly forceful music that follows.
12:48 [m. 278]--The piano, with sudden force, bursts forth with a new variant of Theme 2a in B minor, complete with a change in key signature to two sharps.  The theme is compressed and initially presented in sixths against a rising left-hand arpeggio.  The sixths are quickly expanded with a lower octave, as is the left-hand arpeggio.  The left hand soon joins the harmonies in sixths.  Only plucked low strings and horns underpin this opening.  The low strings, however, quickly take over the upward arpeggio.  The violins enter on the compressed theme and combine it with the upward arpeggio as the piano breaks into arching triple octaves.  These arching octaves are then isolated in the left hand as the right again begins the theme.
12:57 [m. 283]--Now both hands of the piano isolate the rising arpeggio in octaves and play it in alternation, the right hand on the upbeat and the left on the downbeat.  The strings drop out, and the woodwinds, who have gradually snuck in, build strongly.  The rising arpeggio slides up a half-step as the trumpets enter, along with the timpani on a rolled D.  Because the piano octaves here are so fast and so difficult, Brahms indicates the upper note can be dropped from the left hand.  The rising octaves move up one more half-step, and then they break.  The piano and winds, in forceful, isolated chords, prepare what appears will be a massive cadence in B minor.
13:06 [m. 287]--Suddenly, the volume drops to piano, and the arrival is not in B minor, but B major.  In an almost playful exchange, a plucked descending line in the violas alternates with a major version of the new Theme 2a variant in the violins.  The piano, meanwhile, plays fast and skittish arching figures that are exchanged between the hands, moving down an octave each time.  These are played against the plucked violas.  Against the violins, the piano moves to a rising arpeggio in triple octaves.  Woodwinds and plucked low strings play brief interjections.  This pattern is stated in sequence on B major, F-sharp major, and E major, the violin melody moving down by step with each exchange.  The violins then swell and veer to the distant C major, supported by winds, as the piano’s fast arching figures tumble down over a full measure
13:14 [m. 291]--The previous passage is repeated a step higher, beginning on C major, moving to G and F, and finally with the violins swelling and moving to D, with the “dominant” note A in the bass.  This arrival of the home key (not yet established as major or minor) signals that the re-transition is imminent.  In two bars bridging to that re-transition, the rapid arching figures of the piano continue over “dominant” harmony, still passed between the hands and moving down (sometimes back up) by octaves.  These piano figures are supported by plucked strings and held wind chords.
13:26 [m. 297]--Re-transition.  The piano briefly cuts off.  The key signature changes back to one flat.  The bass establishes itself on a long “pedal” point on the “dominant” note A.  This sustained A is provided by a low horn, a continuous timpani roll, and the string basses.  The Theme 2a variant in oboe, then clarinet, alternates with the descending line in bassoon and plucked cellos, still more in major than minor.  The upper strings play shifting harmonies in tremolo.  The volume is still soft.  The piano enters with the Theme 2a variant, but this blossoms into an ominous rising line in triple octaves hinting more at minor.  This is played in three waves, first as a scale, then adding leaps between half-steps by the third “wave.”
13:34 [m. 301]--The rising line moves to the oboes, clarinets, violas, and cellos while the piano reiterates a low A.  Trumpets, flutes, and bassoons enter with supporting chords and interjections.  The rising line is played in two waves, each starting with the Theme 2a variant, and including leaps between half-steps.  Minor ie firmly established by the second wave.  The woodwinds then drop out, and the piano takes over the rising line.  It appears to play it in three “waves” as before, but the third is expanded over another full measure, reaching very high.  The string tremolo, the timpani roll, and the bass pedal all swell in volume.
13:44 [m. 306]--In a tremendous climax, the full orchestra enters at the top of the piano’s run.  The first blast is followed by a piano chord, and then the subsequent chordal blasts are all preceded by fanfare-like triplets.  Piano chords are played between each orchestral outburst on beats 2 and 5 over two measures.  Then the orchestral and piano chords alternate directly in a hemiola (implied 3/2), with piano chords on beats 2, 4, and 6.  An inner voice in the piano chords has descended a full octave before the extraordinarily powerful arrival at the recapitulation. 
RECAPITULATION
13:54 [m. 310]--Theme 1.  The arrival is a huge cadence onto bare octave D’s.  The timpani roll and bass pedal point are established there, as at the very beginning.  The piano soloist now takes the thematic presentation, and in one of the most notable and commented-upon aspects of this vast movement, it is not on the B-flat harmony heard at the beginning, but on a very full and bright E-major chord supported by clarinets, albeit with the persistent D in the bass (which essentially converts it to a “dominant” chord).  The angular opening also outlines that chord.  The trills (now on F), leaps, and descents are in triple octaves.
14:11 [m. 317]--Analogous to 0:18 [m. 8], the primary differences being the continued piano presentation and the pitch orientation.  The long trill (led into by a rising triplet) is again on F, with connecting grace notes leading down to the short trills on D and B-natural.  Significantly, and differing from the beginning, the “pedal point” changes here in the low strings (but not the timpani and horns), making a striking move down a tritone to G-sharp (which supports the E-major environment).  The jagged up-down motion is on the E-major chord.  The last note is D, which will move down to C-sharp.
14:18 [m. 320]--Analogous to 0:26 [m. 11].  The theme arrives on C-sharp, and the bass “pedal” slides down to G, a reversal from the opening, but since the notes are the same, the presentation on the chord of A major can occur as in the original statement.  Thus, the striking E-major chord was not as remote as it seemed.  A chord in the winds prepares the thematic statement, still in the piano.  The imitations of the trills and leaps, previously in the cellos, are now in first violins and violas, as the cellos are still holding the “pedal” note G.  As before, the timpani roll moves to A.  The woodwinds thin to just clarinets.
14:34 [m. 327]--Analogous to both 0:41 [m. 18] and 4:24 [m. 110].  The piano approaches the trill on B-flat with another rising triplet in octaves.  First violins and violas play the upward sweep, imitating the trill motion and harmonizing the short trills.  The bass “pedal point” moves down to C-sharp, finally matching the original presentation.  Oboes, clarinets, and horns provide a background.  The piano plays the jagged descent.  Violins sweep up to the long trill on E-flat.  The “pedal point” moves down to C, and woodwinds enter in imitation, harmonizing the short trills.
14:46 [m. 332]--Analogous to 0:52 [m. 23] and 4:35 [m. 115], but more closely to the latter.  In the previous passage, correspondence to the orchestral exposition had subtly shifted to the solo exposition, and that shift is completed here.  In fact, the passage matches 4:35 [m. 115] almost exactly, with the long trill on A-flat and the following shorter trills in piano octaves, the jagged descent in violins and violas, the low strings moving to B and B-flat, and the timpani roll motion to D.  The bass instruments begin the lead-in to the new transition.  The only real difference is the participation of woodwinds in the two short chords.
14:52 [m. 335]--Transition.  Analogous to 4:42 [m. 118].  The dialogue-like exchanges between the upper strings/horns and the bass instruments on the Theme 1 opening are dispensed with, and only the bass retains its statements of that gesture.  The upper strings and horns are replaced by powerful (con forza) chords and octaves in the piano (which had dropped out in the previous passage).  This piano material does follow the expected harmony.  Jagged descents and thrusting upward chords are followed by rapid upward scales in octaves that bridge to the second sequence.  A third begins, but the jagged descent restarts, moves down, and builds strongly, extending the passage by a measure, the bass sliding from B to B-flat.
15:05 [m. 341]--Most unexpectedly, the full orchestra, led by violins and high woodwinds, erupts into the piano’s introductory material to the solo exposition from 3:38 [m. 91], which has not been heard since then.  The piano itself almost ironically drops out here.  The melodic outline and the harmony follow the first four measures exactly, but the character is completely transformed by the loud entry (it had been subdued) and the tremolo strings.  The volume rapidly diminishes, and the orchestra is cut off on an abrupt turn to major.  The turn to the original transition is omitted, and that music, last heard at 12:00 [m. 259] will not return.
15:14 [m. 345]--The piano makes a mysterious entry on rapidly ascending triplet-rhythm arpeggios, doubled at the octave in both hands, that suggest “diminished” harmony.  At the same time, the horns play a snippet of the principal theme in major against a timpani roll.  This is fragmented and passed to the violas and cellos.  These instruments move to pizzicato and fade away, as do the rippling piano arpeggios, which turn the harmony up a step to E minor.
15:21 [m. 348]--The woodwinds now state the “introductory” material in E minor, far more subdued than the presentation at 15:05 [m. 341].  The strings discreetly accompany the statement and briefly double it, with some tremolo in the (now bowed) violas.  The cellos remain pizzicato. Once again, there is a turn to major at the end.
15:31 [m. 352]--The piano again enters with its mysterious triplet arpeggios.  The major-key fragment of the principal theme is now in bowed cellos and second violins instead of the horn.  The continuation leads as before to pizzicato violas and cellos, moving up a step to F-sharp minor as they fade away.  That is the target key, where Theme 2a will soon appear.
15:38 [m. 355]--The “introductory” material is now taken by its original instrument, the solo piano, in the key of F-sharp minor.  This is not, however, a continuation of the sequence.  Instead, the piano’s presentation closely matches that at 3:48 [m. 95], transposed to the new key.  As it was there, the accompaniment is sparse, with plucked string interjections, but now there is a background of held woodwinds.  There is a brief suggestion of the “relative” A major, but as would be expected, the passage ends on “dominant” harmony in F-sharp minor.
15:54 [m. 361]--Because Theme 1 and the transition have already been heard, all of the material that had followed 3:48 [m. 95] does not appear.  It is replaced by this brief bridge to Theme 2a played by the piano alone.  It is simply a downward-winding passage in firm octaves that emerge into an implied 3/2 grouping.    These octaves in turn dissolve into a sequence of dolce arpeggios on the “dominant” chord.  These move up an octave twice before the third one is repeated at the same level leading into Theme 2a.
16:11 [m. 366]--Theme 2a (F-sharp minor), corresponding to 5:39 [m. 142] and 1:48 [m. 46].  This is the fourth key in which this theme appears, none of which is the “home” key.  As in the solo exposition, it is given in delicate and decorative piano octaves, but the constant triplet arpeggios are replaced by more irregular arpeggio patterns in straight rhythm.  As before, the melody can be discerned in the higher notes.  This time, the accompaniment is in low strings alone, and they enter immediately with a new arpeggio and slow descent before playing their original later arpeggio.  There is no woodwind entry. 
16:29 [m. 372]--The continuation follows the pattern from 5:54 [m. 148], which itself was derived from 2:03 [m. 52], but a crucial structural point is hidden.  The tremolo violins (now with violas), low string arpeggio, melodic clarinet entry (now continued by the low strings), and flute arpeggio are as expected.  The piano entry, however, is delayed by a measure and begins with an arpeggio against the violin takeover of the melody (now doubled by clarinet instead of horn).  Its trill starts a measure later, and here, the violins (doubled by oboe and horn) significantly but unobtrusively drop the melodic repetition by a third, shifting the key toward D major.  From this point, the recapitulation is a literal transposition of the solo exposition.
16:41 [m. 376]--Analogous to 6:04 [m. 152].  With the delayed arrival of the home major key, Brahms allows himself to literally follow the remainder of the solo exposition.  The violin continuation is played against the piano’s upward-reaching two-note groups before the implied 3/2 “hemiola” and the high trill in fast nine-note-group triplets, which tumble down before slowing in preparation for the return of Theme 2b.
16:56 [m. 381]--Theme 2b (D major, Poco più moderato), corresponding to 6:19 [m. 157].  This is a direct transposition of the long-awaited piano solo theme from the “relative” F major to the “parallel” or “home” D-major key.  The rising gestures, chords, left-hand octaves, syncopation, and cadential turn are presented.
17:36 [m. 390]--Corresponding to 6:56 [m. 166], the piano emerges into the dolce fanfare figure against undulating triplets and wide left-hand arpeggios.  The fanfare figure rises over three measures as before, favoring the “subdominant” (now G-major) harmony and including the colorful “diminished seventh.”
17:55 [m. 395]--Climax with right hand triplets whose top notes outline an angular melody, played against thirds in the left hand, corresponding to 7:13 [m. 171].  As the piano works down and diminishes in volume, the “dominant” A major is suggested, with the hint of minor provided by F-natural.  Then both hands move to static reiterations and up-down alternation, and the dissonant note B-flat is introduced.
18:12 [m. 400]--Wind passage corresponding to 7:30 [m. 176], beginning with the chord of B-flat and with significant rescoring.  The upbeat and leaps are now played by clarinet instead of flute (the first upbeat is omitted in the older editions, including the Breitkopf Sämtliche Werke reprinted by Dover--a review of the editing and source questions is outside the scope of this guide).  The flowing sixths are now divided between flute and bassoon, and the reiterated B-flat is now taken by the horn. The clarinet also continues where the flute had passed to the oboe.  An arrival on E-flat is averted with a harmonic shift back toward D, and the rising gesture and descent from Theme 2b is more richly scored approaching the D-major cadence.
18:44 [m. 408]--String statement of Theme 2b, corresponding to 8:00 [m. 184].  The piano again sneaks in with the rising, partly chromatic line doubled in both hands, breaking into a trill-like downward zigzag and then tumbling down in fast triplet rhythm with the left hand on lower pedal-like notes.
19:00 [m. 412]--String continuation, analogous to 8:15 [m. 188].  Piano decorations work up and stall on an A-D alternation.  Buildup in volume over the next two gestures with a turn toward G, the piano decorations working very high.  Woodwind entry, joining the strings on powerful long-short punctuations with breaks in the joyous piano figures.
19:13 [m. 416]--Corresponding to 8:28 [m. 192], the loud punctuations land on F-sharp major.  The piano breaks into figures with doubled thirds in the right hand and wide leaps in the left, as before.  The fanfare enters dramatically, as expected, but now the horns do not play it, but instead support the violas, who had previously played the second statement.  The statements of the fanfare are thus shifted, with the second violins on the second one (on B) and the first violins on the third one (on E).  The fourth statement is given in imitation between second and first violins (on A), but the fanfare gesture itself is cut off (which it was not before).  The forceful shifts with chord punctuations follow the previous pattern.
19:24 [m. 420]--Piano continuation , corresponding to 8:38 [m. 196], with double fourths in right-hand triplets against wide descending arpeggios and leaps in the left.  Unlike the corresponding passage, the low strings and horn hold a note beyond the violin descent as the piano quiets down and slows in “straight” rhythm to its gentle descent onto the D-major chord.
19:35 [m. 423]--Closing material, corresponding to 8:49 [m. 199].  Murmuring strings in triplet rhythm against the horn entry with “sweet” version of the fanfare idea.  The scoring of the supporting instruments is as before.  The horn reaches high, and the piano bass surreptitiously enters with low string support.
19:44 [m. 425]--Rhapsodic piano passage, analogous to 8:57 [m. 201].  Decorative melody in “straight” rhythm against triplet arpeggios in the left hand.  The imitative counterpoint begins, the bowed strings enter, and the horn reiterates its second fanfare gesture.
19:56 [m. 428]--Second statement of piano melody, analogous to 9:09 [m. 204].  The harmonic shift is to B-flat major, against a low F in the cellos.  The counterpoint adds new triplet figures, as before.  The extension of the phrase slides to D minor.  The pair of violins enters unobtrusively as before, with downward-moving broken octaves, but this time there is no low horn note.  The piano figures shift to D major and slow to an arrival as he left hand oscillates on a low “dominant” note A.
20:23 [m. 434]--Piano motion to quietly rippling, melodically and harmonically active triplet arpeggios in both hands, analogous to 9:35 [m. 210], over a reiterated bass D.  The horn solo on the fanfare figure begins against the piano arpeggios, extended by the three reiterations of the opening leap with the low note moving down.  The second horn joins for the slow descent, now to a low D.  From here, the pattern deviates, replacing the serene conclusion with a more ominous transition to the surprisingly grim coda.
20:40 [m. 438]--Transition to coda.  As the horns drop to the low D, the piano arpeggios deviate strikingly from the earlier model.  They move down instead of up and turn worryingly to D minor, undermining the expected close of the recapitulation in major.  At the same time, in another ominous sign, the timpani enter on a reiterated A-D, reminiscent of the fanfare.  This continues for four measures, and in the last two, the left hand moves from triplets to “straight” rhythm, interlocking with the right-hand triplets.  Instead of the “bell-like” effect, however, these figures become threatening, narrowing to buzzing half-step and whole-step alternations in a fifth measure as the timpani beats move to steady alternation.  A sixth measure reaches a half-close on the “dominant,” but the low strings enter with the familiar arpeggio lead-in to Theme 2a.
CODA--Tempo I poco più animato
21:07 [m. 444]--Theme 2a has been heard in four different keys, none of them the home key.  Now, out of the suspended half-close, that theme is finally given in D minor.  It is not the original version, however, but the agitated variant from the development section at 12:48 [m. 278], played by piano alone.  It begins with some hesitation.  The right hand plays the compressed version in sixths, but the left-hand arpeggios are initially slower.  Soon, however, it picks up and builds with the marking più agitato, as the left hand breaks into octave arpeggios and the right also adds octaves.  There is no orchestral support, the previous string parts being taken by the piano.  The first two measures of arpeggios from 12:48 [m. 278] are included.
21:21 [m. 451]--The Theme 2a variant is suddenly interrupted by the forceful entrance of the orchestra with Theme 1 in major.  The piano continues with octave arpeggios, now with both hands together.  The presentation of the theme in major gives another illusion of triumph that will be thwarted.  After the first Theme 1 gesture, the piano plays two block chords and drops out.  The orchestra continues, expanding the Theme 1 trills, which rise in the first violins while the second violins, violas, clarinets, and bassoons play a series of downward arpeggios beginning with long notes.  This appearance of Theme 1 in major could be the beginning of the coda proper, the Theme 2a variant corresponding to the passage from 10:01 [m. 216].
21:37 [m. 459]--The last passage, with the rising trills and hammer-like arpeggios, has already moved away from major.  Now, the orchestra emerges into a grand hemiola (implied 3/2 measure), with three sustained chords followed by two shorter ones that restore the 6/4 feel.  The return of minor is briefly assuaged by a grand arrival on the “dominant” A-major chord.  At that point, the piano again enters with octaves in both hands in an arching pattern.  The A-major chord is reiterated twice more over the next two measures, with the response from the arching piano octaves being placed higher each time.  After the third chord, the octaves rise without arching back down.
21:48 [m. 464]--Now the piano octaves break into a hammering pattern that sounds somewhat familiar, punctuated by descending orchestral chords that move away from the “dominant.”  The hammering pattern becomes more active, and it becomes apparent that it is derived from the long-absent closing material of the orchestral exposition at 3:03 [m. 76], which also generated the piano’s introductory passage first heard at 3:38 [m. 91].  After a descent over a rising orchestral scale, the “hammering” pattern continues, now against short leaping notes from the strings, which stop as the piano octaves move to two rising gestures.
22:01 [m. 470]--The “hammering” pattern starts again with a dissonant “diminished” chord leading into the descent.  The strings rise, then again break into the short leaping notes.  The piano octaves once again emerge into the two rising gestures, which now lead to a strong cadential arrival punctuated by trumpets and timpani.
22:09 [m. 474]--Now it is apparent that the D-minor ending is inevitable and will be emphatic.  The violins take over the “hammering” gestures, converting them into an inexorable wind-up to the conclusion.  The lower strings below them have plucked chords.  As for the piano, it now abandons the “hammering” pattern in favor of sweeping gestures in triplet rhythm that briefly rise, then tumble down.  This “wind-up” is given two full statements, with timpani punctuating the end of each.
22:17 [m. 478]--The “hammering” violins now rise toward the final arrival as the swirling piano triplets continue unabated.  For most of the “hammering” passage since 21:48 [m. 464], the strings have been discreetly supported by winds, primarily bassoons and horns, before the entry of trumpets and timpani.  These latter instruments now become prominent.  After two measures, the strings march up as the piano triplets change from the swirling figures to a winding ascent.  Finally, both piano and orchestra thunder down in an arpeggio, the former in triplets and the latter in “straight” rhythm.  Four monumental D-minor chords close a monumental movement.  The first three rise, crashing down on the final held one.
22:40--END OF MOVEMENT [484 mm.]

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2^nd  Movement: Adagio (Ternary form).  D MAJOR, 6/4 time.
A Section--D major
0:00 [m. 1]--The orchestra’s lengthy opening statement presents the reverential principal theme.  The violins (with mutes throughout the movement) and violas play the broad theme in unison.  A long note is followed by a leap up a fourth and a yearning descent.  This turns searchingly upward to the “dominant” A.  The cellos and basses initially hold a low pedal D before descending to a low A at the end.  Brahms marked this opening melody with the liturgical phrase “Benedictus qui venit in nomini Domini,” which fits if the slurred notes are given a single syllable.  The bassoons have an active, prominent counterpoint in thirds, steadily arching down and back up, usually contrary to the strings.  The horn enters on the closing A.
0:39 [m. 6]--The cellos, doubled by the horn that has just entered, continue the melody with a five-note figure derived from its opening, which will become prominent throughout the movement: an upward leap beginning on a weak beat, followed by a stepwise descent.  The violins and violas respond to this figure and extend it as the cellos and basses imitate and harmonize their response, beginning with a wider leap of a seventh.  The descent now begins with a third.  The string extension concludes with a downward octave leap and a short ascent to another A.  The bassoons continue their active counterpoint, now no longer in parallel thirds, and the horn holds notes after its initial gesture.
1:03 [m. 9]--The bassoons attempt to finish the cadence, but the flute, with clarinet support, interrupts with the leaping seventh and descent.  This is imitated by the low strings after three notes, but the patterns deviate after the first four notes.  The violins and violas then have their own imitation beginning a fourth higher, hinting at the “subdominant” key of G.  The flute and clarinets drop out, and the upper strings, with support from bassoons, horn, and lower strings, emerge into the short ascent to A.  This time the A drops down to D, creating a full and closed D-major cadence with trailing bassoon.
1:40 [m. 14]--The piano enters with the conclusion of the orchestral cadence, and the orchestra now drops out.  The piano presents its theme, which is loosely derived from the opening orchestral melody, molto dolce espressivo.  With full and active harmony doubled in both hands, the melody descends.  Each of three two-note syncopated descents is followed by a longing upward leap.  The third of these leaps extends into a descent with a dotted (long-short) rhythm.  The active harmony consists largely of radiant thirds.  The melody reaches higher, to the familiar “dominant” A.  Syncopated descents against rolled chords complete the harmonic arrival there.
2:18 [m. 19]--The bassoon and horn have entered with the piano’s arrival on A.  They follow with the five-note figure, supported by a chromatic rising line in flute and clarinet (the latter with an added harmony).  The piano briefly pauses here.  The strings respond to the five-note figure with a fragment of the theme, colored by minor-key harmonies.  They again arrive on A in preparation for the piano’s re-entry.
2:38 [m. 21]--The piano’s next statement begins much like the first, including harmony in sighing thirds, but the five-note figure is heard in the bass before the hands are doubled.  It steadily rises and builds.  The horns enter against it with a descending fifth in octaves.  The piano’s buildup hints at the “subdominant” G.  When the low strings enter with a rising line, the buildup intensifies.  A three-note upbeat leaping down to a longer note becomes prominent at the climax.  This is heard three more times as the piano recedes from that climax and descends again, the sighing thirds asserting themselves.  The low string accompaniment also meanders downward.  A drawn-out D-major cadence concludes with sliding motion in a “tenor” voice.
Transition to B Section
3:20 [m. 27]--Very quietly, the strings enter against the piano cadence, with the cellos and basses on the now-familiar descent, the first violins following.  The harmony ventures toward E major (as the “dominant” of A major) in a second descent with first violins following the lower strings.
3:37 [m. 29]--With the strings’ arrival, the piano enters with no accompaniment.  The left-hand bass initially remains anchored to a low E, alternating with steadily rising notes above it.  The right hand, meanwhile, breaks into rhapsodic triplets that wind down with some syncopation over a slower-moving middle voice.  The triplets clash with the “straight” rhythm in the left hand.  The low bass note becomes more active, circling around the E, although the top left-hand notes still rise.  The overall sound is quite dissonant, despite the dolce marking.  The arrival point is again E major as the “dominant” of A.
3:51 [m. 31]--The strings have another, darker version of their previous passage with the first violins following cellos and basses.  An initial motion to B minor is diverted to F-sharp major (its “dominant”) on the second descent.
4:07 [m. 33]--The piano again enters with similar material, a left-hand bass anchored to and then circulating around F-sharp, with a rising upper left-hand voice in alternation.  The right hand’s “rhapsodic” triplets are again heard with their characteristic syncopation.  These triplets are extended, and the left hand’s upper voice begins to move down, which it had not done before.  The extension continues into another measure as the bass drops to a low F-sharp and then drops out.  At that point, the triplets lose their syncopation and begin to meander down with several chromatic notes, reaching into the tenor range before turning back up on a colorful “diminished” arpeggio, leading to the arrival on B minor.
B Section--B minor
4:36 [m. 37]--The beginning of the B section is somewhat obscured because it happens in the middle of a very long piano solo passage without orchestra.  Its arrival is marked by the first forte of the movement.  The right hand has two octave leaps that outline B minor, separated by a leap down to a rising half-step.  The left hand has a rising bass line along with mid-range octaves on the half-beats.  The right hand then plunges down, emerging into strong syncopations and pungent “diminished” chords against the continuing left-hand pattern.  That pattern subtly drops the bass line, leaving the syncopated off-beat octaves.  The right-hand chords become steadier, working down, and moving toward the “dominant” F-sharp.
5:01 [m. 41]--The pattern with the octave leaps begins again, aborting the motion to F-sharp.  The second leap is widened to a tenth.  Instead of the downward plunge, the right hand emerges into a decorative five-note turn figure before another wide leap.  The left-hand octaves become closer harmonies, and the bass line on the beat is not abandoned.  The right hand continues with angular leaps before flowing down as the volume diminishes.  The anticipated shift to F-sharp arrives, but it is the minor version of that key.  The piano begins a pattern of flowing arpeggios before the upbeat, rising once before continual falling patterns.
5:26 [m. 45]--The first orchestral instruments to enter after the long piano solo are the clarinets, which come in on the upbeat with a mournful melody harmonized in thirds and sixths, a bassoon soon entering against them.  The piano arpeggios continue to fall, establishing a “pedal point” on a low C-sharp.
5:39 [m. 47]--With a sudden forte, the remaining woodwinds join to echo the clarinet melody as the piano bass drops to F-sharp.  The strings also enter with a forceful harmonized F-sharp-minor arpeggio.  This is passed to the piano (C-sharp minor) and then back to the strings (A major) as the woodwinds continue, manipulating and intensifying the mournful melody, making it more triumphant with some piano support. The forceful arpeggios are passed to the piano a second time (E major) as the woodwind melody continues with another statement.  Finally, the strings plunge back down on C-sharp minor, receding as they do.
5:53 [m. 49]--The orchestra once again drops out, and the piano restates the pattern from 5:01 [m. 41], now decorating the top of the leaps with rising half-steps.  The five-note turn figure follows as expected.  The left hand follows the previous pattern exactly for two and a half measures, but more decorations are added to the right hand, with the downward-flowing line largely in faster triplet rhythm.  The end of the passage is changed harmonically to arrive back at B minor instead of F-sharp minor for the flowing arpeggios.
6:19 [m. 53]--The mournful melody in thirds begins as at 5:26 [m. 45], but it is now the oboes that enter to play it instead of the clarinets, and it is in the section’s main key of B minor.  They are joined by the bassoon, as the clarinets had been.  The piano arpeggios now establish the “pedal point” on F-sharp.
6:33 [m. 55]--Instead of the sudden forte, the clarinets now enter, beautifully shifting the melody in thirds to B major with bassoon support.  The piano arpeggios continue, and the strings surreptitiously enter, beginning with second violins.  The major version of the melody is not quite completed, as its last note is cut off.  The violas and cellos echo the last gesture, turning back to minor.  The piano arpeggios slow to triplets.  The cellos and basses have a final echo of the gesture in ominous pianissimo.  The piano answers with mysterious chords, including a “diminished seventh,” seeming to delay the last anticipated arrival on B minor.  But this is completely avoided with the abrupt return of the A section material.
A’ Section--D major
6:59 [m. 58]--Brahms mitigates the sudden return of the opening orchestral statement by altering the first measure.  The melody, now in solo oboe and cellos, begins on F-sharp instead of D, easing the transition from B minor, and the opening note is split into three half-notes that mildly disrupt the 6/4 meter.  The clarinets join the bassoons on the active counterpoint in thirds, and the horns are present from the outset, joined on the low pedal D by the basses in the second measure.  From that second measure, the melody is as before, but forte, and the thirds move parallel to it, not contrary.  By the fourth measure, the first clarinet joins the oboe on the melody, the cellos join the basses, and the bassoons have their original motion.
7:34 [m. 63]--From this point, the statement is scored the same as before, exactly matching 0:39 [m. 6].  The cellos and horn have the five-note figure, the violins and violas respond, then the cellos and bases imitate that response.
7:58 [m. 66]--This continuation closely matches 1:03 [m. 9], but the leaping seventh and descent are played by the oboe instead of the flute.  The strings are as before, with the hint at the “subdominant,” and the bassoons are the same, but the flutes now join at the point where the upper winds had dropped out before, supporting the string motion an octave higher, and the oboe continues in support.  The first horn, which had rested entirely in the earlier statement, has a new line.  These additions add to the richness of the cadence.
8:34 [m. 71]--The piano entry with doubled hands appears at first to match 1:40 [m. 14], but it already deviates by the end of the first measure, adding more colorful harmony.  By the second measure, the actual motion is changed.  The two-note syncopated descents are now followed by narrower upward motion that is also syncopated.  The third descent (at the beginning of the third measure) is now a downward leap from a higher level, and at this point the volume builds powerfully.  A second downward leap and a closing turn figure give this measure a disruptive “triple” 3/2 division that undermines the feel of the 6/4 motion.
8:54 [m. 74]--The volume has reached forte, and the buildup continues, molto crescendo sempre.  The entry of the horns and cellos with octaves in the “triple” or “3/2” division indicates that the piano has conflated its statement with the one at 2:38 [m. 21], omitting the orchestral interruption.  The horns and low strings establish a low D “pedal point.”  The first two measures closely correspond to the first two measures of the entry at 8:34 [m. 71], with two-note syncopated descents and narrower upward syncopated motion, but the “melodic” line is now embedded below the upper notes of the harmony.
9:06 [m. 76]--The continuation establishes an undulating, generally descending motion in groups of two and four notes under rich harmonies, building up to fortissimo.  The undulation, doubled in both hands, includes downward leaps of fifths, fourths, and thirds as well as stepwise motion.  The descents are extended to six notes after two measures, with a strong pull toward G major before the descent is arrested and the “pedal point” ends. 
9:28 [m. 80]--On the upbeat, with a low piano trill on C-natural (a note indicating the motion to G major), the woodwinds enter with the leap of a fourth familiar from the five-note figure, led by flutes and oboes and harmonized by clarinets, bassoons, and horns.  At the same time, the piano erupts into an unmeasured two-beat arching arpeggio in “near”-32nd notes.  That pattern is repeated on the second half of the measure.  The winds now complete the “extended” version of the figure as the piano flows into continuing rapid arpeggios, mostly descending in near or actual 32nd notes and moving back to D.  The strings are absent.
9:40 [m. 82]--The winds have the same upbeat, but now the piano arpeggio outlines D major, and the pattern is only stated once.  The second half of the measure is a sort of reset, with the piano arpeggios rapidly rising and shifting the key with trills again, now to C major.  Now the winds begin the same pattern a fourth higher, but they deviate in the second half of the measure as the piano arpeggios continue to arch, punctuated by low trills.  The volume begins to diminish.  The winds begin the familiar descent, extending it even more (to nine notes) as the piano arpeggios move back toward G major, including minor inflections and other chromatic colors.  The volume diminishes even more as the piano arpeggios are compressed.
Transition to Cadenza/Coda
10:02 [m. 85]--The winds and piano drop out, passing to the lower strings.  The violas and cellos have a quiet descent like the one that began the transition at 3:20 [m. 27].  The violas now follow the cellos and basses.  The intervals and distances are narrower than before, but the goal is D (now functioning as the preparatory “dominant” in G).
10:18 [m. 87]--The piano solo from 3:37 [m. 29] is transposed down a step, focusing on D instead of E.  The two-against-three clash, the “anchored” low bass, and the rhapsodic triplets are all as they were there.
10:33 [m. 89]--This string passage is like 3:51 [m. 31], with the first violins entering as they did there (as opposed to the violas at 10:02 [m. 85]), but it is not an exact transposition.  The initial motion is to A minor (as would be expected with the transposition down a step), but the second descent is further diverted, toward G as the “dominant” of C instead of the expected E, which would correspond to the former F-sharp.  The orchestra now drops out for an extended period that includes the cadenza.
10:50 [m. 91]--This corresponds to 4:07 [m. 33], but with great deviation.  Initially, the piano figures are transposed up (not down), with the bass anchored on G instead of F-sharp.  The right hand, however, becomes more active, with new leaps and motion where there had been rest.  Brahms adds the marking molto espressivo e legato.  The bass remains on G through the second measure with the upper notes of the left hand moving down, and the right hand now moves steadily up to the heights, still with syncopation.
11:04 [m. 93]--In the third measure, the bass descends, mostly chromatically by half-step, and the right-hand triplets plunge down, still with syncopation and with downward leaps of a fifth.  There are three “waves” of descent, with large upward leaps between them, but each beginning much lower.  Each one closes with a descending half-step.  The downward leaps in each “wave” are A-D, E-A, and D-G.  The bass finally arrives on a low A as the “dominant” in the home key of D.  The right hand has reached down to the bass range, and begins a trill on C-sharp, which will lead into the unmetered cadenza.
Cadenza and Coda
11:22 [m. 95]--The unmetered cadenza is all marked as m. 95, without bar lines.  Following the notation, it is a total of 35 beats.  The first 15 of these are a series of exchanges, with both hands playing trills, but with one of them emerging into an arpeggio leading to the next one.  The trills have a lower note on C-sharp (right hand) or G (left hand).  At first, the right hand continues its trill on C-sharp while the left hand enters on the G above it, crossing over.  The right hand then emerges into an arpeggio leading to the C-sharp an octave higher.  The left hand follows suit, leading to the G an octave higher.  The alternations are such that each hand moves above the last, with much intertwining over five three-beat statements.
11:38 [m. 95, cont.]--The right hand has moved up three octaves, the left two.  Now they continue their last trills for three beats, both in the high treble register, the right hand above the left.  After three beats, the trills are closed off and emerge into descending chords in triplet rhythm, derived from the main theme.  After the initial descent over two beats, the right hand begins to leap up and down, still in triplets, while the left hand descends with some syncopation, also retaining the triplet rhythm.  Brahms adds the marking molto Adagio at this point.  The left hand emerges in contrary motion to the right and adds a lower “pedal” voice.  The hands come together.  This all takes up six more beats (eleven total in this passage).
12:05 [m. 95, cont.]--The cadenza is closed off by the usual series of trills over “dominant” harmony.  First the right hand plays one on E over the continued syncopated “pedal” in the left hand.  The right hand decorates the trill in a lower voice with a “turn” notated in grace notes, as the left hand “pedal” drops two octaves to a low A.  This takes up three beats.  The right hand then continues its trill for another six, the first three against the low A, now with a lower harmony a third below (also trilled).  In the last three, the left hand leaps up to join the right-hand trill an octave below.  The trills take up a total of nine beats, but the ending is marked with a fermata before the close with anticipatory grace note.
12:27 [m. 96]--Coda.  As the piano closes off its cadenza, the orchestra enters after its long absence to close off the movement.  The piano drops out and does not re-enter.  The first three measures closely match the very beginning of the movement, with the main melody against the bassoons in thirds.  It is altered, though, as the bassoons colorfully lower the leading note to C-natural, and the melody does this as well.  Half the cellos replace the second violins and violas, who do not enter here.  The bassoons reinstate the expected C-sharp after two measures, subtly altering their line.
12:51 [m. 99]--On the upbeat, where an upward turn would be expected, the melody continues down.  At the same point, the first oboe enters with an upward leap of a fifth, A-D.  The violas then enter to restart the melody.  The violins drop out, and the cellos and basses continue downward with counterpoint, adding the “chromatic” C-natural and the “minor” note F-natural.  The bassoons continue to accompany.  The second flute doubles the violas on its upward melodic leap of a fourth.  The first flute then has an upward leap like the oboe, but on C-natural-G.  The violas restore the C-sharp in the melodic descent. 
13:10 [m. 101]--The melody and counterpoint both stall over two measures in the “triple” 3/2 grouping with chromatic half-step motion.  Only bassoons and low strings are playing here.  But then there is the only timpani entry of the whole movement, beating out the last five beats of the penultimate measure on the “dominant” A.  This emerges into a roll underlying the final D-major chord in all winds and strings.
13:48--END OF MOVEMENT [103 mm.]

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3^rd Movement: Rondo - Allegro non troppo (Rondo form with development and large coda). D MINOR (ending in D MAJOR), 2/4 time.
RONDO THEME (A)
0:00 [m. 1]--All themes in this movement share the same basic rising shape, reminiscent of Theme 2b (the piano solo theme) from the first movement.  The piano alone has the first statement of the energetic, impassioned, relentless rondo theme.  The initial syncopated rising gesture leads to two faster rising figures harmonized in sixths.  The initial rising gesture is then stated higher (an octave plus a fourth), leading to a forceful downward motion in high chords.  Through all of this, the left hand has a perpetual motion of sixteenth notes, generally marching down with leaps and scales, gradually taken over by broken octaves.
0:11 [m. 9]--A fast triplet arpeggio in both hands leads to the orchestral restatement of the theme.  It is presented by violins, with the other strings (often including second violins) playing downward-marching pizzicato.  The piano continues its driving sixteenth notes, now doubled in octaves between the hands.  The horns have punctuating interjections against the faster rising figures.  Woodwinds (except clarinets) join on the higher statement of the initial gesture and the forceful downward motion.  At the point of this higher statement, the piano’s hands diverge, creating harmony with continual broken octaves.
0:21 [m. 17]--The orchestra drops out, and beginning with an upbeat trill, the piano reiterates the concluding forceful downward motion, still with the active, leaping sixteenth notes in the left hand.  The passage is extended with syncopated notes held over bar lines and more trills.  A bassoon quietly enters, providing a gentle counterpoint, and the piano itself settles down, più dolce.  The syncopated note and trill are reiterated three times, the last one turning the key a half-step lower, to C-sharp minor.
0:28 [m. 22]--The piano again reiterates the syncopated note, but this emerges into a repeated rising third.  The bassoon’s last note fades out, and the piano is left alone.  After three more syncopations with the rising third, that third becomes continuous, the hands now doubled in octaves, moving down the keyboard.  The alternations then broaden from the third on a downward note, the top note remaining on C-sharp.  The piano builds and these figures hammer home the C-sharp-minor key, obscuring the bar lines with lower-note accents on weak parts of the beat.  A rising “diminished” arpeggio leads back to D minor, and both hands cascade down in a scale, speeding from six-note figures to seven- and eight-note groups.
0:42 [m. 32]-- The arrival point of the cascading piano scale coincides with another statement of the rondo theme opening.  The pianist is asked to merge right into this, accompanied by plucked strings and horns, again with the perpetual sixteenth notes in the left hand.  The full orchestra enters for the higher statement, and the pianist is given a merciful reprieve, even passing the sixteenth notes to the lower strings.  Trumpets and timpani enter to give weight to this moment.  The orchestra uses the faster rising figures to deviate from the original theme, moving toward the “relative” F major.  The strings are suddenly left alone, and they quietly give out halting, increasingly fragmented dolce figures in dotted rhythm over a cello tremolo.
1:00 [m. 46]--Transition.  The dotted figures pass to the piano, which rapidly alternates broken octaves on C between the left and right hands, each beginning off the beat with a short note.  A horn supports these.  The first violins, supported by violas, then enter with a sweeping upward line that suggests an arrival on F major.  The right hand of the piano moves up with this violin line, but the left hand remains anchored on C.  The clarinets punctuate the sighing end of the figure over a held oboe note.  The violins and violas now play it again but turn toward minor.  Again, the piano bass remains anchored.  The flutes punctuate the end.
1:10 [m. 55]--The violin figure begins again, but now it takes an extremely gentle turn toward the remote G-flat and D-flat major.  The lower strings enter to support this, and even the bass of the continuing dotted-rhythm alternations in the piano moves away from C.  All winds also participate in this motion.  The top of the right-hand figures now remains on D-flat for a few alternations before moving down.  Here, the upper strings, then the winds drop out, leaving only the cellos to support the piano on a held D-flat.  The piano continues, still with the dotted-rhythm alternation, then colorfully turns back toward F, with minor-key inflection.  The cellos and horns support a satisfying full cadence merging directly into the new theme.
FIRST CONTRASTING THEME (B)--F major
1:24 [m. 66]--The piano alone is left to present the noble contrasting theme, which retains the basic rising shape.  Brahms directs a steady, continuous buildup.  The melody is richly harmonized in the right hand while the left again has perpetual sixteenth notes, this time opening each group with a wide upward leap, often larger than an octave.  The first phrase of the theme has a prominent rising triplet halfway through.  Plucked cellos then discreetly enter to support a motion toward the “dominant” harmony, which is punctuated by grace notes.  The next phrase emphasizes syncopated motion, with longer notes held over bar lines, and with several chromatic chords and notes.  The plucked cellos continue their unobtrusive support.
1:39 [m. 78]--A dissonant “diminished seventh” chord interrupts an expected cadence on F.  The supporting cellos begin to play with the bow.  The continuous sixteenth notes in the left hand slow to flowing triplets, which clash with the main rhythm in the right hand.  The right hand itself continues with syncopated motion, adding an active lower voice under some gestures.  After two upward-striving gestures, the left hand moves back to the sixteenth-note motion and the right hand continues its syncopated patterns, again with some chromatic notes, and the cellos are plucked again.  The buildup has reached forte.
1:50 [m. 86]--Another cadence is delayed.  The left hand halts its sixteenth-note motion, and now plays bass octaves with syncopation.  The right hand has a descending melody in two waves, supported by a lower voice in clashing triplet rhythm.  The cellos are bowed again, supporting the piano bass.  Once again, the left hand moves to the sixteenth-note figures while the right hand strives upward.  The remaining strings enter, along with bassoons and horns.  The buildup continues, becoming passionate.  The top of the upward-striving right hand culminates in bell-like syncopated reiterations before the supporting instruments drop out (except for a low cello C) and the piano cascades down in octaves, still avoiding a full cadence.
2:05 [m. 98]--The piano drops out, and very quietly, the strings begin a series of harmonized two-note repetitions, with each one slurred to the next one (and, if it is the same note again, tied in syncopation).  The cellos remain on a syncopated low C throughout.  The motion is narrow and chromatic, and the slurs are punctuated by woodwinds, first clarinets and bassoons, then, as the upper strings leap higher, by flutes and oboe, then clarinets and bassoons again as the strings leap back down.
2:18 [m. 108]--The harmonized two-note descents land on a series of repetitions where the first violins leap from F down to C, then back to F on the downbeat.  The other strings are more harmonically active.  There are two clear F-major arrivals, but they are brief, and the low pedal C in the cellos undermines them.  The wind punctuations vary, flutes and bassoon, then bassoon and horn, then a single clarinet.  Finally, the first violins also land on the syncopated C while the second violins and violas continue to move.  The two-note repetitions cease, the first violins drop out, and the other strings trail down with repeated patterns in isolated notes off the beat.  The second violins also drop out.  Basses join the others as they fade away.
2:32 [m. 118]--Re-transition.  The strings, at their quietest level, begin an ominous tremolo.  As the timpanist joins this tremolo, the opening figure of the main D-minor rondo theme is heard in the horns, then the trumpets over an extremely rapid buildup.  The piano enters with four powerful chords, then cascades down in a chromatic scale, played in fast triplet rhythm doubled in both hands.  Against it, the strings play the opening rondo figure three times, moving from low to high instruments.  The strings not playing the figure punctuate with chords, as do the brass and timpani, joined by the woodwinds after two measures.
The piano finally settles on a low trill-like motion (A and G-sharp), still in fast triplet rhythm.
2:45 [m. 128]--The piano, with the right hand only, extends the written-out trill over four full measures and rapidly quiets down.  The winds (with violas) play held chromatic chords under the trill.  These instruments then drop out, leaving the piano alone, still with just the right hand.  The trill merges into a filigree of wave-like figures that work up to the heights.  The left hand enters with a solid descending arpeggio against the fast triplet filigree, which also works its way down.  The left-hand arpeggio slows to half the speed as the decorative right hand moves into the bass clef range.  The left hand then settles on a low octave A as the churning right hand stalls its tenor-range motion, establishing D minor as the volume powerfully builds.
RONDO THEME (A’)
3:04 [m. 144]--The piano merges directly into a statement of the main rondo theme, matching its presentation at the opening.  The syncopated rising gestures, the perpetual left-hand motion in sixteenths, and the forceful downward motion are all as they were.  The big difference is that now there is light accompaniment from horns and plucked low strings.
3:14 [m. 152]--The orchestral statement is omitted, and the piano moves directly to the passage from 0:17 [m. 21], beginning with the upbeat trill.  The reiterations of the downward motion follow as expected, as do the syncopated notes held over bar lines.  The bassoon counterpoint is replaced by new interjections from woodwinds with violas and second violins, and with continued plucked support from the lower strings.
3:21 [m. 157]--The passage from 0:28 [m. 22] is given in full, with the repeated rising thirds, then the motion down the keyboard, heading toward C-sharp minor and back to D minor with the rising “diminished” arpeggio and accelerating downward scale.  The plucked strings continue for the first two measures before dropping out, and there is a held E on the horn that persists throughout the passage, unlike the bassoon note in the previous presentation.  The second horn adds a lower A with the arpeggio and scale.
3:35 [m. 167]--Instead of merging directly into another presentation of the main rondo theme, as it had done at 0:42 [m. 32], the piano is mercifully given an extended period of rest.  Instead, the expected statement is now given by the orchestra, whose earlier entry was omitted.  It resembles the first orchestral entry at 0:11 [m. 9], but with the piano now absent instead of continuing with its perpetual motion, that perpetual motion is assigned to the lower strings.  The wind entry is more richly scored, with the bassoons joining the perpetual motion.  A full cadence with trumpets and timpani replaces the previous half-close.
3:44 [m. 175]--The orchestral statement is extended, first with a repetition of the forceful downward motion, then a powerful arpeggio, punctuated by trumpets and timpani, leading to an even stronger D-minor cadence.  All instruments quickly drop out except for low strings, two horns, and one bassoon.  Suddenly quiet, these instruments play a simple rising third from D to F, and that F artfully becomes the preparatory “dominant” that leads to the new key, B-flat major, for the second contrasting section.
SECOND CONTRASTING THEME (C)--B-flat major
3:54 [m. 181]--The piano’s much-earned rest continues with the first measures of the new theme.  It is gentle and yearning, but still based on the basic rising motion.  The strings have the first presentation, the violins imitated by violas and then cellos.  There is unobtrusive accompaniment from bassoons and horns.  The second rising gesture reaches higher with almost aching beauty.  This time, the violas and cellos have a single imitation, and clarinets enter to join them on it.  The phrase ends with a half-close.  This merges with the entry of the piano, whose break ends with a rising arpeggio.
4:05 [m. 189]--The piano takes over, playing a highly varied, but recognizable version of the new theme, with melodic notes played in syncopation off the beat and doubled in both hands.  Bass notes on the beat, meanwhile, descend chromatically by half-steps, then by whole steps to the half-close.  The melodic notes leap up and down, then descend smoothly in the middle and at the end.  The accompaniment comes from the lower strings, with cellos and violas alternating on rising plucked arpeggios.  A horn enters halfway through the statement with a held B-flat.  The piano’s bass closes it off with its own rising arpeggio.
4:16 [m. 197]--The plucked strings and horn drop out, and the piano plays a rhapsodic extension, still with the syncopated melodic notes.  These are played first against arpeggios, then a winding inner voice, all against solid bass notes which are also in syncopation.  A descent is followed by a yearning upward leap, then another descent before the extension closes with another high upward reach.  The phrase lasts a measure longer than expected.
4:29 [m. 206]--There is now an abrupt key shift to D-flat major, led by the violas and cellos, who enter with a rising arpeggio and a syncopated leaping descent.  The other strings punctuate with plucked notes, while flutes, clarinets, and bassoons hold a chord.  The piano, meanwhile, plays fast upward two-note gestures alternating between the hands.  The strings have a second gesture, this one higher and played by second violins and violas.  The piano then emerges into a rising scale motion in the right hand, still with the two-note slurs, supported by slower sighing, leaning chords in the left hand.  These alternate with similar figures in the wind instruments.
4:37 [m. 212]--The piano’s right hand now breaks into a long trill that steadily rises.  The “leaning” gestures are passed between the upper strings and the left-hand chords.  The key makes another striking shift, to C-flat major (as notated--it sounds the same as B major).  The piano trill pauses on a dissonant note against a dissonant chord, then continues to reach ever higher in longer notes.  A horn, with plucked cellos and basses, maintains a “pedal point” on G-flat as the “dominant” in C-flat major.  Meanwhile, prominent rising gestures are passed from clarinet to oboe to the second and first flutes, these now in alternation with the downward-leaping gestures in the left hand (the upper strings now holding a long and dissonant chord).
4:46 [m. 218]--The piano trill now plunges down in faster quarter notes, harmonized above by flute, then clarinet.  The left hand has one more downward-leaping gesture.  The winds, then the strings drop out, and after the big descent, the trill breaks.  The right hand is left alone, and it very quietly meanders upward with flowing sixteenth notes.  These emerge into three-note rising patterns that obscure the meter.  They are increasingly chromatic, moving back toward B-flat major before restoring the metric sense.
4:56 [m. 226]--Back in B-flat, the varied, syncopated version of the theme as heard at 4:05 [m. 189] is played by a solo horn, the descending bass played by cellos against a held note in the string basses.  The piano emerges out of its transition to accompany these entering instruments with more flowing sixteenth notes in both hands.  These move from rising two-note slurs to turn figures and descending arpeggios.  This basic pattern is played twice, once for each half of the theme in the horn.  The second half of this horn presentation is altered to change the half-close and extend down to a full arrival on B-flat.  The violas enter here, and the strings move to held chords.
5:07 [m. 234]--As the horn theme is extended down to arrive on a low B-flat, the piano figures now gain an arching character, slightly rising, then reaching further downward.  They are directed to fade, perdendosi.    The left hand emerges into rising two-note slurs.  After this brief transition, the piano will drop out for the extended orchestral fugato beginning in B-flat minor.
DEVELOPMENT WITH FUGATO (D)--B-flat minor, F minor, and F major
5:12 [m. 238]--The second violins begin the hushed fugato with a subject based on the second contrasting theme.  It starts with the rising line, then angles down and back up before skittering down in faster notes.  It moves from B-flat minor to its “dominant” minor, F minor.  There, the cellos have the second entry.  The second violins continue with a countersubject consisting of “sighing” gestures and then a syncopated downward line.  This all moves back to B-flat minor, and is closed off with an extra measure for a cadence.
5:23 [m. 247]--The violas have entered, but not with the subject.  At first, they dovetail with the second violins on a descending line derived from the subject.  The subject itself is stated again by the cellos, now with string bass support and starting in B-flat minor.  The second violins continue with the “sighing” and syncopated countersubject, but the violas do something totally unexpected by playing the familiar opening of the main rondo theme.  This will infiltrate itself more and more before it totally disrupts the fugato.  The key moves back to F minor in another extension measure, with the cellos and basses on a rising arpeggio.
5:29 [m. 252]--The first violins finally make their entry, and the full string section is now active.  They play the subject beginning in F minor.  The second violins also move upward in fast notes before moving back to the “sighing” gestures.  The cellos march down, and then, joined by the basses, they subtly insert the next statement of the rondo theme opening.  The violas take over the faster-moving upward notes.  The first violins complete their statement of the subject as the cellos and basses finish the rondo theme gesture.  The subject statement in the first violins is altered to remain in F minor instead of moving back to B-flat minor.
5:35 [m. 256]--The fugato has now effectively ended, even though the strings are still in counterpoint.  The subject is not heard again.  The horns intrude on what has been an all-string affair, playing syncopated octave F’s.  The second violins, then first violins, play the faster notes, now descending, while the lower strings march up in an arpeggio.  Now they move back to B-flat minor.  All of this happens with the first real buildup in volume since the fugato started.  Now forte, the violas once again play the rondo theme opening in B-flat minor, and they are immediately imitated by the second violins.  The horns now hold a long F.  The fast notes are passed to the violas, joined by second violins as they finish the rondo gesture.
5:43 [m. 263]--Back down to a hushed level, the first violins are left alone on a fast, detached arching arpeggio.  The clarinets and bassoons make an unexpected entry to punctuate this in harmony.  The arching line is passed to the cellos, punctuated by the upper strings.  Now the entire string section pauses as the first flute enters with the arching arpeggio, punctuated by oboes and clarinets.  The dialogue continues as the bassoons are isolated on the arching arpeggio, punctuated by upper strings and horns.  The flute takes the rising fragment, then passes it back to the bassoon.  The punctuations come from violins and horns.  Brahms directs the instruments to fade further, perdendosi.
5:51 [m. 269]--The dialogue continues, having moved back to F minor.  The rising fragment is now played by the oboe, then the bassoon again, then passed to clarinet, back to bassoon, and finally to the flute.  At the clarinet entry, the lower strings have joined the punctuations in pizzicato.  The harmony has also moved to C major, functioning as a confirming “dominant” in F and signaling a full arrival there.  The C-major area is confirmed by quiet rising arpeggios passed up the string section, the flute joining the first violins at the end.  This closes the unusually long orchestral passage without the featured solo piano.
5:58 [m. 275]--The key signature has retained the two flats used for the second contrasting theme, although the fugato and the subsequent counterpoint has focused on B-flat minor and F minor.  Now it changes back to the one flat of F major or D minor.  The piano has been absent for 37 measures.  It now enters, gracefully and beautifully, on a magical high F-major transformation of the rondo theme, playing its opening and then delicately skipping down, underpinned by a long low F in cellos and basses.  The left hand plays continual sixteenth-note arching patterns in the upper middle range of the keyboard.  The rondo opening is then heard even higher, rising to B-flat.  Both hands, spread widely, tumble in mildly chromatic arching patterns.
6:10 [m. 283]--Re-transition.  The piano’s patterns speed up to six-note groups in triplet rhythm, and its left hand moves to tremolo.  The flute and bassoon have an arching line that moves to G minor (“relative” to B-flat).  The oboe and clarinet respond with a similar line that moves to A major, the preparatory “dominant” in the home key of D minor.  The lower strings underpin both arching lines with slow rising motion.  The piano speeds up even more, to 32nd notes.  The strings and winds drop out on an A-major chord, and the piano breaks into rapid arpeggios, alternating between rising in the right hand and falling in the left.  These continue, gradually descending over six measures, slowing to triplets in the last two.
6:21 [m. 293]--The rapid motion breaks, and the piano emerges into a forceful downward plunge, with solid left-hand octaves serving as the first notes of triplet patterns that are completed by broken octaves in the right hand, the first notes of which mirror the top notes of the left-hand octaves.  The range of this plunge extends more than three octaves, and merges directly into the full return of the rondo theme.
RONDO THEME (A”)
6:28 [m. 297]--The piano’s cascading descent leads into a powerful statement of the theme.  It is played by the orchestra, with the strings largely as in their first statement at 0:11 [m. 9].  They are supported by more instruments now, flutes, oboes, horns, trumpets, and timpani.  The piano does not drop out, but continues its plunging octave pattern, with upward “reset” jumps that happen first at two measures distance, then one measure.  The higher statement of the initial gesture surprisingly replaces the forceful downward motion with the faster harmonized rising figures from the lower statement, which make a full turn to the “dominant” A major.  The piano’s continuing octave pattern becomes irregular, briefly arching back up.
6:39 [m. 305]--The piano’s continuation is as at 3:14 [m. 152], with the upbeat trill, and scored the same.
6:45 [m. 310]--The continuation is an intensified variation of that heard at 3:21 [m. 157].  After the first two measures with rising thirds, the right hand changes its rising patterns to triplets, adding a third note an octave higher than the second.  The left hand is unchanged, still in “straight” rhythm, and the overall downward motion is as expected, with the shift to C-sharp minor and back.  The triplets continue with the rising “diminished” arpeggio.  The accelerating downward scale originally began with triplets, and the only difference here is that the right hand is an octave higher than it was in the previous two statements.
6:59 [m. 320]--For this closing statement of the rondo theme, corresponding to 0:42 [m. 32] and 3:35 [m. 167], the strings take the lower first rising gesture, supported by trumpets and timpani (the perpetual motion in the lower strings), and the piano takes the second and higher gesture, with horns joining the support (the perpetual motion now in powerful, highly difficult octave doubling).  As at 6:28 [m. 297], the forceful downward motion is replaced by more of the harmonized rising figures.
7:10 [m. 328]--Transition.  The full orchestra begins a new extension and intensification, repeating the rising figures in A minor.  The piano then takes up the continuation of these rising figures, shifting to F major.  Once again, the orchestra takes over, with the figures now arching back down and the bass moving actively toward G (functioning as the “dominant” in C major).  The first violins hover on a high tremolo G while the other high instruments continue with the faster figures, which are now more dynamic.  There are two strong reiterations of a cadence motion on G in the first violins, complete with a swooping motion between them, trumpet fanfares, and timpani rolls.  There is a persistent reiteration of G in the bass.
7:23 [m. 338]--The piano enters again, with two sweeping motions to a G-major chord (of three, then five fast notes on an upbeat, doubled in both hands), punctuated by two low string descents to G.  The piano then has three more sweeping motions, each of seven notes, answered by a bass descent.  The winds join here in support.  There is now motion away from G with the next piano/bass exchange, both playing shorter triplet-rhythm sweeps, the piano adding short, forceful descents.  The piano then has three triplet sweeps in quick succession.  A longer forceful descent leads to A-major harmony, clearly the preparatory “dominant” in the home key of D minor.  The orchestra trails after the piano on the solid and expectant arrival.
FIRST CONTRASTING THEME (B’)--D minor 
7:36 [m. 348]--The piano presents it like it did the earlier version in F major, with noble rising harmonies and perpetual sixteenth notes in the left hand, each group again beginning with a wide upward leap.  Brahms marks it con passione.  It is again supported by plucked cellos.  The first two measures are a third lower than they were before, but by the third measure, the melody is where it was in the F-major statement.  The harmony is just different enough to keep it in the D-minor realm.  After the culminating grace note figure, the harmony lands on A minor.  There is now stronger deviation, as the bowed upper strings enter and the piano descends forcefully in colorful chords on the beat, landing on the “dominant” harmony.
7:53 [m. 360]--The piano now has a series of powerful octaves doubled in both hands and broken in the right hand.  Three short descents, each beginning higher, are given isolated punctations by the strings.  The octaves then leap continually up and down, with a general rising motion.  The strings drop out, and the piano octaves plunge downward from on high, now broken in both hands, making a massive descent over four measures, again ending on the “dominant” harmony.
8:05 [m. 369]--The piano suddenly drops out, and the strings and timpani just as suddenly enter with a quieter tremolo and roll that immediately builds.  Violas and bassoons, supported by horns, play the familiar syncopated opening gesture from the rondo theme.  The rest of the orchestra enters, and the opening gesture is given grandly by flutes, oboes, and horns.  A chord, a brief pause, and two more chords end up on the pre-dominant “six-four” harmony typically heard and held before a cadenza in a classical-era concerto.  Brahms indicates that both the chord and the pause after it should be drawn out with a fermata.
FIRST CADENZA (CADENZA QUASI FANTASIA)
8:19 [m. 376]--The solo cadenza begins with a series of three upward-winding arpeggios in triplet rhythm, all over a low bass A, and all of which culminate in downward-arching figures.  The first emphasizes A-minor harmony.  The second is on a colorful “diminished” harmony, and the third is on the “dominant” harmony based on A.  After the third of these large gestures, the right hand begins to work its way downward with several chromatic notes in “straight” rhythm.  The motion is in groups of three notes, each beginning with a higher note, and these go against the meter.  Over its held bass A, however, the left hand adds an upper voice with a descending chromatic line (by half-steps) played on the beats.
8:36 [m. 390]--The three-note groups subtly end, and the left hand descending chromatic line stops.  The right hand comes to rest on quieter upward-arching figures, still in the same “straight” rhythm, gradually descending.  After two measures, the right hand emerges into a measured trill as the left hand drops out.  This trill speeds up to triplets and then faster 32nd notes, the pitch steadily moving up until it reaches A on the top.  It begins as a whole-step trill, then moves to half-steps as it reaches up, and back to a whole step when it reaches the top A.  But this also then condenses to a half-step as it stretches over two bars.
8:46 [m. 395]--The trill has built in volume and now becomes unmeasured, with B above the continuing A on the bottom.  A dominant-harmony arpeggio under the trill is followed by a winding left-hand line in octaves, itself mostly consisting of rising half-steps.  The left hand also maintains a reiterated bass A under this line.  The trill moves steadily down above it.  Then the trill reaches back up as the left-hand octaves become more melodic and the bass moves down from A to F-sharp, then back up to G.  The trill culminates in a rhapsodic five-note turn figure.
9:06 [m. 402]--The left-hand harmony arrives back at the preparatory “six-four” chord that led into the cadenza.  The right hand moves to a winding, urgently yearning chromatic line in slower triplets.  The “six-four” harmony changes from major to minor.  The “yearning” line reaches very high, then descends on a “dominant” arpeggio, slowing to “straight” rhythm and then to a slow quarter-note triplet as the arpeggio reaches the low bass and fades in volume.  The “six-four” chord changes to a “dominant” one, then drops out for the descending arpeggio.  The last slow low bass notes bring the cadenza to a close.
CODA WITH SECOND CADENZA--D major
9:23 [m. 410]--The key signature changes to D major and will stay there until the end of the movement, overcoming the relentless minor-key ending of the first movement.  It begins with the second contrasting theme (C).  It is given by the wind instruments in a skillfully wrought canon over a gentle drum roll and descending low strings.  The theme is stated by the horn and immediately imitated by clarinet and bassoon.  The horn completes its phrase, but the imitation is passed to the oboe for its completion.  The flute then continues with the second phrase.  It is imitated, but not strictly, by oboe, then clarinet, and it is extended upward in the last measure.  The imitating instruments harmonize the theme after the initial rising gesture.
9:34 [m. 418]--The low strings, in tremolo, enter with a slightly ominous repeated descending third emphasizing the “subdominant” key (G major).  The piano enters against this with rapid nine-note arpeggios on the back beats.  The drum roll continues, then drops out, but there is still a wind background.  After three statements of the descending thirds, the low strings continue down before the basses hold on the “dominant” note A.  The violas enter and double the horns, moving against the cellos in tremolo.  The piano breaks into florid arching figures passed back and forth between the hands and descending.  The roll begins again on the timpani.  The tremolo violas and cellos are supported by descending chords in the winds.
9:45 [m. 426]--The whole canon sequence on C begins again as at 9:23 [m. 410], with subtle differences in scoring.  The supporting violas and cello play the descending line in tremolo against a held A in the basses.  The horn begins the canon as before, but this time the oboe decorates its completion of the imitation by adding its own rising arpeggio before it, creating a continuous chain on this motion.  The clarinet also adds an extra rising line against the oboe’s completion of the canon, and the horn doubles the flute at the beginning of the second phrase.  Plucked violin chords played against this second phrase are also new.
9:56 [m. 434]--The low string tremolo begins as at 9:34 [m. 418], now with the continuing pizzicato chords in the violins.  The rapid back-beat piano arpeggios are heard as before.  The continuation in the fourth measure is redirected so that the held note begins on the “home” keynote D instead of A.  The florid arching figures in the piano and their supporting chords are different because of this, adding an upward reach.  The bass does move to the “dominant,” but now it seems more demanding of a cadence and arrival.
10:08 [m. 442]--Brahms inserts a “soft” double bar line here and heads the next passage “Meno mosso.”  In what sounds like a noble but pastoral march at this slower speed, the bassoons present the opening gesture of the rondo theme, now in major against a long-short “drone” in the cellos, punctuated by timpani.  A varied version of the continuation is heard in the oboes, molto dolce.  The rising figures arch back down but are clearly derived from the theme, harmonized mainly in sixths with passing fifths and thirds, the oboes almost resembling bagpipes.  The principal horn and bassoon take over from the oboes in a repetition, then the second horn replaces the bassoon.  The pattern resembles “horn fifths,” and an oboe joins the descent.
10:19 [m. 448]--The piano, which has been resting since the noble march began, enters with an intensified variant of the “horn fifth” arching figure just heard in the oboes, bassoon and horns, doubled in both hands.  It adds a higher reach and includes one fourth.  The violas join the cellos on the “drone.”  Against the piano statement, the flute plays a high trill.  The piano extends its presentation, rising in thirds and emerging into a trill.  The harmony, including the drone and flute trill, moves from a solid, established D to the “dominant” in A.  The bassoons take over the rising thirds from the piano as it emerges into its trill.
10:26 [m. 452]--The cellos hold a low E, as does the piano bass.  The trill in the right hand works its way downward, interrupted by leaps down to three-note turning figures.  This chain of trills, linked by the lower turn figures at the end of each bar, have a distinctive bell-like sound.  The bassoons, harmonized in thirds, move down with the trill.  While it appears that A major is established by its “dominant” harmony, there is not a full arrival there.  At the end of the trill and turn chain, fading in volume, the trill stalls for two measures.  The left hand and the cellos move up to A (now as a “dominant” in the home key), and the trill moves down for another two-measure meditation.
10:38 [m. 459]--Now the right hand breaks into rapid waves of basically unmeasured fast notes, grouped against a steady long-short rhythm on a “dominant” bass pedal in the left hand.  The upper notes of the left hand move between G and E before settling on the upper A.  Wind instruments provide a harmonic background.  The wave of right-hand notes sweeps up and down three times, building powerfully in volume and reaching higher each time.  After the third sweeping motion, having reached the heights of the keyboard, the right hand falls five octaves over a measure and a half in an enormous scale run.
10:46 [m. 463]--Più animato.  Back in a faster tempo, the bass, in the left hand and the plucked cellos, finally establishes itself firmly on D.  The violins, with the firsts following the seconds in alternation, play four statements of the major-key rondo theme opening in a rising chain, each group adding a descending harmony after passing the figure.  Against this, the right hand re-establishes the familiar sixteenth notes in perpetual motion, working down and back up against each statement of the thematic gesture and the reiterated bass D.  The volume builds even more.
10:54 [m. 471]--Having reached the heights through their successive statements, the violins, now in octaves, joyously proclaim a climax in thrilling syncopation.  The piano, marked con forza, plays wide upward-arching arpeggios.  The bass D continues to be reiterated in the left hand and the cellos.  Oboes and bassoons provide the background.  The violins break their syncopation and begin to play hammering figures leaping rapidly down and back up.  The phrase ends with a brief motion off the bass D to enable a forceful cadence, with the piano playing three straight downward arpeggios.
11:02 [m. 479]--The pattern from 10:46 [m. 463] is intensified.  The violins begin the chain, as before, but the piano’s perpetual motion is grander, with both hands participating, doubled in octaves.  The bassoons and low strings add descending punctuations, and the bass D is not reiterated.  Instead, there is a strong emphasis on the “subdominant” side, with motion to G and C.  The third statement of the chain in the second violins rises more than expected, and the first violins join in.  They play the fourth statement together, also rising higher.  Clarinets, then flutes and oboes join for a powerful arrival on C major.
11:10 [m. 487]--The full orchestra, minus trumpets and timpani, blasts out a C-major chord in syncopation.  The piano responds with an upward-shooting arpeggio in fast triplet rhythm.  More syncopated figures, now with trumpets and drums, alternating with the piano arpeggios, lead down by thirds, to A, F, and D, but this D functions as the “dominant” of G.  After the fourth exchange, the piano and orchestra alternate in hammering chords reiterating a cadence in G (which could also be seen as a “plagal” cadence in the home key of D).  But then the chords move to A (as the “dominant” in D), pausing there to prepare for the brief second cadenza.
11:23 [m. 499]--Cadenza ad lib.  The piano, in octaves doubled between the hands, plays four fast rising arpeggios on the “dominant.”  On the fourth one, the left hand moves down against the right.  This emerges into descending syncopated chords in the right hand against leaping motion over a “pedal point” in the left.  Both hands become more active and dissonant, still with heavy syncopation and notes held over bar lines in the right hand, the left moving to rising arpeggios.  These figures speed up dramatically, with Brahms indicating molto accelerando.  Suddenly, the motion is arrested.  After a bar of rest marked with a fermata, both hands shoot up together in a rapid arpeggio concluding the short cadenza and leading to the final bars.
11:42 [m. 518]--Tempo I.  The piano emerges into a double trill on E, aching to descend down a step to the keynote.  There are then six straight statements of the opening syncopated gesture of the rondo theme, all beginning at the same level, with the second, fourth, fifth and sixth reaching higher to a full octave.  The first two come from two horns in alternation.  They are joined by bassoons on the third and fourth.  Low strings and horns play the fifth, and they are joined by trumpet and oboe on the last.  Against the last two, the piano moves the trill up to G, rapidly repeating the E below it in both hands.
11:51 [m. 526]--As the piano trill moves up to the extremely anticipatory “leading” C-sharp, with E and G in a quasi-tremolo below, the low strings and horns play four rapid upward-shooting gestures, supported by trumpets and a timpani roll, along with the other winds.  Violins join on the last two gestures.  Over these two measures, there is a powerful buildup to the cadence, whose arrival is extraordinarily satisfying.  The closing figures here are famous.  At the cadence, the strings and bassoons shoot up again, now in harmony, and the piano plays a continuation to a new joyous cadence with winds.  The timpanist leaps rapidly back and forth between A and D.  This thrilling exchange is then played a second time.
11:58 [m. 532]--The orchestra hammers home the movement and the concerto with the concluding chords, leaping back and forth and then reaching up.  At the top, four chords, separated by short rests, lead to the final held one punctuated by a timpani roll.  Brahms does not indicate that the piano should join these final chords, showing that the soloist should stop with the second statement of the “joyous” cadence, but in performance, the soloist invariably joins the orchestra in the conclusion.
12:16--END OF MOVEMENT [536 mm.]
END OF CONCERTO


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