Themes and development
Note - having a copy of the score to hand will be very helpful when studying the following.
The first subject (A) is stated immediately as the first four bars of the clarinet part, and consists of a number of important motifs and intervals (Ex 1). The first four notes are distinctive: a note (the tonic), its two neighbours either side, and a return to the original note. This motif (Ex 1:1) is in a sense a complete entity, but it is insufficient to constitute a melody. Its last two notes with the next two form another distinctive shape: falling appoggiatura - falling sixth - rising fourth (Ex 1:2), and the next bar contains a falling diminished fifth, an interval characteristic of A. This completes the falling element of A, which is balanced by a rising element of equal length (two bars), consisting of two sequential statements of a rising third (already heard in bar 1), falling fourth and rising octave. So far the bass line has made a scalic ascent from the tonic at the rate of one note per bar. As it reaches the dominant, Brahms begins to develop the material: the rising third becomes a tenth and is inserted into the double-neighbour formation which is thus expanded - in inversion of its original shape - over five notes (one effect of this is to separate its last three notes, which are imitated in the next bar - see Ex 1). The rising third then becomes a chain of three associated with semiquavers, which is followed by a new falling cadential figure incorporating chromatic passing notes (bars 7-8), which settles on the dominant. The development so far is then repeated in diminution - in one and a half bars the notes in the clarinet part are the same (but an octave lower) as previously covered two and a half bars, and the chain of thirds is extended into an arpeggio that takes the music into the octave above that in which it originally closed in bar 8. Whilst this diminution is taking place, the double neighbour formation is applied to the dominant in the bass (bars 9-10). One reason this arpeggio makes a satisfying conclusion to the opening statement is that its pitch span encompasses all that the clarinet has so far played, running from the instrument's lowest note through nearly three octaves over to and coming to rest on the dominant above the previous highest note, the A flat (N.B. Notes in the clarinet part are always referred to by actual sound: the printed note is a tone higher) in bar 5.
At this point the music cadences back to the tonic for what could be a varied repeat of A with the melody in the bass, where as a result the double neighbour formation round the tonic (see bar 11) answers that just heard round the dominant. The next three notes are heard at their original pitch in the clarinet part (i.e. Ex 1:2 is divided between the two instruments - see bar 11). In fact, this is another development, or to be precise a fragmentation of A, for a rising sequence ensues, in the third bar the upper neighbour is abolished (see bar 13), and the tension rises to the music's first climax, an energetic piano solo based on the extended formation from bar 5 (Ex 2a). This is virtually a canon at the (octave +) fifth, as may be observed by removing the neighbour notes from the groups of semiquavers, but the fifths are a mixture of perfect and diminished (Ex 2b), which is very interesting in view of the role these intervals are destined to play in both distinguishing A from B and developing the links between them.
Close inspection of the route by which the second subject (B) arrives reveals an approach that is far from conventional, even though the melody is in the correct dominant key. One would expect the music to modulate so as to arrive on the dominant of the dominant: instead, a perfect cadence in B flat major is interrupted by four bars (18-21) in which a chain of dominant sevenths progresses from the tonic minor to its minor third, whereupon the seventh of this point of arrival is converted enharmonically into an augmented sixth. The standard resolution of the augmented sixth chord on G flat is Ic-V-I in B flat major, but the cadential chords are omitted, and the second subject begins immediately in root position.
One function of these four bars is to provide the necessary focal point for the loud passage begun three bars previously and enable a diminuendo to be made in preparation for the very quiet second subject. They also form part of a scheme to inject harmonic interest into the movement, preparing for the most obvious manifestation of this, the return of B in the recapitulation where the subject is preceded by the same chord (The journey round the circle of fifths is longer in the recapitulation by one step at each end: from B flat in bar 112 to C flat in bar 120) as in the exposition; but this time it is expressed and treated as a dominant seventh whose resolution brings B (this move justifies the omission of the two chords in the exposition, emphasising that the two passages are parallel) into the wrong key, C flat major, whose enharmonic minor B plays a significant role in the development section. If this piece of music were a story, the exploration of keys related to the tonic minor via its relative major would be the sub-plot.
The second subject is presented as a canon at the twelfth, a device foretold by the climax of the first, and begins with a rising octave, an interval also used overtly in A, so within its first half bar one is already aware of three links (the third being its quiet, lyrical nature) between it and the preceding ideas. The next bar introduces the important feature that is characteristic of B, but not of A. The clarinet part in the preceding four bar interruption explored some diminutions of the first bar of A, ending with one of its distinctive intervals, the diminished fifth. The falling fifth of B is perfect, the difference being stressed by the close proximity of the two. The next three notes form rising and falling fourths, which because of their rhythm and position in the bar are near enough to an inversion of the last three notes of bar 1 to act as a reminder (Ex 3). Brahms never misses an opportunity to relate an accompaniment to its tune: the rising octave is immediately answered by one falling, and there are more falling fifths in the accompaniment than in the melody, the first being inserted just before that in the second bar of the tune.
As in A, a varied repeat of the subject is prepared, but soon becomes a development: after one and a half bars the bass settles to a dominant pedal and the melody begins to rhapsodise, taking a slightly different direction. The piano is allowed a brief variation on the rhapsody, introducing elements from A (Ex 3b), then diminution and increasing harmonic rhythm over the continuing dominant pedal generate a climactic bar (39) for piano leading to the codetta. There is never a hint of deviation from the quest for motivic unity: in this bar the notes of the top line are those of the rhapsody (as in clarinet, bar 30), and the bass is an inversion of it.
The codetta (C) has a partly developmental role, for it explores some possibilities for linking elements of A and B (Ex 4), whilst being distinguished from both by being loud. Its first bar contains a falling augmented fourth (equivalent to the diminished fifth typical of A), and its next begins with a shape strongly reminiscent of the second half of bar 1 (A), but which by reducing the sixth to a fourth incorporates the inversion of the fourths from the second bar of B. The semiquaver figure in the next bar includes the diminution of this pattern and a rising arpeggio - respectively more akin to A than B and more to B (bar 38) than A (bar 10). It is logical that this should culminate as it does, in a passage developing the motivic feature unmistakably common to A and B - the rising octave, which eventually emerges from a few bars of distant harmony as both the prelude to and bass line of the first bar of A (see bars 51-53). This version of A shows a feature destined to be crucial: the third across the barline is filled in to form an appoggiatura.
Given the extent of development and establishment of links between themes that has already taken place in the exposition, one may wonder what more may be done by way of a development section. In fact, there are several more discoveries in store. At the fifth bar (60), we think we hear again the passage of leaping octaves from the climax of A: the rhythm and character are the same, but closer inspection reveals substantial differences - there are no tenths, nor is it a canon. It leads - without interruption this time - to B, also no longer a canon, and strikingly linked to A by the replacement of its falling perfect fifth with one diminished (bar 66). This statement also extends the fourths of B into a chain of undulating intervals (bars 67-68) whose rhythm reminds us of bars 46-47, themselves the extension of the first half of the third bar of C.
This new version of B becomes a canon at the tenth/third, and leads to some more ideas that incorporate elements of both A and B. The version of A in which the double neighbour formation appeared in the piano and the next few notes in the clarinet is invoked, with the third across the barline filled in as in the codetta, recreating a four note figure (bars 73-74) that previously appeared arranged so that its last note fell on the first beat of the bar (bars 13-14). This figure proves far more significant than hitherto suspected, for its three note falling element is about to become the end of a new combination destined to motivate modulation towards the tonic later in the development, and eventually to be the thematic material of the closing bars of the movement. Since this theme is the subtlest of all the links between A and B, it makes a remarkably fitting summary of the whole process (Ex 5). It is presented (sometimes inverted) first as a dialogue between the two instruments, then divided between them (bars 80-82) - in a way that unwary performers might overlook - with its first (the fourths from the second bar of B) and third (three notes from A) elements in the piano, and the intervening broken arpeggios (which seem to be a fresh idea, although there is a precursor in the accompaniment of bars 1-2) in the clarinet.
There are a few more new developments of individual motifs - notably a triplet figure across bars 89-90 incorporating both the four note figure from 73-74 and a double neighbour formation (Ex 6), and the development (bars 97-102) of a rising third from bar 34 into yet another canon leading into the recapitulation - but the foregoing completes the story of the themes and how the links made between them constitute the main argument sustaining the whole piece. One may observe that, exhaustive as it is, this is contained within no more than half the movement, and one may wonder how it comes about that such an important concept is not spaced evenly throughout. The answer lies in the classical convention of the recapitulation: in other words, a substantial chunk of the process is repeated. Evidently Brahms did not regard this as a weakness, or he could not find a solution, possibly because there is another argument going on alongside the motivic - a harmonic process of which the recapitulation forms an essential part. This movement is an example of evidence in his works that Brahms was interested in the idea of continuous development of motifs. The presence of a conventional recapitulation prevents such a process running through an entire movement: this is one reason why some later romantic composers found classical forms inhibiting.