Harmony
Turning to the tonal layout, one notes that Brahms does not use many different keys and generally does not modulate far from the tonic - even a substantial chunk (about half) of the development section is in the relative minor - which heightens the effect of excursions into such remote areas as B and E. The harmonic story of this piece is fascinating for its subtlety: for the most part, statements are made in conventional keys, but there is one major exception - the return of B in the recapitulation - which advises us that not all is straightforward, and inspection reveals an important, reasoned and complete argument involving very flat keys (it is helpful in this context to think of B and E as C flat and F flat, since the relationship is to the tonic minor through its relative major, G flat).
Brahms' use of chord viib to harmonise the falling diminished fifth in bar 2 opens up the possibility of considerable harmonic variety, for it is not necessarily a complete chord: it could be a dominant seventh without its root (as demonstrated in the restatement at bar 12) or part of a diminished seventh which could be used as a pivot: this aspect is exploited at the beginning of the development section, where for two bars (56-57) there is a suggestion of a varied or rescored repeat of the exposition which is dismissed by treating the viib as a diminished seventh leading to two others. Chord vii is utilised again as the second chord in the harmonisation of C: in fact, there is another link between themes in the bass lines. That of A ascends the scale from the first degree to the seventh, whilst in C the scale is inverted: it is harmonised with a chain of descending first inversions, which in the restatement runs from first degree to third.
An intriguing feature of bars 2 and 3 is the way in which the first note of the rising element of A forms a dissonance: it is the seventh of the chord. Comparison with the equivalent passage in the recapitulation reveals sevenths being added to the harmony in bars 104 and 106. One point to bear in mind is that the seventh need not be a merely functional device, but may also be colouristic, adding richness to the harmony. Both aspects may be seen in the chains of dominant sevenths which lead to the second subject, and the colouristic ideal reaches its zenith in the tranquillo section of the coda, where a procession of major and minor chords describes a circle of fifths (teasingly, one of the fifths is diminished) which would make absolute sense as common chords, but each has a major or minor seventh added.
An interesting and significant chord occurs in a cadence in bar 8, presenting simultaneously a vii (of the dominant) and the tonic minor - the seed from which the use of very flat keys is to grow. The sum of these two parts functions as a chord of the eleventh with a diminished ninth, the root being the unstated second degree of the scale (Ex 7).
The next appearance of the tonic minor is dramatic, when at bar 18 it interrupts the cadence that eventually resolves into the second subject. The remainder of the development of this strand occurs after the appearance of the theme that makes the final, most subtle link between A and B, so it could be said that the harmonic argument takes over upon the completion of the motivic.
The outcome of the diminished sevenths previously observed at the beginning of the development appears to be a version in G minor of the climax of A, which marks the beginning of a long passage of motivic development over static tonality, which changes mode to major at approximately its mid point, and ends in an insistent plagal cadence. This cadence is repeated so many times as to raise the awareness of its also being an imperfect cadence in C minor: looking back from bar 82 as far as bar 60, one notices that there has not ever been a perfect cadence in G, so it is now seen that G was an extended dominant, and the actual key throughout the passage was C, the relative minor of the home key.
In this passage, it is noticeable that even an apparent dominant pedal in bars 65-68 failed to establish G as the tonal centre. Brahms uses dominant pedals to emphasise cadences at important junctures, at which times they lead clearly to their tonics, so that there is no doubt as to their identity. In this instance, the pedal is kept distant by being played quietly on the clarinet's lowest note, and its tonic in bar 69 is inverted. Another dominant pedal appears to be implied by the low bass G's in bars 73 and 75: this again does not lead to a clear tonic, but to the insistent cadence to which the preceding paragraph refers. The approach to the recapitulation involves three indisputable dominant pedals and their tonics. All pedal notes are included in the graph.
The escape from the spell of harmonic stasis is achieved by downward steps to B minor and then B flat major, each achieved by starting the final, three note element of the theme on a note from the broken arpeggio and using the dominant chord as a pivot, treating it as a neapolitan sixth of the dominant in the new key (see bar 83). During this process comes the next glance at very flat keys, for the neapolitan of the dominant in B flat is G flat major, the relative of E flat minor and also enharmonically the dominant of B, in which guise it appears again in another dramatic interruption to a cadence in B flat major (bars 93-98). In bar 97 the dominant seventh of B is ingeniously used as a pivot to prepare for the return of the home key: the root of the dominant triad descends to the seventh, creating an ambiguous vii-type chord which also functions as a dominant minor ninth in A flat (Ex 8a). A simpler, equally valid view of this modulation is to observe that the dominant of B is enharmonically the relative major of the tonic minor, and there is a progression by step of three parts to the dominant seventh of A flat (Ex 8b).
The use of B minor in these late stages of the development prepares the way for the outwardly surprising use of C flat (=B) major in the recapitulation. Because it is not the appropriate key, a route to the home key must be found, and Brahms uses another ambiguous vii-type chord - which could represent IIb of C flat or the dominant minor ninth of E flat - as a pivot (see bar 124). This is more of an escape route than a resolution, for which one must wait until the coda, which begins in E major - a surprise when the key prepared was A flat, but also a normal progression from its dominant, C flat (B). In the exposition the second subject was approached by the enharmonic conversion of a dominant seventh into an augmented sixth: now this procedure is used again (think of the dominant seventh chord of E at the beginning of bar 161 as C flat-E flat-G flat-A), resolving this chord and, by implication, the whole issue of very flat keys, into the home key. Because of their roles in a linked series of events, B minor, C flat (B) major and E major are included on the same line in the graph.
Finally, a few issues are raised and resolved in the tranquillo section which ends the movement. The return of the broken arpeggios from the development and the apotheosis of the seventh are combined with a variation on the rhapsody from B in the piano right hand. This closes with the rediscovery of the three concluding notes that followed the broken arpeggios when they originally appeared, and bars 165 to 169 show that this figure may be accompanied by either a perfect or a plagal cadence, raising the question of which type should end the movement. The answer is unexpectedly assertive - an emphatic chord iid7 of the dominant on the second beat of bar 170: it contains the dominant in three octaves including the bass (the A natural in the clarinet part also shows that this is a chord of B flat major) and can resolve to the tonic only by a perfect cadence. The authoritativeness of this move generates a final, brief forte, which satisfactorily completes the dynamic scheme of the piece.
Bibliography
Frisch, W (1984) - Brahms and the Principle of Developing Variation (University of California)
Musgrave, M., ed. (1986) - Brahms 2 - Biographical, Documentary and Analytical Studies (Cambridge University Press}