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It would be unthinkable to proceed directly from a movement such as this to the concluding fugue. Thirty years earlier, Mozart knew that, after the Gethsemane which he had portrayed in the slow movement of his G minor string quintet, he must resort to the unusual expedient of an introduction by way of bridge to the finale proper, in order to grant the listener time for recovery from what he has just heard. In the case of the Hammerklavier, it would be impossible to emerge from the experience of the adagio directly into the light. A faint parallel exists with Beethoven's own ninth symphony (1822-1824), where there is an extended instrumental introduction to the choral finale; as the bass soloist explains on his first, startling vocal entry, it is necessary that the purely instrumental music heard earlier in the symphony be rejected in order to make imaginative space for the singing of Schiller’s ode, which is the main business of the last movement. In the introduction to the finale of Op 106, Beethoven looks forward to what is to come, not back to the adagio. The free fantasy which retrieves us from its depths begins quietly and passes through many keys in its improvisatory quest to find its way back to B flat, and in doing so experiments with various forms of 18th-century counterpoint (there are two near-quotations from Bach’s Well-Tempered Clavier) — as if its function is actually to will into existence the succeeding fugue.

This last movement is once more written in a very fast tempo. It has always terrified pianists. To the problems of physical execution and intellectual grasp are added those of memorisation: 19th-century champions of the sonata, such as Miss Arabella Goddard, could play the other three movements from memory, but were supplied with the score of the finale. There is in certain pedantic quarters a prejudice against fugues, which are seen as an archaic form of “academic” exercise, being placed within the more dramatic forms of sonata, quartet or symphony, but as Tovey says in relation to Beethoven’s late fugues, “a dramatic force at white heat underlies them”. He compares the presence of a fugue in a sonata with a playwright inserting a trial scene into a play: while this proceeds in accordance with its own internal rules, nothing else can happen and nothing else matters; in the right hands, however, such scenes can be the most exciting of all.

For Philip Barford, this collision between the analytic procedures of fugue and the synthetic dialectic of harmonic contrasts that is the essence of the sonata principle is like the wrenching of iron bars. This movement indeed conveys an impression of overwhelming intellectual force; Beethoven employs every learned device of fugue-writing: he turns the long and complex main subject upside down (inversion), he slows it down (augmentation) and changes its character; he ratchets up the tension by accelerating the timing of its entries (stretto). His most spectacular trick (though the hardest to appreciate aurally) is the “cancrizan” (crabs for these purposes, like those in Hamlet, being deemed to walk backwards, not sideways), in which the subject is played back-to-front. At a comparable moment of absolute mastery in the Prelude to Meistersinger, Wagner signalled his contrapuntal genius with a single stroke on the triangle; it by now comes as no surprise that Beethoven announces his own supreme achievement in the key of B minor.

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