SONATA FORMS. In this, and in many other instances, his method is that of the air et doubles, which grows to a natural climax which can subside into the rhythm of the plain theme. Until his latest works, such sets of variations are never finished. Their dramatic intent is that of a repose which is too unearthly to last; and at the first sign of dramatic motion or change of key the sublime vision "fades into the light of common day," a light which Beethoven is far too great an idealist to despise. See the andante of the B flat trio (op. 97) ; and the slow movement of the violin concerto, which contains two episodic themes in the same key.
In his later works Beethoven found means, by striking out into foreign keys, of organizing a coda which finally spins down in fragmentary new variations, or even returns to the plain theme. Thus he was able to end his sonatas, opp. 109 and III, with solemn slow movements.
Beethoven also found other applications of the variation forms. Thus the finale of the Eroica symphony has not only the theme but many other ideas in common with the brilliant set of varia tions and fugue for pianoforte on a theme from Prometheus (op. 35) ; and the fantasia for pianoforte, chorus and orchestra, and the choral finale of the 9th symphony, are sets of melodic varia tions with freely-developed connecting links and episodes. In the case of the 9th symphony, a second thematic idea eventually combines with the figures of the first theme in double fugue.
But Beethoven's highest art in variation-form is independent of the sonata. From his earliest display of pianoforte playing, the wonderful 24 variations on a theme by Righini, to his supreme variation-work, the 33 on Diabelli's waltz, he uses and transcends every older means of variation and adds his own discoveries.
Before Beethoven the basis of variations might be a ground bass, a melody or a harmonic scheme. Beethoven discovered that rhythm and form can, with a suitable theme, be a solid basis for variations. The aria of Bach's Goldberg variations is in its phrasing as uniform as a chess-board; and if its harmonies had not a one-to-one correspondence with each variation the form would be lost. But there are themes, such as Haydn's Chorale St. Antoni, which Brahms varied, where the phrasing is interest ing in itself. A similar example is the theme by Paganini (Ex. 2a) which inspired Brahms to compose two complete sets on it.
The climax in the history of variations dates from the moment when Beethoven was just about to begin his 9th symphony, and received from A. Diabelli a waltz which that publisher was send
ing round to all the musicians in Austria, so that each might con tribute a variation to be published for the benefit of the sufferers in the late Napoleonic wars. Diabelli's theme was absurdly pro saic, but it happened to be, perhaps, the sturdiest piece of musical anatomy that Beethoven (or any composer since) ever saw; and it moved Beethoven to defer his work on the 9th symphony! The shape of Diabelli's waltz may be illustrated by a diagram which represents its first i6 bars; the upright strokes (not the spaces) being the bars, and the brackets and dots (together with the names underneath) indicating the rhythmic groups. The sec and part also consists of 16 bars, moving harmonically back from the dominant to the tonic, and rhythmically the same as the first part. This plan is astonishingly elastic. The alternation of tonic and dominant in the first eight bars may be represented by another familiar form in which three bars of tonic and a fourth of domi nant are answered by three bars of dominant and a fourth of tonic; as in variation 14 (which must be reckoned in half-bars). Again, when the theme answers the tonic by the dominant it raises the first melodic figure by one step, and this may be translated by the answer on the supertonic harmony. In the course of 5o minutes a few of these 33 variations become vague as to more than the beginnings and cadences of the theme ; and there are three simple variations in which one would like to ask Beethoven whether he had not inadvertently omitted a bar; but the momen tum of the theme is never lost ; and after a group of three slow and rather free variations this momentum breaks into an entirely free fugue (variation 32) on a salient feature of what must by courtesy be called Diabelli's melody. A free fugue is a favourite solution of the problem of the coda in a set of variations. The momentum produced by the revolution of true variations in the orbit of the theme gives the key to the whole problem. A fugue solves it by flying off at a tangent. Very sublime is the way in which Beethoven, after letting his fugue run its torrential course, returns to the orbit of his theme in an ethereal little minuet with a short coda of its own which, 16 bars before the end, shows signs of beginning to revolve again.