��Ex.24. (Variation 13). Vivace.^
��Another most wonderful variation is the twen- tieth, in which again there is a mere suggestion of the theme woven into mazes of transitions, passing away from the harmony of the theme in the less essential points, but always making the balance even again at the close, melodic and structural principles being mixed up almost in- extricably. Example 25 shows the portion of this variation corresponding to the part of the theme given in Ex. 23 :
Ex. 25. (Variation ao).
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��In almost all the variations except the fugue (no. 32) the periods are kept quite clear, and match the original faithfully; and this is the strongest point in helping the hearer or reader to follow the connection. The free fugue, which comes last but one, is exactly in the very best place to break any sense of monotony in the recurrence of these exact periods, while the last variation sets the balance even again in a very distinct and weighty way, in favour of the plan and melody of the theme.
In connection with the point illustrated by the fugue in this set, it is noticeable that Beethoven from the first seems to have aimed at relieving in some striking and decisive way the monotony which is liable to result from the constant recurrence of short sections, and the persistence of one key. His codas are frequently very long and free, and often contain extra variations mixed up with telling passages of modulation. The early set of variations on a theme by Righini (1790) affords one remarkable illustration of this, and the twelve on the Russian air from 'Das Walclmadchen ' (1797), another. In the last movement of op. 1 1 1 the same end is gained by the stringof transitions in the body of the movement before the last two variations; a similar passage occurs in the slow movement of the 9th Symphony ; and in a few instances he gained the same end by putting some of the variations in a different key, as in those of the Eb Quartet, which also contain a modulating episode near the end.
The history of variations seems to be summed up in the set we have just been considering. In the earlier stages of the art the plan of the bass and the harmonies indicated by it was generally the paramount consideration with composers, and great technical ingenuity was expended. In characteristic sets of the earlier sonata-period the melody became paramount, and technical ingenuity was scarcely attempted. In Beetho- ven's latest productions structural and melodic elements are brought to a balance, and made to minister in all the ways that artistic ex- perience and musical feeling could suggest to the development of the ideas which lie in the kernel of the theme, and to the presentation of them in new lights.