variation is also double, but in a different sense, the repeats being given in full with different treatment of the same figures. Moreover the balance is still kept up, since the first half is chiefly structural, and the second resumes the melody of the theme more clearly. The next two are more obscure, and therefore serve all the better to enhance the effect of the very clear reappearance of the theme in the final variation. This plan of making double variations was a favourite one with Beethoven, and he uses it again in the fourth variation in op. 111, and in the Diabelli set. In op. 111 it is worth noticing that there is an emotional phase also. The first two variations gradually work up to a vehement climax, culminating in the third. After this outburst there comes a wonderful stillness in the fourth (9–16), like the reaction from a crisis of passion, and this stillness is maintained throughout, notwithstanding the two very different manners of the double variation. Then there is a codetta and a passage wandering through mazes of curious short transitions, constantly hinting at figures of the theme; out of which the theme itself emerges at last, sailing with wind and tide in perfect fruition of its freedom; the last variation of all seems to float away into the air as the tune sings through the haze of shakes and rapid light passages that spin round it, and the whole ends in quiet repose. In such a sense Beethoven gave to his variations a dramatic or emotional texture, which may be, by those who understand it, felt to be true of the innermost workings of their emotions, but can hardly be explained in words.
Technically the most remarkable set of all is that of thirty-three on the Diabelli valse. In this appear many traits recalling those in Bach's set of thirty. For instance, there is a fugetta, cast in the structural mould of the theme; there are imitative variations, of thoroughly modern type; and there are also examples of the imitations being treated by inversion in the second half, as was the manner of Bach. But in style there is little to recall the methods of the older master, and it is useless to try and lay down hard and fast technical rules to explain the detailed connection of theme and variation. In all these last sets, and in the Diabelli set especially, Beethoven is making transformations rather than variations. He takes the theme in all its phases—harmonic, melodic, or rhythmic and having the idea well in his mind, reproduces it with unlimited variety in different aspects. At one moment a variation may follow the melody of the theme, at another the harmonic structure, at another it will be enough that some special trait like the persistence of an inner portion of the harmony in thirds or otherwise is reproduced, as in the second phrase of Variation No. 8. At other times he will scarcely do more than indicate clearly the places where the cadences and signs of the periods fall, as in Variation 13, with the long pauses; while at other times he works by nothing more than analogy, as in the relations of the end of the first half and beginning of the second half of Variation 5, and the beginnings of the second halves of Nos. 9, 13, and 22. In other cases there are even more complicated reasons for the connection. An example occurs as early as the first variation. The strong type of figure, moving by diatonic steps, adopted at the beginning, is worked out in longer reaches in the second half, until it forces the harmony away from the lines of the theme into short transitional digressions. These occur in two successive periods, which are brought round again and rendered externally as well as ideally intelligible by the way in which the periods are made to match. In a few other cases nothing but the strong points of the periods are indicated, and the hearer is left in doubt till he hears the strong cadence of the period, and then he feels himself at home again directly, but only to be immediately bewildered by a fresh stroke of genius in a direction where he does not expect it. The happiest example of this is Variation 13, already alluded to, which is principally rhythmic, just indicating by a sort of suggestion here and there a humorous version of the theme, and making all the progressions seem absurdly wrong at first sight, though they come perfectly right in the end. The two following examples are the first halves of the theme and of Variation 13:—
