In bar (b) the first position of the chord of the Dominant is implied instead of its first inversion; in bar (c) there is a similar interchange, and in bars (d) and (g) the principal emphasis of the bar falls upon a first inversion instead of a first position of the same chord.
In other variations he goes much further still. In the ninth the strict succession of chords is frequently altered, but in such a way that the character and general contour of the harmonic succession is still to be felt in the background. For instance, in the passage corresponding to bars (e) and (f) the harmonies of E minor and G are forced in in the place of those of G and A. Then the harmony of C and A, which really represents bar (f), is driven into the bar corresponding with (g); and in order to make the final chord of the cadence answer in position with the original, all that appears of the chord corresponding to bar (g) is the last quaver. The following example will show the nature of the change, beginning at the half-bar corresponding with (d) where the first half close falls, up to the first close in the principal key in bar (h):—
This appears to be rather an extreme instance, but in reality the change is caused by nothing more than the happy idea of turning the passing note in bar (d) in an opposite direction, and so leading to the intrusion of the chord of E; thus causing the chords of G and C, which follow in their proper order, to come one step too late, and forcing the penultimate chord of the cadence into very close quarters. But the form of the cadence is preserved all the same, and so the change turns out to be more in superficial appearance than reality; while the regularity of the succession is still sufficiently obvious to identify the theme.
The manner in which all the variations are written is contrapuntal, and in many cases they are cast in some one or other of the old contrapuntal forms. Every third variation throughout, except the last, is a Canon of some sort, with a free bass which generally follows the outlines of the bass of the theme. These take all the intervals in regular order—a Canon at the unison in the 3rd variation, a Canon at the second in the 6th, and so on up to a Canon at the ninth in the 27th variation, the Canons at the fourth and fifth being complicated by making them in contrary motion. Variation 10 is a complete Fughetta, and Variation 16 an Overture after the French model, managed by making the part which represents the first half of the theme into the Maestoso movement, and the latter part into the fugal one. The last variation is a 'Quodlibet'; that is, a movement in which several bits of familiar tunes are worked in together. The tunes are 'Volkslieder' of a very bright and happy type. It begins with one to the words 'Ich bin so lang nicht bei dir g'west,' on the top of which another, 'Kraut und Ruben haben mich vertrieben,' is introduced; and the fragments of the two, and probably bits of others which are not identified, are mixed up together in amusing but artistic confusion throughout, always following the harmonic succession of the original aria. After the Quodlibet the theme is directed to be played again, so as to make the cycle complete—a plan followed by Beethoven more than once, most notably in the last movement of his Sonata in E, op. 109. Every variation in the series has a perfectly distinct character of its own, and is knit together closely and compactly by the figures used; which vary from the most pointed vivacity to the noblest dignity and calm; and are so distributed as to keep the action always going, and the interest alive at every step; the result of this many-sided technical workmanship being a perfectly mature art-form. In this respect, as in many others, Bach seems to sum up in his own lifetime the labours of several generations, and to arrive at a point of artistic development which the next generation fell far behind; for a height equal to that of his work was not again reached till Beethoven's time. But the aspect of Bach's work is peculiar to himself and his time. The technical side is brought into extreme prominence. This is shown most obviously in the canons and fugues, but it is also shown in the texture of the other variations. Some few are extremely expressive and beautiful, but it was not with the paramount object of making them all so that Bach attacked his problem, for his variations are rather developments of ideas embodied in vigorous and regular rhythmic figures than romantic or dramatic types. Both the ideas and the way of treating them belong to the old contrapuntal school, and that style of variation-writing which is most richly and comprehensively shown in this series of variations, comes to an end with Bach.
He produced several other sets in the same manner, notably the famous Chaconne in the Suite in D for violin solo; but it is not necessary to analyse that work, since the same principles are observed throughout, even to the repetition of the theme at the end to clench it all together. As in the previous case, the basis of the variation is the harmonic framework of the theme; and the melody hardly ever makes its reappearance till its resumption at the end. The bass steps are just as freely dealt with as in the previous case, from which it may be gathered that Bach considered the harmonic structure the chief thing in a Chaconne (which has the reputation of being a movement on a ground-bass) as much as in a regular Theme and variations. He also produced an example of a different kind, in a little set of eight variations on a very beautiful and melodious theme in A minor. In this the harmonic framework is not nearly so noticeable, and the variations are not made to depend upon it so much as in the other cases. Some few of them
