showing a confusion in his mind even as to the difference between a 'ground' and a tune. In Corelli's work the bass is not repeated at all regularly, so it is to all intents and purposes a series of free variations. These are most of them very simple, being different forms of arpeggios on the harmonies of the theme, but they are well devised so as to contrast and set off one another, and are effective in their way for the violin. The tempos vary from Adagio and Andante to Allegro and Vivace, and the time-signatures also, as 3-4, 4-4, and 3-8. Corelli evidently took an easy view of variations, for both in this set and in the Chaconne in the twelfth Sonata of op. 2, the harmonies are not at all strictly followed, and occasionally have next to nothing to do with the theme for several bars together; and this appears to have been rather a characteristic of the Italian style of writing such things. The treatment of the form in this instance, and in many others of nearly the same period (as those by Blow, and many by Locatelli and others a little later), together with the lax way in which Hawkins speaks of the subject, tend to the conclusion that this popular form of Ground-bass movement was gradually becoming mixed up with the form of Theme-and-Variations, and trenching on its province. Even the length of the bass in the Follia and other examples is in favour of this view, because the effect of the ground-bass is lost when it extends beyond very moderate limits. The best examples are after such a concise fashion as the bass quoted from Purcell, and such superb specimens as the 'Crucifixus' in Bach's Mass, his Passacaglia in C minor, and similar works by Buxtehude for the organ. If the ground-bass has several clauses, as in Corelli's Follia or Blow's piece (Ex. 6), it loses its effect and has to be treated after the manner of a theme; and the adoption of long periods led composers to that treatment, at the same time that the habit of looking at their subject in the direction of the bass rather than the upper part, influenced their manner of dealing with variations.
This condition of things throws an interesting light upon J. S. Bach's thirty Variations on an Aria in G major for a harpsichord with two rows of keys, which is the first very important work of its kind, and still among the most remarkable in existence, though it is never played in public in consequence of the difficulty of giving due effect on one row of keys to the rapid crossing passages which are written for two. The Aria which serves for theme is not after the manner of a modern aria, but is a dance movement like those in the Suites. It is in fact a Sarabande of the expressive and elaborate kind familiar among Bach's works; it has plenty of fine melody but no catching tune, and nothing to invite melodic variations of the modern kind. On the other hand, it is constructed of very broad and simple successions of harmony, with the bass moving a step of some sort in almost every bar; and upon this motion of bass or harmonies the whole series of variations is really constructed. It is therefore actually almost as much of a ground-bass movement as Corelli's Follia, or Blow's example. The actual bass figure is not repeated, but either the steps by which it moves or the regular changes of the harmony are always represented in some way under the elaborate texture of the figures. In fact, what Bach does is to take out the harmonic framework upon which the Aria is built, and use it to build thirty other little movements upon. The way in which these are developed from the original will be best understood by a comparison of the opening bars of some of the variations with the corresponding portion of the bass of the theme.
The following is the bass of the first eight bars of the Aria, with figures to represent the principal harmonies:—
In a good many variations, such as the 1st, 2nd, 4th, 12th, and 22nd, these steps are very clearly maintained. The bass figure of the 2nd variation will serve to illustrate this:—
It is very rare however that the same positions of the chords are rigidly adhered to throughout. All positions are held to be interchangeable. This would be less possible in dealing with a modern theme with weak or irregular motions of harmony; but where the changes are so strict and clear, the successions are traceable even through a looser treatment of the original. An example which will illustrate Bach's method of interchanging positions of the same chords, and the ingenuity with which he builds one form upon another, is the opening of the tenth variation, which is a complete little four-part Fughetta:—
