Along with the monumental Die Kunst der Fuge (The Art of Fugue), Bach’s Goldberg Variations are a supreme testament to Bach’s contrapuntal mastery and his grasp of form. Beyond that, and unlike the later work, Bach manages to integrate within a tight formal structure a whole variety of forms, dances, toccatas, fugues, even a French Overture, and above all nine magnificent canons.
There is a large literature of Bach’s use of numbers in his works (not least the famous 14; B+A+C+H, 2+1+3+8). Some of this reaches beyond fantasy, but, in a very interesting paper Ruth Tatlow discusses Bach’s obsession with numeral formal organisation and shows how he modified draft versions of some works to regularise bar numbers and overall structural balance mathematically.
Unfortunately we have no draft material for the Goldbergs but we can see this phenomenon in extremis in this work at multiple levels.
The theme on which the work is based, the bass line of the aria, consists of thirty two notes taken one per bar from the 32 bars of the aria. The theme itself is binary in structure, in two 16 note parts. You can find this scheme easily on the internet. In particular the Wikipedia entry presents the theme very clearly along with what looks to me like a summary of the notes from Kirkpatrick’s edition of the score referred to by Jane.
Because this bass line forms a continuous thread in the variations, some writers her preferred to see the Goldberg Variations as a giant passacaglia. As we shall see and no doubt discuss in due course I expect, the fragmentation of that bass line in many of the variations is perhaps a good reason not to push this concept too far.
So, from the 32 notes of the theme Bach has arranged a work consisting of 32 pieces.
As the theme is divided into two 16 note parts, so too each variation is divided into two equal parts, usually of 16 bars each. Exceptions include some of the canons with 8 bars per equal part, and the French Overture (No.17, Var.16) divided unequally with 16 bars in the first ‘half’ and 32 in the second. Even so we see the symmetry, 8,16, 32, 48.
Now there comes a different level of formality which binds the work even more tightly together. Of the 30 variations (i.e. excluding the theme and its da capo) every third variation, starting with the third is in the form of a canon. Again these are all in binary form with two equal halves of 8 or 16 bars. As a further discipline, each successive canon is increased by an interval of one note of the scale, starting with entries in unison, then at a second etc.
Finally in a brilliant coda, in Variation 30, instead of adding another canon, Bach finds a quite extraordinary way of re-introducing part of the unmodified theme-bass.
For our discussion, much of this obviously goes beyond an analysis of each individual variation, and we’ll need to keep the form of the whole work in mind in our discussion.
However, we now come to one of the most extraordinary aspects of the work, because for the first two variations of each group of three, without breaking the strict bonds of the formal structure Bach has imposed on himself, he presents an astonishingly varied array of dances, arabesques (Kirkpatrick’s word), toccatas, and a fugue, not to mention a French Overture: in fact just about every sort of individual style he used in his instrumental music - and plenty of scope for discussion.
So, on to the first three variations.
Will this do for an introduction?
I have to stop for lunch now!