Form
After a statement of the aria at the beginning of the piece, there are thirty variations. The variations do not follow the melody of the aria, but rather use its bass line and chord progression. The bass line is notated by Ralph Kirkpatrick in his performing edition as follows.
The digits above the notes indicate the specified chord in the system of figured bass; where digits are separated by comma, they indicate different options taken in different variations.
Every third variation in the series of 30 is a canon, following an ascending pattern. Thus, variation 3 is a canon at the unison, variation 6 is a canon at the second (the second entry begins the interval of a second above the first), variation 9 is a canon at the third, and so on until variation 27, which is a canon at the ninth. The final variation, instead of being the expected canon in the tenth, is a quodlibet, discussed below.
As Ralph Kirkpatrick has pointed out, the variations that intervene between the canons are also arranged in a pattern. If we leave aside the initial and final material of the work (specifically, the Aria, the first two variations, the Quodlibet, and the aria da capo), the remaining material is arranged as follows. The variations found just after each canon are genre pieces of various types, among them three Baroque dances (4, 7, 19); a fughetta (10); a French overture (16); and two ornate arias for the right hand (13, 25). The variations located two after each canon (5, 8, 11, 14, 17, 20, 23, 26, and 29) are what Kirkpatrick calls "arabesques"; they are variations in lively tempo with a great deal of hand-crossing. This ternary pattern - canon, genre piece, arabesque — is repeated a total of nine times, until the Quodlibet breaks the cycle.
All the variations are in G major, apart from variations 15, 21, and 25, which are in G minor.
At the end of the thirty variations, Bach writes Aria da Capo è fine, meaning that the performer is to return to the beginning ("da capo") and play the aria again before concluding.
Read more about this topic: Goldberg Variations
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