As my first delve into counterpoint, I decided to take a look at Bach’s Goldberg variations. These are mostly somewhat simpler than the fugues in his masterpiece ‘The Well Tempered Clavier’ and I have always found them immensely satisfying to play, although I have never sat down to analyse any of them. Nine of the variations are written as canons, and the two I particularly like are numbers 9 and 12.
Number 9 is written such that the second entry of the canon starts exactly a bar later than the first, and pitched a third lower. The fact that it is a canon is quite evident from listening to or playing it, but I hadn’t appreciated that it is in fact, note for note a completely perfect canon throughout. There is also a lot of imitation in the bass line – for example the first bar in the second section is imitated in the following bar, a fourth higher (and leads us into the key change really effectively).
Number 12 is an inverse canon; the first entry starts on a G, and the second entry comes in a bar later on a D, but with the melody completely inverted interval for interval. I started annotating the score to show all of the entries and inversions, but realised that like number 9, it is simply a perfect (inverted) canon from start to finish. In the second half the canon is started by the lower voice. Also like number 9, the bass line contains much imitation of itself, as well as of the main canon parts.
The genius in these pieces seems to lie not so much in the variety of musical devices, but in Bach’s ability to design such a long canon that makes a coherent, beautiful piece of music. I’m at a bit of a loss to know *how* he does this, but here are a few general observations:
- There is a mix of similar and contrary motion between the parts
- He sometimes brings a sustained note close to the other canon part creating effective suspensions (e.g. bars 21-22 in number 12)
- By starting a canon part after a quaver or semiquaver rest it creates the effect of the second part continuing the first (e.g. bars 9-10 in number 12)
- The bass line is often an important line in its own right (particularly in number 9). When the texture of the main canon is more complex, the bass line provides key harmony notes, and often reinforces one of the canon parts e.g. in thirds