This is part 2 of a series on my forthcoming oboe concerto. This is a commission for the Handel Collection, and will be performed on 5 July 2011, 13:00–14:00 at St Stephen Walbrook (warning: site plays music), 39 Walbrook, London, EC4N 8BN. Please come along if you can!
I mentioned last time that the Sarabande is built on a meta-canon. Here’s how it works.
This movement is 156 bars long which is equal to 12 × 13 or 2 × (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12). This second formula is salient, because it’s based on a triangular number, and I’m rather fond of triangular numbers.
The oboe and bassoon parts are each divided into 12 sections, each of a different length 2n where n is a number from 1 to 12. The oboe’s sections are ordered n = 12, 9, 6, 3, 2, 5, 8, 11, 10, 7, 4, 1, and those of the bassoon n = 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3, 1, so they both similar types of pattern.
As the sections are of different lengths, the beginnings of sections rarely coincide in the two parts, and only once on the same length of section: n = 1 in the final 2 bars. Other coincidences of note are that oboe 2 and bassoon 12 start together (mirroring the beginning of the movement, where oboe 12 starts with bassoon 2), bassoon 11 and oboe 11 overlap by 16 bars, and bassoon 7 and oboe 7 by 6 bars.
This structure then forms the basis of the meta-canon: the material for each value of n is the same in both voices, wherever they occur. This means that in sections 11 and 7 the voices really are in canon, and in section 1 they are in rhythmic unison. All of the other sections are not self-contiguous, so the voices perform a canon-at-a-distance. In addition to this basic canonic principle, odd-numbered sections are inverted between oboe and bassoon, while even-numbered sections are performed recte.
There’s not really much in the way of musical example I can post until I’ve explained the derivation of the material (and finished writing it all!), so in the mean time, here’s a colourful illustration of the structure of the canon: