A Seasonal Musical Offering

In his contribution to C.P.E. Bach Studies (Cambridge UP, 2006), David Yearsley reprints a sixteen-measure composition by the composer that tackles a particularly challenging musical problem: the closed augmentation canon. In an two-voice augmentation canon (also called mensuration or prolation canon), one voice presents a melody and the other voice presents the same melody in counterpoint with the first, perhaps transposed higher or lower, perhaps starting earlier or later, but with the durations increased or decreased by a certain factor, usually a factor of two. If both voices begin together, and the augmentation factor is 2, then the faster voice will finish its melody in half the time that the longer voice needs to finish—typically, to continue the two-part counterpoint, the faster voice then uses unrelated material. However, in a closed augmentation canon, the faster voice repeats its first half verbatim; to construct not only well-formed counterpoint but an attractive composition under such fiendish restrictions requires great skill.

But to do so with preexisting materials that were ostensibly not designed for such canonic treatment is pure serendipity, as in the following, which achieves near-flawless* counterpoint.

Happy Holidays and Merry Christmas to you!

* The three instances of a harmonic fourth in mm. 2, 5, and 6 can be well justified as involving tones passing through measure-long prolonged harmonies. Perhaps the weakest point is an instance of "middleground" parallel octaves from beat 2 to beat 3 in m. 7. The similar motion to the octave at the beginning of m. 5 is not ideal, either.