April 2015

On Feb 12 I posted a puzzle canon — a single melody that can be copied so it harmonizes with itself. For instance, this famous portrait of J. S. Bach shows him holding a puzzle canon.

Here is the full story of Bach’s canon, which is closely related to a group of canons Bach wrote on the bass line of the Goldberg variations.

I based my canon on the theme of The Musical Offering by J. S. Bach. Here it is in puzzle form.

Shown below is the solution. This canon has three voices — the second and third voices are copies of the first voice, progressively delayed by 6 quarter notes, and moved down an octave. In the first 32 bars of the written-out score the three voices enter one at a time. In the second 32 bars all the voices are sounding in an infinite loop. I added a brief closing cadence in the recording to end the canon. My goal in writing this canon was to try something Bach did not cover in The Musical Offering; in this case the new twist is to employ three canonic voices instead of just two. In case you are wondering, the canon does not work if you add a fourth voice.