Here’s a neat video showing one of J.S. Bach’s “crab” canons. The melody of this piece in retrograde produces a very clever canon. This video by YouTube user Jos Leys shows how this works very clearly, including showing how the melodies line up on a mobius strip.
Even though it’s a short piece, it’s really amazing that Bach was able to compose a melody that created harmonious counterpoint when played in retrograde like this.
Just to warm up myself to work on a composition project I decided to try writing an 8 measure crab canon myself. You’ve got to keep in mind the harmonic motion must work in retrograde as well as keeping track of the intervals and melodic motion. As I wrote the first measure I went to the end and filled in the bottom part’s final measure and worked a couple of measures this way. Then I worked on composing the bottom part for the first couple of measures and filled in the top part towards the end, modifying the melodies as I needed to in order to make the harmonic and melodic motion fit the rules of baroque counterpoint. The middle four measures were the most challenging for me. I wanted to get away from being completely diatonic here and it took me a little work to get everything to work out.
The results, well, not quite as good as Bach’s. Here is what I came up with and a MIDI realization. Try it out yourself as an exercise and see how you do.