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.
Mozart wrote a “Mirror Canon” which is even more ridiculously clever. The single sheet of music is placed on a table between the two players, and has a clef at each end of the stave. Each player reads the music “top down” as he sees it and ignores the upside-down clef and key signature at the end of each line.
http://imslp.org/wiki/4_Spiegelkanons,_K.Anh.10.16_%28Mozart,_Wolfgang_Amadeus%29
Thanks for reminding me about that! I’ve heard that performed by a couple of flute players. And thanks for the IMSLP link to the music. I’ve forgotten about that piece and remember wanting to take a closer look at it someday. It really is ridiculously clever!