The Genius of J.S. Bach’s “Crab Canon” Visualized on a Möbius Strip

The enigmatic Canon 1 à 2 from J. S. Bach’s Musical Offering (1747), The manuscript depicts a single musical sequence that is to be played front to back and back to front.
Video by Jos Leys ( and Xantox ( )

The most impressive of Johann Sebastian Bach’s pieces, musicophiles may have told you, will knock you over with their ingeniousness, or at least their sheer complexity.

If you process things more visually than you do aurally, pay attention to the video above, a visualization of the piece by mathematical image-maker Jos Leys. You can follow the score, note for note, and then watch as the piece reverses itself, running back across the staff in the other direction. So far, so easy, but another layer appears: Bach wrote the piece to then be played simultaneously backwards as well as forwards. But prepare yourself for the mind-blowing coup de grâce when Leys shows us at a stroke just what the impossible shape of the Möbius strip has to do with the form of this “crab canon,” meaning a canon made of two complementary, reversed musical lines.