Hofstadter’s Gödel, Escher, Bach is one of my all-time favorite books. As the name implies, there are many references to Bach’s music, particularly his fugues and canons. When I was reading the book back in high school, it was hard to track down and listen to all the music that came up in the book, let alone their musical scores. The world is different now, though. Take Bach’s Crab Canon, for example. Now you can find sites aplenty that describe it, show you the music, and play it. It’s called a crab because it is played against itself forward and backwards simultaneously. Don’t believe me? Look at this MIDI roll visualization (it looks like a crab!), and then listen to the audio file played backwards. You can’t do that to too many pieces of music and still have something worth hearing.
But wait! Why not look at how Bach’s canons resemble functions, and our friend the crab is g(t) = f(18-t). And if you print the piece out on a Möbius strip, you and a friend can play it together, assuming you’re on the same differentiable manifold (ha ha! you knew that). But don’t take my word for it. Watch the video.
Curiously, when it comes to Möbius music, Bach is not the only game in town. I was thoroughly charmed by this video of Vi Hart playing her comparatively recent composition, the Harry Potter Septet on a Möbiola. I like how the variable crank speed is part of the performance.
PLEASE NOTE: I don’t know if it’s really called Möbiola, but that’s what I would call it if I were king.