Friday math movie: Bach Crab Canon

By Murray Bourne, 03 Jun 2011

Johann Sebastian Bach was a brilliant German composer of the early 18th century.

Much of his music involves a complex geometry of repeated patterns. Some snippets of music may be repeated up or down a note, or perhaps inverted (while the original goes up in pitch, the inversion goes down) or even played backwards.

The brilliance comes from combining all these up, down, forwards and backwards musical themes into something that “works” as a musical composition.

Think of Bach’s Crab Canon as a complex round (remember Three Blind Mice, or maybe Frere Jacques? The music can be read from either end.

The following video demonstrates the idea well. It uses a Mobius strip to show how the parts work upside down and back to front. (A Mobius strip can be made by twisting a long, thin rectangle of paper and joining the ends. Such an object has one surface and one edge only. See more at Mobius strip.)

Related article

I wrote a piece on some of the geometry involved in music here:

Music and transformation geometry

Bach’s Toccata and Fugue in D Minor

Here’s another piece by Bach, containing similar complexity (a fugue is a kind of round).

This video illustrates the music with a “bar-graph” score.

And to finish – a joke

Question: Why did the chicken cross the Mobius strip?

Answer: To get to the same side.

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