Johann Sebastian Bach was a brilliant German composer of the early 18th century.<\/p>\n
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.<\/p>\n
The brilliance comes from combining all these up, down, forwards and backwards musical themes into something that \"works\" as a musical composition.<\/p>\n
Think of Bach's Crab Canon<\/em> as a complex round (remember Three Blind Mice<\/em>, or maybe Frere Jacques<\/em>? The music can be read from either end.<\/p>\n The following video demonstrates the idea well. It uses a Mobius strip<\/i> 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<\/a>.)<\/p>\n