Mobius Music

I just finished a fascinating book by Clifford Pickover about the Mobius strip.  A Mobius strip is a loop that has only one side.  They are really easy to make: simply tape together the two ends of a strip of paper, after first giving it a half twist.  The two-sided-ness of the paper disappears and you are left with a one-sided object.  You can test this by coloring the paper.  Try to color one side green and the other red.  It can't be done on a Mobius strip, because there is only one side to color.

The Mobius strip was discovered by August Mobius in 1858, and it's remarkable that it wasn't discovered sooner.  Studying the strip is a great introduction to topology, the study of surfaces and spatial relationships.

Topology doesn't really have anything to do with music, but it is possible to write music that can be adhered to a Mobius strip.  Music played on such a strip will result in music that can be played forwards and backwards, and upside down and right-side up.  Our good man J. S. Bach wrote something like this, called the Crab Canon from the Musical Offering.  This piece can be performed forward, then the musician can turn the page upside down and play it again.  Plus, the musician can read the music backwards to produce a different melody.  Then, using both hands, the player can perform the piece as a two-handed duet, with the canon flipped over and reversed in one hand and right-side up and forward in the other hand.

Bach wasn't the only musical genius to experiment with these musical puzzles.  Arnold Schoenberg (I've talked about him recently.  Remember Schoenberg?) also wrote canons, that he called "mirror canons" that could be flipped over and turned around.  Schoenberg was also interested in "twelve-tone music", which uses the same one-sided idea as the Mobius strip.  With the 12-tone rows, the composers would assemble all 12 pitches in a row, sometimes at random, but only using each pitch once within the row.  From here, they can reverse the pitches, invert them, and invert and reverse them.  The result can be applied to atonal music.

I know.  Just accept the fact that you are going to learn more about atonal music than you thought you wanted to this year.

:-)