A little mathematics of Bach

This column does not have a single author, but is submitted by a number of experts that contribute regularly to our news source.  Some are in Canada, some in the UK and one is in the far east

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We present for your enjoyment some music of Bach that is transformed in very interesting ways.. This is called Crab Cannon on a Moebius Strip.. 

As most people know, music is very mathematical and this video illustrates some of it.  Music can be transformed quite easily in time and pitch, but certain transformations are not well known.

For example, some music can be played end to beginning or by two players starting at different ends and passing one another.  The video in the second column does all of that and then forms a Moebius strip of the music and plays that too.

A Moebius Strip is a geometric shape that has no beginning and no end and only one side and one edge.  You can make one easily by taking a thin strip of paper and gluing or taping one end with a twist to another.  You can see this in the video shown below:

Making a Moebius Strip

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12/09/2009 04:40 PM

In the video linked to below, the music is cut like it was a Moebius Strip and then played.  There are all sorts of things you can do with Music.  For example a piece by Mozart can be played upside down to great effect.

Here is s good thing for your children/grandchildren. 

Cut out a Moebius Strip like the video instructs  (stop at the first cut)

1.  After using the marker to draw a line on the strip, please note that the pen does not leave the surface and returns to the start point without leaving the paper, showing that it has only one side.

2.  Take the same marker and mark the edge with it.  You/ll notice that it only had one edge too!

Here is the Bach piece.  Watch closely and listen too.

Bach transformed