Sun Jan 2 20:48:09 EST 2011
The 7 divisions of the string.
This is a simple algorithm for constructing musical interval ratios,
starting with small numbers. We stop when the denominator corresponds
to a regular polygon not constructable by ruler and compass.
Now that sounds quite magical, but what does it mean? I think the
non-constructable polygons (by ruler and compass) are the same as the
n-th order polynomials factorizable by radicals. This problem is
really about symmetry / discrete groups.
The question is then: is this a coincidence, i.e. simply a question of
where the brain decides ``well, this is enough beating to be called
stable sound'' or does it really have something to do with the
symmetry behind the non-constructable polygons.