Re: Shape of music

>>    http://www.seedmagazine.com/news/2008/07/the_shape_of_music.php
> Nice article. I may archive it for use in some HS music cl***** or the
> principles more simply demonstrated in some lower grades. I thought
> that Pythagoras  already knew the rations or at least knew the sound
> of the 5th and when he heard these sounds being produced by two
> different anvils in the blacksmith shop, that he then got the idea to
> weigh (to determine the mass) of the anvils and found that they had
> the same ration in music!

That makes no acoustic sense at all and is obviously pure legend.

Tymoczko's stuff is incompatible with pure ratio-based tunings.
It makes essential use of equal temperament - if you don't have
closed cycles you don't have compact manifolds/orbifolds.

It doesn't actually consider the sonorities of chords at all.
They're described in a purely combinatorial way.  It's neat that
you can get so much descriptive structure out of so little acoustic
input, but it's always going to leave a lot of the real world out.

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