RE: [tuning] octave-equivalent harmonic entropy

There was an error in the previous post:

767 4.9626 14/9 7

should reas

767 4.9626 14/9 9

So I ran N=223, and I was right -- the 15/8 and 16/15 go away (thank
goodness -- primality is still unimportant). Please look at the graph at
http://www.egroups.com/files/tuning/perlich/o006_223.jpg.

Here are the local minima for this case -- s=0.6%, N=223 (I pushed my
machine up to 1.28 gigs of virtual memory for this one):

cents entropy ratio limit
0 3.4476 1/1 1
131 5.5531 ? -
180 5.5377 10/9 9
204 5.5367 9/8 9
231 5.5041 8/7 7
267 5.4976 7/6 7
316 5.4142 6/5 5
350 5.5473 11/9-16/13 -
386 5.4167 5/4 5
436 5.5246 9/7 9
498 5.1541 4/3 3
582 5.4901 7/5 7
618 5.4901 10/7 7
702 5.1541 3/2 3
764 5.5246 14/9 9
814 5.4167 8/5 5
850 5.5473 13/8-18/11 -
884 5.4142 5/3 3
933 5.4976 12/7 7
969 5.5041 7/4 7
996 5.5367 16/9 9
1020 5.5377 9/5 9
1069 5.5531 ? -

Now the one-footed bride pattern extends all the way through the 9-limit:
the entropy is 3.44 for ratios of 1, 5.15 for ratios of 3, 5.41 for ratios
of 5, 5.50 for ratios of 7, 5.52-5.53 for ratios of 9, and higher for the
other local minima (of which there are only 2 pairs). Note that, like
Partch's bride, this analysis indicates that the increase in dissonance from
one limit to the next gets smaller and smaller the higher you go.