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The 81/80 and 31 mob

🔗Gene Ward Smith <gwsmith@svpal.org>

6/29/2004 5:14:00 PM

The TM basis for 31 is {81/80, 126/125, 1029/1024} which we can use to
find mobs as large as we like for 31 and a chosen comma; however only
finitely many will make even minimal sense. Below I cut the mob off at
eight members, which seems to be plenty. I give the Graham complexity,
the TOP error and the corresponding badness on the second line. Note
that all except for a rather useless version of meantone have the
exact same TOP tuning!

meantone
[1, 4, 10, 4, 13, 12] [[1, 2, 4, 7], [0, -1, -4, -10]]
10 1.698521 169.852100

supermajor seconds
[3, 12, -1, 12, -10, -36] [[1, 1, 0, 3], [0, 3, 12, -1]]
13 1.698521 287.050049

squares
[4, 16, 9, 16, 3, -24] [[1, 3, 8, 6], [0, -4, -16, -9]]
16 1.698521 434.821376

semififths
[2, 8, -11, 8, -23, -48] [[1, 1, 0, 6], [0, 2, 8, -11]]
19 1.698521 613.166081

[5, 20, 19, 20, 16, -12] [[1, 4, 12, 12], [0, -5, -20, -19]]
20 1.698521 679.408400

-31 nexial adjusted meantone
[1, 4, -21, 4, -36, -60] [[1, 2, 4, -6], [0, -1, -4, 21]]
25 1.762367 1101.479671

[7, 28, 8, 28, -7, -60] [[1, 0, -4, 1], [0, 7, 28, 8]]
28 1.698521 1331.640464

[6, 24, 29, 24, 29, 0] [[1, 1, 0, 0], [0, 6, 24, 29]]
29 1.698521 1428.456161