Temperaments sorted by "geometric badness"

Here is a list of 45 7-limit linear temperaments I've given before, this
time sorted according to a badness measure computed using geometric
complexity.

[18, 27, 18, -34, 22, 1]
comp 58.84077764 rms .1304491741 bad 451.6459719

[1, 4, 10, 12, -13, 4]
comp 15.10180563 rms 3.665035228 bad 835.8645488

[6, -7, -2, 15, 20, -25]
comp 24.92662917 rms 1.637405196 bad 1017.380173

[2, 25, 13, -40, -15, 35]
comp 46.45156501 rms .5851564738 bad 1262.620148

[2, -4, -4, 2, 12, -11]
comp 11.92510945 rms 10.90317755 bad 1550.521640

[3, 0, -6, -14, 18, -7]
comp 14.16874336 rms 8.100678834 bad 1626.237914

[0, 5, 0, -14, 0, 8]
comp 10.25428060 rms 15.81535241 bad 1662.988586

[7, -3, 8, 27, 7, -21]
comp 25.42062964 rms 2.589237496 bad 1673.187049

[16, 2, 5, 6, 37, -34]
comp 43.84212122 rms .8753631224 bad 1682.563113

[1, -8, -14, -10, 25, -15]
comp 24.41447354 rms 2.859336356 bad 1704.354666

[5, 13, -17, -76, 41, 9]
comp 46.68750453 rms .8458796028 bad 1843.783292

[6, 5, 22, 37, -18, -6]
comp 34.26986563 rms 1.610555448 bad 1891.474472

[5, 1, 12, 25, -5, -10]
comp 21.62473825 rms 4.139050792 bad 1935.541443

[1, 4, -2, -16, 6, 4]
comp 9.836559603 rms 20.16328150 bad 1950.956872

[3, 12, -1, -36, 10, 12]
comp 24.63368765 rms 3.579262150 bad 2171.962729

[9, 5, -3, -21, 30, -13]
comp 27.04575319 rms 3.065961726 bad 2242.667503

[0, 12, 24, 22, -38, 19]
comp 38.80790985 rms 1.496892545 bad 2254.400806

[3, 5, -6, -28, 18, 1]
comp 18.24110330 rms 6.808961862 bad 2265.599328

[3, 0, 6, 14, -1, -7]
comp 12.01994256 rms 16.59867843 bad 2398.160778

[8, 18, 11, -25, 5, 10]
comp 34.23414359 rms 2.064339812 bad 2419.357927

[1, 9, -2, -30, 6, 12]
comp 19.47032028 rms 6.410458352 bad 2430.162271

[2, -9, -4, 16, 12, -19]
comp 19.94265308 rms 6.245315858 bad 2483.820897

[4, 4, 4, -2, 5, -3]
comp 11.40589690 rms 19.13699259 bad 2489.617178

[10, 9, 7, -9, 17, -9]
comp 27.53173943 rms 3.320167332 bad 2516.675801

[4, -3, 2, 13, 8, -14]
comp 14.72969739 rms 12.18857055 bad 2644.480840

[4, 2, 2, -1, 8, -6]
comp 10.57420044 rms 23.94525150 bad 2677.407524

[2, 6, 6, -3, -4, 5]
comp 11.92510945 rms 18.86388876 bad 2682.600333

[4, -8, 14, 55, -11, -22]
comp 34.89878325 rms 2.250483424 bad 2740.920186

[2, -4, -16, -26, 31, -11]
comp 26.97297092 rms 3.821630536 bad 2780.393514

[2, 8, 8, -4, -7, 8]
comp 15.87113260 rms 11.21894132 bad 2825.971103

[1, -3, 5, 20, -5, -7]
comp 12.33750942 rms 18.58450012 bad 2828.823679

[5, -11, -12, 3, 33, -29]
comp 32.44371031 rms 2.697384486 bad 2839.251640

[1, 4, -9, -32, 17, 4]
comp 19.68579597 rms 7.652394368 bad 2965.536698

[2, 8, 1, -20, 4, 8]
comp 15.29862604 rms 12.69007837 bad 2970.086938

[7, 9, 13, 5, -1, -2]
comp 24.36497795 rms 5.052931030 bad 2999.683372

[2, 8, -11, -48, 23, 8]
comp 28.86573677 rms 3.732363180 bad 3109.919806

[3, 17, -1, -50, 10, 20]
comp 34.40312184 rms 2.729116326 bad 3230.113288

[6, 5, 3, -7, 12, -6]
comp 16.38306753 rms 12.27380956 bad 3294.350648

[5, 1, -7, -19, 25, -10]
comp 19.98216004 rms 8.727168682 bad 3484.642557

[12, 10, -9, -49, 48, -12]
comp 42.88340322 rms 1.896512488 bad 3487.660430

[15, -2, -5, -6, 50, -38]
comp 45.81266906 rms 1.731229740 bad 3633.506097

[12, -2, 20, 52, 2, -31]
comp 45.66691576 rms 1.753213789 bad 3656.269843

[9, 10, -3, -35, 30, -5]
comp 30.78274747 rms 4.052704060 bad 3840.251351

[13, -10, 6, 42, 27, -46]
comp 48.03151023 rms 1.678518039 bad 3872.384715

[8, 6, 6, -3, 13, -9]
comp 21.57627467 rms 10.13226624 bad 4716.930933

--- In tuning-math@y..., Gene W Smith <genewardsmith@j...> wrote:

> [2, 25, 13, -40, -15, 35]
> comp 46.45156501 rms .5851564738 bad 1262.620148

Because of its high rank (#4) on my list of 45, it might be time to give this more-or-less-microtemperament a little respect, and an actual name. Below I give a Fokker block for the commas
<64/63, 5120/5103, 2401/2400>, and a tempering by the 239-et.

[1, 28/27, 21/20, 49/45, 9/8, 7/6, 189/160, 49/40, 80/63, 1029/800,
4/3, 441/320, 10/7, 196/135, 3/2, 14/9, 63/40, 49/30, 27/16, 343/200, 16/9, 147/80, 40/21, 3087/1600]

12 7-limit intervals, no triads, not connected :(

[0, 12, 17, 29, 41, 53, 58, 70, 82, 87, 99, 111, 123, 128, 140,
152, 157, 169, 181, 186, 198, 210, 222, 227]

59 intervals, 24 triads. It may not win a prize, but it does show the importance of tempering in some cases.

Since 239 wants to be an 11-limit system, I also checked the 11-limit
numbers: 97 intervals, 100 triads. Smokin'!