An 11-limit linear temperament top 100 list

This isn't *actually* top 100, since I left in some temperaments which were plainly too inaccurate for study purposes, but 100 is a lot of temperaments so I'm not worried.

If we define "epimericity" for p/q > 1 reduced to its lowest form as
log(p-q)/log(q), then as I suggested in Message 4458, we can use a list with bounded epimericity as a comma list. While Carl thought my consideration of superparticular temperaments was a dud, it inspired me to think this idea is a good plan, especially now that I have a better computer and version of Maple in hand.

The extra commas I suggested were all that was needed in the 7-limit all had epimericity less than .46. I suggested .5 as a cutoff for
the 7-limit and .3 for the 11-limit; I boosted this to .35, with a 50 cent cutoff for size. This gave me the following list of 51 commas,
in order of badness of the corresponding planar temperament:

[9801/9800, 3025/3024, 3294225/3294172, 151263/151250, 441/440, 385/384, 225/224, 2401/2400, 56/55, 176/175, 4375/4374, 540/539, 64/63, 100/99, 250047/250000, 5632/5625, 36/35, 1375/1372, 126/125, 45/44, 99/98, 43923/43904, 896/891, 81/80, 49/48, 50/49, 121/120, 117649/117612, 55/54, 41503/41472, 1771561/1771470, 77/75, 4000/3993, 6250/6237, 8019/8000, 6144/6125, 1029/1024,5120/5103, 3388/3375, 3136/3125, 32805/32768, 245/242, 243/242, 128/125, 12005/11979, 245/243, 1728/1715, 19712/19683, 625/616, 1331/1323, 2200/2187]

Wedging these three at a time led to 6135 wedgies. Taking the best 100 of these by geometric badness gave me my list. As I remarked, some of the resulting temperaments should be tossed as too inaccurate, but I left them as examples to consider in connection with the straightness discussion. We now have so many versions of Meantone we might need to beat them off with a stick; the one I called "Meanpop" I gave that name to since it has a fifth which is poptimal for seven-limit Meantone. Many names familiar from the seven-limit or named before appear here.

Hemiennealimmal
[36, 54, 36, 18, 2, -44, -96, -68, -145, -74] [[18, 28, 41, 50, 62], [0, 2, 3, 2, 1]]

generators [66.6666666667, 17.6128210979]
bad 2055.541669 rms .198798 comp 256.276437

Miracle
[6, -7, -2, 15, -25, -20, 3, 15, 59, 49] [[1, 1, 3, 3, 2], [0, 6, -7, -2, 15]]

generators [1200., 116.672264296]
bad 2362.204792 rms 1.901466 comp 71.868304

[38, 38, 114, 76, -28, 74, -11, 158, 45, -181] [[38, 60, 88, 106, 131], [0, 1, 1, 3, 2]]

generators [31.5789473684, 7.15256754222]
bad 2665.433369 rms .129891 comp 386.646417

[0, 0, 0, 1, 0, 0, 2, 0, 3, 3] [[1, 2, 3, 3, 4], [0, 0, 0, 0, -1]]

generators [1200., 140.882982221]
bad 3059.967157 rms 517.602977 comp 2.904237

[2, -16, 78, 58, -30, 118, 85, 226, 190, -107] [[2, 3, 6, -1, 2], [0, 1, -8, 39, 29]]

generators [600.000000000, 101.758845067]
bad 3156.846100 rms .208485 comp 322.186595

[20, -30, -10, -80, -94, -72, -196, 61, -82, -190] [[10, 16, 23, 28, 34], [0, -2, 3, 1, 8]]

generators [120.000000000, 8.93614137404]
bad 3203.569897 rms .254545 comp 288.351390

[102, 210, 216, 222, 96, 56, -1, -88, -211, -124] [[6, 11, 17, 20, 24], [0, -17, -35, -36, -37]]

generators [200.000000000, 17.5327039657]
bad 3334.010974 rms .036009 comp 954.841112

Unidec
[12, 22, -4, -6, 7, -40, -51, -71, -90, -3] [[2, 5, 8, 5, 6], [0, -6, -11, 2, 3]]

generators [600.000000000, 183.182783130]
bad 3535.629462 rms 1.249417 comp 117.775665

[14, 6, 74, 52, -23, 78, 34, 155, 100, -110] [[2, 4, 5, 10, 10], [0, -7, -3, -37, -26]]

generators [600.000000000, 71.1037242400]
bad 3709.724174 rms .352551 comp 258.983392

[44, -10, 6, 79, -118, -114, -27, 42, 218, 201] [[1, 3, 2, 3, 6], [0, -44, 10, -6, -79]]

generators [1200., 38.5948091514]
bad 3815.546980 rms .219371 comp 350.127551

Wizard
[12, -2, 20, -6, -31, -2, -51, 52, -7, -86] [[2, 1, 5, 2, 8], [0, 6, -1, 10, -3]]

generators [600.000000000, 216.784022808]
bad 3830.786400 rms 1.584515 comp 107.160572

[8, -64, -30, -110, -120, -70, -202, 110, -34, -205] [[2, 2, 14, 10, 23], [0, 4, -32, -15, -55]]

generators [600.000000000, 175.435046942]
bad 3951.940564 rms .205760 comp 371.595182

Quartaminorthirds
[9, 5, -3, 7, -13, -30, -20, -21, -1, 30] [[1, 1, 2, 3, 3], [0, 9, 5, -3, 7]]

generators [1200., 77.9320061602]
bad 4041.237407 rms 4.418576 comp 59.805237

[18, 15, -6, 9, -18, -60, -48, -56, -31, 46] [[3, 6, 8, 8, 11], [0, -6, -5, 2, -3]]

generators [400.000000000, 83.1441780398]
bad 4104.955169 rms 1.357052 comp 122.582132

Pajara
[2, -4, -4, -12, -11, -12, -26, 2, -14, -20] [[2, 3, 5, 6, 8], [0, 1, -2, -2, -6]]

generators [600.000000000, 107.105867271]
bad 4125.050690 rms 9.552922 comp 38.122013

Octoid
[24, 32, 40, 24, -5, -4, -45, 3, -55, -71] [[8, 13, 19, 23, 28], [0, -3, -4, -5, -3]]

generators [150.000000000, 16.0721625528]
bad 4139.349018 rms .768706 comp 173.261857

Tripletone
[3, 0, -6, -6, -7, -18, -20, -14, -14, 4] [[3, 5, 7, 8, 10], [0, -1, 0, 2, 2]]

generators [400.000000000, 87.7987973153]
bad 4275.784995 rms 12.772525 comp 32.722273

Orwell
[7, -3, 8, 2, -21, -7, -21, 27, 15, -22] [[1, 0, 3, 1, 3], [0, 7, -3, 8, 2]]

generators [1200., 271.444627222]
bad 4352.766535 rms 5.548615 comp 54.544189

[2, -4, -16, -24, -11, -31, -45, -26, -42, -12] [[2, 3, 5, 7, 9], [0, 1, -2, -8, -12]]

generators [600.000000000, 103.783535999]
bad 4368.478166 rms 3.182069 comp 76.308394

Meantone
[1, 4, 10, 18, 4, 13, 25, 12, 28, 16] [[1, 2, 4, 7, 11], [0, -1, -4, -10, -18]]

generators [1200., 502.999427608]
bad 4405.132983 rms 6.584357 comp 49.575532

Magic
[5, 1, 12, -8, -10, 5, -30, 25, -22, -64] [[1, 0, 2, -1, 6], [0, 5, 1, 12, -8]]

generators [1200., 380.713812625]
bad 4474.854562 rms 4.730404 comp 61.027896

[0, 0, 0, 5, 0, 0, 8, 0, 12, 14] [[5, 8, 12, 14, 17], [0, 0, 0, 0, 1]]

generators [240.000000000, 99.1170177792]
bad 4584.543716 rms 53.042760 comp 14.521183

Duodecimal
[0, 12, 24, 36, 19, 38, 57, 22, 42, 18] [[12, 19, 28, 34, 42], [0, 0, -1, -2, -3]]

generators [100.000000000, 16.8004014251]
bad 4602.747844 rms 1.886540 comp 107.748365

[38, -3, 8, 64, -93, -94, -30, 27, 159, 152] [[1, -7, 3, 1, -11], [0, 38, -3, 8, 64]]

generators [1200., 271.110310111]
bad 4668.827965 rms .383188 comp 282.799004

[1, -1, 3, 4, -4, 2, 3, 10, 13, 1] [[1, 2, 2, 4, 5], [0, -1, 1, -3, -4]]

generators [1200., 455.784552041]
bad 4694.936246 rms 44.341252 comp 16.401858

Pentoid
[2, 3, 1, -2, 0, -4, -10, -6, -15, -9] [[1, 2, 3, 3, 3], [0, -2, -3, -1, 2]]

generators [1200., 262.017672737]
bad 4792.041040 rms 40.160927 comp 17.620981

Catakleismic
[6, 5, 22, -21, -6, 18, -54, 37, -66, -135] [[1, 0, 1, -3, 9], [0, 6, 5, 22, -21]]

generators [1200., 316.707652223]
bad 4805.477920 rms 1.697137 comp 117.818038

Nonkleismic
[10, 9, 7, 25, -9, -17, 5, -9, 27, 46] [[1, -1, 0, 1, -3], [0, 10, 9, 7, 25]]

generators [1200., 310.147077476]
bad 4830.505211 rms 3.316530 comp 79.065160

[8, -64, -30, 61, -120, -70, 69, 110, 363, 275] [[1, 1, 7, 5, -1], [0, 8, -64, -30, 61]]

generators [1200., 87.7196164898]
bad 4849.969370 rms .241148 comp 382.009103

[2, -57, -28, 46, -95, -50, 66, 95, 304, 226] [[1, 1, 19, 11, -10], [0, 2, -57, -28, 46]]

generators [1200., 351.114995251]
bad 4873.582183 rms .331141 comp 316.738528

Hemithird
[15, -2, -5, 22, -38, -50, -17, -6, 58, 79] [[1, 4, 2, 2, 7], [0, -15, 2, 5, -22]]

generators [1200., 193.222638998]
bad 4937.466578 rms 1.772097 comp 116.683657

[0, 0, 0, 3, 0, 0, 5, 0, 7, 9] [[3, 5, 7, 9, 11], [0, 0, 0, 0, -1]]

generators [400.000000000, 140.882982221]
bad 4948.732044 rms 134.144184 comp 8.712710

Dominant Seventh
[1, 4, -2, -6, 4, -6, -13, -16, -28, -10] [[1, 2, 4, 2, 1], [0, -1, -4, 2, 6]]

generators [1200., 495.145082634]
bad 4962.157739 rms 18.933026 comp 28.253374

[1, -3, -4, -1, -7, -9, -5, -1, 8, 11] [[1, 2, 1, 1, 3], [0, -1, 3, 4, 1]]

generators [1200., 526.844177545]
bad 4967.542223 rms 36.627981 comp 19.028176

Schismic
[1, -8, -14, -18, -15, -25, -32, -10, -14, -2] [[1, 2, -1, -3, -4], [0, -1, 8, 14, 18]]

generators [1200., 497.529640592]
bad 4970.055833 rms 5.290179 comp 60.776340

[24, -9, -66, 12, -70, -172, -64, -128, 59, 262] [[3, 2, 8, 16, 9], [0, 8, -3, -22, 4]]

generators [400.000000000, 137.769752422]
bad 5047.036500 rms .354706 comp 310.384815

[1, -1, 0, 1, -4, -3, -2, 3, 6, 3] [[1, 2, 2, 3, 4], [0, -1, 1, 0, -1]]

generators [1200., 459.070228117]
bad 5056.794051 rms 130.796462 comp 8.961229

Septimal
[0, 0, 7, 0, 0, 11, 0, 16, 0, -24] [[7, 11, 16, 20, 24], [0, 0, 0, -1, 0]]

generators [171.428571428, 85.5877110034]
bad 5184.550217 rms 22.636347 comp 26.058106

[24, 20, 16, -12, -24, -42, -102, -19, -97, -89] [[4, 6, 9, 11, 14], [0, 6, 5, 4, -3]]

generators [300.000000000, 16.8775244692]
bad 5185.657721 rms 1.086899 comp 161.127182

[6, -48, -108, 3, -90, -188, -16, -116, 173, 382] [[3, 4, 13, 22, 10], [0, 2, -16, -36, 1]]

generators [400.000000000, 150.873707764]
bad 5244.564671 rms .228287 comp 413.748659

[0, 0, 0, 2, 0, 0, 3, 0, 5, 5] [[2, 3, 5, 5, 7], [0, 0, 0, 0, -1]]

generators [600.000000000, 140.882982221]
bad 5347.782721 rms 284.929289 comp 5.808473

[12, 34, 20, 30, 26, -2, 6, -49, -48, 15] [[2, 4, 7, 7, 9], [0, -6, -17, -10, -15]]

generators [600.000000000, 83.1977090004]
bad 5359.187204 rms 1.462302 comp 137.542589

[23, -1, 13, 42, -55, -44, -13, 33, 101, 73] [[1, 9, 2, 7, 17], [0, -23, 1, -13, -42]]

generators [1200., 386.859261176]
bad 5380.665034 rms 1.013641 comp 171.779435

[0, 2, 2, 2, 3, 3, 3, -1, -2, -1] [[2, 3, 5, 6, 7], [0, 0, -1, -1, -1]]

generators [600.000000000, 266.469146634]
bad 5407.715441 rms 129.838957 comp 9.370554

Supersupermajor
[3, 17, -1, -13, 20, -10, -31, -50, -89, -33] [[1, 1, -1, 3, 6], [0, 3, 17, -1, -13]]

generators [1200., 234.451570240]
bad 5412.588259 rms 3.005389 comp 89.805421

Meanpop
[1, 4, 10, -13, 4, 13, -24, 12, -44, -71] [[1, 2, 4, 7, -2], [0, -1, -4, -10, 13]]

generators [1200., 503.595073256]
bad 5420.225629 rms 5.644271 comp 61.580856

[3, -5, -6, -1, -15, -18, -12, 0, 15, 18] [[1, 3, 0, 0, 3], [0, -3, 5, 6, 1]]

generators [1200., 562.608972648]
bad 5472.363478 rms 13.781284 comp 36.251932

Schismatic
[1, -8, -14, 23, -15, -25, 33, -10, 81, 113] [[1, 2, -1, -3, 13], [0, -1, 8, 14, -23]]

generators [1200., 497.816548050]
bad 5478.851624 rms 2.447559 comp 102.323143

[0, 0, 0, 4, 0, 0, 6, 0, 9, 11] [[4, 6, 9, 11, 14], [0, 0, 0, 0, -1]]

generators [300.000000000, 140.882982221]
bad 5506.167087 rms 92.405127 comp 11.616947

[1, -3, -2, -1, -7, -6, -5, 4, 8, 4] [[1, 2, 1, 2, 3], [0, -1, 3, 2, 1]]

generators [1200., 510.517333268]
bad 5513.617840 rms 54.982509 comp 15.875495

[6, -19, -26, -21, -44, -58, -54, -7, 17, 31] [[1, 2, 1, 1, 2], [0, -6, 19, 26, 21]]

generators [1200., 83.3216367302]
bad 5534.523131 rms 1.883084 comp 120.483135

[6, -36, -84, -132, -71, -150, -230, -94, -182, -80] [[6, 10, 11, 10, 10], [0, -1, 6, 14, 22]]

generators [200.000000000, 97.7979183888]
bad 5608.137311 rms .259073 comp 399.243757

Superkleismic
[9, 10, -3, 2, -5, -30, -28, -35, -30, 16] [[1, 4, 5, 2, 4], [0, -9, -10, 3, -2]]

generators [1200., 321.939679550]
bad 5706.061896 rms 5.302952 comp 65.931245

[2, -2, -2, 0, -8, -9, -7, 1, 7, 7] [[2, 3, 5, 6, 7], [0, 1, -1, -1, 0]]

generators [600.000000000, 145.338368448]
bad 5731.615600 rms 46.396405 comp 17.991842

[2, -16, -40, -60, -30, -69, -102, -48, -84, -30] [[2, 3, 6, 9, 12], [0, 1, -8, -20, -30]]

generators [600.000000000, 101.618164890]
bad 5760.166908 rms .979643 comp 182.650266

Porcupine
[3, 5, -6, 4, 1, -18, -4, -28, -8, 32] [[1, 2, 3, 2, 4], [0, -3, -5, 6, -4]]

generators [1200., 162.926556665]
bad 5765.207416 rms 11.793935 comp 41.067070

[6, 0, 3, 3, -14, -12, -16, 7, 7, -2] [[3, 4, 7, 8, 10], [0, 2, 0, 1, 1]]

generators [400.000000000, 152.119884703]
bad 5804.051786 rms 14.472091 comp 36.468676

[0, 1, 0, 0, 2, 0, 0, -3, -4, 0] [[1, 2, 3, 3, 4], [0, 0, -1, 0, 0]]

generators [1200., 338.888056433]
bad 5837.190159 rms 483.720277 comp 4.456211

[2, 1, 3, 5, -3, -1, 1, 4, 8, 4] [[1, 1, 2, 2, 2], [0, 2, 1, 3, 5]]

generators [1200., 344.800380608]
bad 5859.936960 rms 55.689539 comp 16.340735

[0, 5, 0, -5, 8, 0, -8, -14, -29, -14] [[5, 8, 12, 14, 17], [0, 0, -1, 0, 1]]

generators [240.000000000, 82.5021142548]
bad 5925.447275 rms 22.089446 comp 28.649813

Injera
[2, 8, 8, 12, 8, 7, 12, -4, 0, 6] [[2, 3, 4, 5, 6], [0, 1, 4, 4, 6]]

generators [600.000000000, 91.3378934315]
bad 5930.390624 rms 13.344995 comp 38.784565

[1, -1, -2, 1, -4, -6, -2, -2, 6, 10] [[1, 2, 2, 2, 4], [0, -1, 1, 2, -1]]

generators [1200., 492.054891356]
bad 5979.311922 rms 96.113418 comp 11.921209

[2, 1, 3, -2, -3, -1, -10, 4, -8, -16] [[1, 1, 2, 2, 4], [0, 2, 1, 3, -2]]

generators [1200., 336.439285435]
bad 6018.139480 rms 52.234534 comp 17.254513

[4, 2, 2, -4, -6, -8, -20, -1, -16, -18] [[2, 4, 5, 6, 6], [0, -2, -1, -1, 2]]

generators [600.000000000, 257.288990758]
bad 6037.202663 rms 22.632565 comp 28.553621

[6, -12, 10, -14, -33, -1, -43, 57, 9, -74] [[2, 4, 3, 7, 5], [0, -3, 6, -5, 7]]

generators [600.000000000, 165.152290841]
bad 6063.419880 rms 2.986631 comp 96.498734

[6, -48, -108, -168, -90, -188, -287, -116, -224, -98] [[6, 10, 10, 8, 7], [0, -1, 8, 18, 28]]

generators [200.000000000, 98.2539292888]
bad 6150.370425 rms .191092 comp 506.518200

[42, 47, 34, 33, -23, -64, -93, -53, -86, -25] [[1, -13, -14, -9, -8], [0, 42, 47, 34, 33]]

generators [1200., 416.714284033]
bad 6156.791026 rms .579519 comp 260.478466

Tritonic
[5, -11, -12, -3, -29, -33, -22, 3, 31, 33] [[1, 4, -3, -3, 2], [0, -5, 11, 12, 3]]

generators [1200., 580.274408364]
bad 6158.168745 rms 5.154394 comp 70.204409

Double wide
[8, 6, 6, -4, -9, -13, -34, -3, -30, -32] [[2, 5, 6, 7, 6], [0, -4, -3, -3, 2]]

generators [600.000000000, 274.687303196]
bad 6195.802215 rms 8.163015 comp 53.474677

[17, 6, 15, 27, -30, -24, -16, 18, 42, 24] [[1, -5, 0, -3, -7], [0, 17, 6, 15, 27]]

generators [1200., 464.880312701]
bad 6229.034828 rms 2.412281 comp 111.479674

Meanertone
[1, 4, 3, -1, 4, 2, -5, -4, -16, -13] [[1, 2, 4, 4, 3], [0, -1, -4, -3, 1]]

generators [1200., 503.381925652]
bad 6235.745072 rms 47.548543 comp 18.648791

Meanenneadecal
[1, 4, 10, 6, 4, 13, 6, 12, 0, -18] [[1, 2, 4, 7, 6], [0, -1, -4, -10, -6]]

generators [1200., 504.558724590]
bad 6252.411315 rms 18.965801 comp 32.422449

[64, 172, 102, 146, 124, -18, 10, -246, -256, 57] [[2, -6, -20, -9, -14], [0, 32, 86, 51, 73]]

generators [600.000000000, 171.934587317]
bad 6258.003982 rms .114672 comp 695.323226

[1, 33, 27, -18, 50, 40, -32, -30, -156, -144] [[1, 2, 16, 14, -4], [0, -1, -33, -27, 18]]

generators [1200., 497.374746314]
bad 6259.261024 rms 1.115730 comp 177.573572

[3, -24, -1, 28, -45, -10, 34, 65, 148, 82] [[1, 1, 7, 3, -2], [0, 3, -24, -1, 28]]

generators [1200., 233.937160254]
bad 6259.999412 rms 1.499793 comp 148.705092

Pajaric
[2, -4, -4, 0, -11, -12, -7, 2, 14, 14] [[2, 3, 5, 6, 7], [0, 1, -2, -2, 0]]

generators [600.000000000, 106.675554557]
bad 6293.616955 rms 27.006882 comp 26.330282

[18, 39, 42, 9, 20, 16, -48, -12, -114, -120] [[3, 2, 1, 2, 9], [0, 6, 13, 14, 3]]

generators [400.000000000, 183.522617689]
bad 6297.037343 rms 1.049818 comp 184.847442

Supermajor seconds
[3, 12, -1, -8, 12, -10, -23, -36, -60, -19] [[1, 1, 0, 3, 5], [0, 3, 12, -1, -8]]

generators [1200., 231.991673974]
bad 6304.096122 rms 6.456792 comp 62.196165

Diminished
[4, 4, 4, 0, -3, -5, -14, -2, -14, -14] [[4, 6, 9, 11, 14], [0, 1, 1, 1, 0]]

generators [300.000000000, 114.119995044]
bad 6306.500152 rms 27.265894 comp 26.212063

Slender
[13, -10, 6, 17, -46, -27, -18, 42, 74, 27] [[1, 2, 2, 3, 4], [0, -13, 10, -6, -17]]

generators [1200., 38.3548342416]
bad 6321.956492 rms 2.438407 comp 111.749905

[18, -9, 18, 9, -56, -22, -48, 67, 52, -37] [[9, 14, 21, 25, 31], [0, 2, -1, 2, 1]]

generators [133.333333333, 17.0160504962]
bad 6325.840259 rms 1.689101 comp 139.340563

[30, 13, 14, 3, -49, -62, -99, -4, -38, -40] [[1, -13, -4, -4, 2], [0, 30, 13, 14, 3]]

generators [1200., 583.380644845]
bad 6326.911371 rms 1.179376 comp 172.871604

Kleismic
[6, 5, 3, -2, -6, -12, -24, -7, -22, -16] [[1, 0, 1, 2, 4], [0, 6, 5, 3, -2]]

generators [1200., 317.610475585]
bad 6369.686860 rms 14.472383 comp 38.560870

[5, 3, 7, 4, -7, -3, -11, 8, -1, -13] [[1, 1, 2, 2, 3], [0, 5, 3, 7, 4]]

generators [1200., 141.164897166]
bad 6400.766041 rms 19.644403 comp 32.195552

[4, 2, 2, 10, -6, -8, 2, -1, 16, 21] [[2, 4, 5, 6, 9], [0, -2, -1, -1, -5]]

generators [600.000000000, 252.994745924]
bad 6414.557575 rms 19.453599 comp 32.426498

[2, 1, 6, 5, -3, 4, 1, 11, 8, -7] [[1, 1, 2, 1, 2], [0, 2, 1, 6, 5]]

generators [1200., 355.041079645]
bad 6442.538585 rms 37.484665 comp 21.934212

[1, -1, 3, -4, -4, 2, -10, 10, -6, -22] [[1, 2, 2, 4, 2], [0, -1, 1, -3, 4]]

generators [1200., 455.251489802]
bad 6476.838112 rms 43.037876 comp 20.253838

Hemiwuerschmidt
[16, 2, 5, 40, -34, -37, 8, 6, 86, 95] [[1, -1, 2, 2, -3], [0, 16, 2, 5, 40]]

generators [1200., 193.827642803]
bad 6485.787554 rms 1.764586 comp 137.781843

[1, 2, 0, 1, 1, -3, -2, -6, -5, 3] [[1, 2, 3, 3, 4], [0, -1, -2, 0, -1]]

generators [1200., 390.155136790]
bad 6547.764893 rms 157.873401 comp 9.346962

Hemiamity
[10, 26, -34, -28, 18, -82, -79, -152, -155, 39] [[2, 1, -1, 13, 13], [0, 5, 13, -17, -14]]

generators [600.000000000, 260.565078209]
bad 6616.465091 rms .881985 comp 211.396985

Arnold
[1, 4, -2, -1, 4, -6, -5, -16, -16, 4] [[1, 2, 4, 2, 3], [0, -1, -4, 2, 1]]

generators [1200., 501.833702413]
bad 6618.437371 rms 39.863722 comp 21.483576

[34, -24, 64, -28, -117, 6, -162, 216, 18, -300] [[2, -3, 9, -6, 12], [0, 17, -12, 32, -14]]

generators [600.000000000, 217.771906631]
bad 6646.001837 rms .339966 comp 375.555942

[2, 1, -4, 5, -3, -12, 1, -12, 8, 28] [[1, 1, 2, 4, 2], [0, 2, 1, -4, 5]]

generators [1200., 353.356606337]
bad 6651.131431 rms 27.107413 comp 27.157168

Pajarous
[2, -4, -4, 10, -11, -12, 9, 2, 37, 42] [[2, 3, 5, 6, 6], [0, 1, -2, -2, 5]]

generators [600.000000000, 109.882784796]
bad 6667.906222 rms 12.267148 comp 43.767076

[6, 29, -2, -21, 32, -20, -54, -86, -149, -52] [[1, 4, 14, 2, -5], [0, -6, -29, 2, 21]]

generators [1200., 483.287995700]
bad 6718.809696 rms 1.555238 comp 151.808898

Ennealimmal
[18, 27, 18, 144, 1, -22, 166, -34, 241, 342] [[9, 15, 22, 26, 37], [0, -2, -3, -2, -16]]

generators [133.333333333, 48.8643746446]
bad 6729.608260 rms .324647 comp 388.997739

[2, -6, 1, -2, -14, -4, -10, 19, 16, -9] [[1, 2, 1, 3, 3], [0, -2, 6, -1, 2]]

generators [1200., 259.236678539]
bad 6745.990413 rms 19.984071 comp 32.886454

[82, 28, 120, 155, -146, -40, -38, 200, 263, 20] [[1, -14, -3, -20, -26], [0, 82, 28, 120, 155]]

generators [1200., 228.072122768]
bad 6759.616416 rms .153762 comp 610.722159

[18, -14, 30, -20, -64, -3, -94, 109, 2, -160] [[2, 4, 4, 7, 6], [0, -9, 7, -15, 10]]

generators [600.000000000, 55.2942867559]
bad 6760.326292 rms 1.000617 comp 198.527159

Opossum
[3, 5, 9, 4, 1, 6, -4, 7, -8, -20] [[1, 2, 3, 4, 4], [0, -3, -5, -9, -4]]

generators [1200., 159.564330324]
bad 6767.545993 rms 22.129858 comp 30.993567

>If we define "epimericity" for p/q > 1 reduced to its lowest
>form as log(p-q)/log(q),

Now we're talking. Looks a lot like the "cent" heuristic...

>then as I suggested in Message 4458,

Apparently, *then* we were talking. I remember reading that,
too, but I just didn't have a clue where it was coming from.
Now, I think I'm catching on.

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:
...
> The extra commas I suggested were all that was needed in the 7-limit
all had epimericity less than .46. I suggested .5 as a cutoff for
> the 7-limit and .3 for the 11-limit; I boosted this to .35, with a
50 cent cutoff for size. This gave me the following list of 51 commas,
> in order of badness of the corresponding planar temperament:
>
> [9801/9800, 3025/3024, 3294225/3294172, 151263/151250, 441/440,
385/384, 225/224, 2401/2400, 56/55, 176/175, 4375/4374, 540/539,
64/63, 100/99, 250047/250000, 5632/5625, 36/35, 1375/1372, 126/125,
45/44, 99/98, 43923/43904, 896/891, 81/80, 49/48, 50/49, 121/120,
117649/117612, 55/54, 41503/41472, 1771561/1771470, 77/75, 4000/3993,
6250/6237, 8019/8000, 6144/6125, 1029/1024,5120/5103, 3388/3375,
3136/3125, 32805/32768, 245/242, 243/242, 128/125, 12005/11979,
245/243, 1728/1715, 19712/19683, 625/616, 1331/1323, 2200/2187]
>
> Wedging these three at a time led to 6135 wedgies. Taking the best
100 of these by geometric badness gave me my list.
...

Hi Gene,

I was looking for names for linear temperaments I had found using
Graham's online finder, and I noticed this 11-limit one wasn't in your
list:

Complex aug fourths
generator mapping [[1, ?, ?, ?, ?], [0, -7, -26, -25, 3]]
minimax generators [1200., 585.14]
minimax error 4.1 c

Does this mean there is another 11-limit comma that should be added to
your list above?

I called it "complex" in deference to this one in your list:

> Tritonic
> [5, -11, -12, -3, -29, -33, -22, 3, 31, 33] [[1, 4, -3, -3, 2], [0,
-5, 11, 12, 3]]
>
> generators [1200., 580.274408364]
> bad 6158.168745 rms 5.154394 comp 70.204409

Dave, I have a different interpretation of what's going on here than
you. Gene has gone about the process of finding 11-limit linear
temperaments in several ways. Proceeding directly from a prescribed
set of commas was never one that anyone thought would capture _the_
top 100, or top N, according to any badness function (of complexity
and error). That's why Gene wrote "An" and not "The" in the title.
Proceeding directly from commas is probably something that I've put
more weight on than anyone else, but when there is more than one
comma being tempered out, *straightness* enters the picture and some
combinations of the "best" commas will be worse than some
combinations that include a "non-best" comma. Gene has always seemed
fully cognizant of this fact. Still, I think Gene should reply for
himself!

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith
> <genewardsmith@j...>" <genewardsmith@j...> wrote:
> ...
> > The extra commas I suggested were all that was needed in the 7-
limit
> all had epimericity less than .46. I suggested .5 as a cutoff for
> > the 7-limit and .3 for the 11-limit; I boosted this to .35, with a
> 50 cent cutoff for size. This gave me the following list of 51
commas,
> > in order of badness of the corresponding planar temperament:
> >
> > [9801/9800, 3025/3024, 3294225/3294172, 151263/151250, 441/440,
> 385/384, 225/224, 2401/2400, 56/55, 176/175, 4375/4374, 540/539,
> 64/63, 100/99, 250047/250000, 5632/5625, 36/35, 1375/1372, 126/125,
> 45/44, 99/98, 43923/43904, 896/891, 81/80, 49/48, 50/49, 121/120,
> 117649/117612, 55/54, 41503/41472, 1771561/1771470, 77/75,
4000/3993,
> 6250/6237, 8019/8000, 6144/6125, 1029/1024,5120/5103, 3388/3375,
> 3136/3125, 32805/32768, 245/242, 243/242, 128/125, 12005/11979,
> 245/243, 1728/1715, 19712/19683, 625/616, 1331/1323, 2200/2187]
> >
> > Wedging these three at a time led to 6135 wedgies. Taking the best
> 100 of these by geometric badness gave me my list.
> ...
>
> Hi Gene,
>
> I was looking for names for linear temperaments I had found using
> Graham's online finder, and I noticed this 11-limit one wasn't in
your
> list:
>
> Complex aug fourths
> generator mapping [[1, ?, ?, ?, ?], [0, -7, -26, -25, 3]]
> minimax generators [1200., 585.14]
> minimax error 4.1 c
>
> Does this mean there is another 11-limit comma that should be added
to
> your list above?
>
> I called it "complex" in deference to this one in your list:
>
> > Tritonic
> > [5, -11, -12, -3, -29, -33, -22, 3, 31, 33] [[1, 4, -3, -3, 2],
[0,
> -5, 11, 12, 3]]
> >
> > generators [1200., 580.274408364]
> > bad 6158.168745 rms 5.154394 comp 70.204409

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> I was looking for names for linear temperaments I had found using
> Graham's online finder, and I noticed this 11-limit one wasn't in your
> list:
>
> Complex aug fourths
> generator mapping [[1, ?, ?, ?, ?], [0, -7, -26, -25, 3]]
> minimax generators [1200., 585.14]
> minimax error 4.1 c
>
> Does this mean there is another 11-limit comma that should be added to
> your list above?

I later added 12 more to my list of 100, but still don't find it on my
top 112 list. The reason seems to be that it is above the badness cutoff.

Here's some information on Complex Augmented Fourths:

Wedgie: [7, 26, 25, -3, 25, 20, -29, -15, -97, -95]

Mapping: [[1, 5, 15, 15, 2], [0, -7, -26, -25, 3]]

MT basis: <540/539, 896/891, 1375/1372>

ets: 41, 80, 121

rms error: 2.583842867
geometric complexity (natural log style): 124.3706717
badness: 8006.869167

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> I later added 12 more to my list of 100, but still don't find it on my
> top 112 list. The reason seems to be that it is above the badness
cutoff.
>
> Here's some information on Complex Augmented Fourths:
>
> Wedgie: [7, 26, 25, -3, 25, 20, -29, -15, -97, -95]
>
> Mapping: [[1, 5, 15, 15, 2], [0, -7, -26, -25, 3]]
>
> MT basis: <540/539, 896/891, 1375/1372>
>
> ets: 41, 80, 121
>
> rms error: 2.583842867
> geometric complexity (natural log style): 124.3706717
> badness: 8006.869167

OK. Thanks. While it isn't anything to write home about, it doesn't
seem as bad to me as the above complexity figure makes it. Can someone
please explain what geometric complexity is, and how the badness
figure is obtained?