[tuning-math] 11-limit planar temperament list
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Sun, 28 Jul 2002 23:03:48 -0700
This is limited by rms error < 20, complexity < 40 and badness < 5000.
There are a lot of 11-limit commas and therefore a lot of reasonable
systems, and the badness is set so as to limit the number, but it's
pretty arbitrary otherwise. Of course if we were to look at, for example,
spacial temperaments in the 19-limit, it would be even more out of hand
with exploding numbers of systems.
[1, 1, -2, -2, 2, -2, -2, 5, 1, -6] {36/35, 56/55}
[[1, 0, 0, 2, 5], [0, 1, 0, 2, 2], [0, 0, 1, -1, -2]]
comp 8.612269456 rms 18.93178096 bad 4120.837552
generators [1200., 1905.077357, 2819.545579]
[1, -2, 1, -2, 2, -2, 5, -2, -1, -6] {56/55, 45/44}
[[1, 0, 0, -5, -2], [0, 1, 0, 2, 2], [0, 0, 1, 2, 1]]
comp 9.294368925 rms 18.94576168 bad 4989.555266
generators [1200., 1894.806413, 2782.197962]
[1, 0, -1, 2, -2, 2, -6, 9, -6, 6] {56/55, 64/63}
[[1, 0, 0, 6, 9], [0, 1, 0, -2, -2], [0, 0, 1, 0, -1]]
comp 9.571162783 rms 11.60092948 bad 3287.793582
generators [1200., 1911.208074, 2806.289813]
[1, -3, 2, 2, -2, 2, 1, 2, -8, 6] {56/55, 100/99}
[[1, 0, 0, -1, 2], [0, 1, 0, -2, -2], [0, 0, 1, 3, 2]]
comp 10.48363973 rms 12.23674678 bad 4354.579196
generators [1200., 1909.065474, 2795.586754]
[2, 0, -2, -1, 1, -1, -4, 10, -4, -3] {56/55, 49/48}
[[1, 0, 0, 2, 5], [0, 2, 0, 1, 1], [0, 0, 1, 0, -1]]
comp 10.63096771 rms 13.11941875 bad 4834.444644
generators [1200., 951.4862286, 2793.240998]
[1, 0, 2, 2, -2, -4, -6, 2, 12, -8] {64/63, 100/99}
[[1, 0, 0, 6, 2], [0, 1, 0, -2, -2], [0, 0, 1, 0, 2]]
comp 11.40622127 rms 7.842944503 bad 3446.145599
generators [1200., 1909.527660, 2790.324320]
[0, 3, -3, 0, 0, 0, -7, 7, 2, 0] {56/55, 128/125}
[[3, 0, 7, 0, 2], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1]]
comp 11.57779068 rms 10.41216358 bad 4749.033317
generators [400.0000000, 1905.928440, 3366.473576]
[0, 0, 2, 0, 4, -4, 0, -11, 12, 2] {64/63, 50/49}
[[2, 0, 11, 12, 0], [0, 1, -2, -2, 0], [0, 0, 0, 0, 1]]
comp 11.92510945 rms 9.546325800 bad 4688.049473
generators [600.0000000, 1907.232522, 4157.670515]
[2, -2, 4, 0, -4, 4, -1, 4, -2, -2] {50/49, 99/98}
[[2, 0, 0, 1, 4], [0, 1, 0, 0, -2], [0, 0, 1, 1, 2]]
comp 12.70642452 rms 8.095335006 bad 4659.005552
generators [600.0000000, 1901.942581, 2777.587752]
[1, -2, 4, -2, 2, 4, 5, -9, -2, 8] {176/175, 99/98}
[[1, 0, 0, -5, -9], [0, 1, 0, 2, 2], [0, 0, 1, 2, 4]]
comp 13.87057757 rms 4.770738943 bad 3418.393201
generators [1200., 1900.667338, 2786.672948]
[1, -2, 2, -2, -2, 8, 5, 2, -14, 6] {100/99, 225/224}
[[1, 0, 0, -5, 2], [0, 1, 0, 2, -2], [0, 0, 1, 2, 2]]
comp 14.53451469 rms 4.698274549 bad 3783.900689
generators [1200., 1903.626101, 2781.116797]
[0, 0, 1, 0, -4, 10, 0, 4, -13, 12] {81/80, 126/125}
[[1, 0, -4, -13, 0], [0, 1, 4, 10, 0], [0, 0, 0, 0, 1]]
comp 15.10180563 rms 5.640679273 bad 4999.235518
generators [1200., 1896.439145, 4147.010107]
[2, -3, 4, 4, -4, -2, -5, 4, 4, -2] {100/99, 245/242}
[[1, 0, 1, 4, 4], [0, 1, 0, -2, -2], [0, 0, 2, 3, 4]]
comp 15.28049091 rms 5.288631285 bad 4827.102898
generators [1200., 1902.349260, 790.0166976]
[1, -3, 5, 2, -2, -4, 1, -5, 10, -8] {176/175, 126/125}
[[1, 0, 0, -1, -5], [0, 1, 0, -2, -2], [0, 0, 1, 3, 5]]
comp 15.38428372 rms 2.743964593 bad 2547.250784
generators [1200., 1902.348538, 2791.393074]
[1, 3, 2, -3, -2, 0, -5, 2, 16, -16] {100/99, 385/384}
[[1, 0, 0, 5, 2], [0, 1, 0, 3, -2], [0, 0, 1, -3, 2]]
comp 15.78362763 rms 4.716489415 bad 4668.054634
generators [1200., 1903.304566, 2780.387947]
[2, 3, 1, -1, 1, 2, -11, 3, 10, 4] {176/175, 121/120}
[[1, 0, 1, 4, 2], [0, 1, 1, -1, 1], [0, 0, 2, -3, 1]]
comp 15.78752896 rms 4.078252712 bad 4038.866834
generators [1200., 1902.084929, -156.7887088]
[1, -2, -3, -2, -1, -4, 5, 12, -9, -19] {225/224, 385/384}
[[1, 0, 0, -5, 12], [0, 1, 0, 2, -1], [0, 0, 1, 2, -3]]
comp 16.93706091 rms 1.584465965 bad 1870.587544
generators [1200., 1900.698768, 2783.222881]
[1, -2, 3, -2, 6, -6, 5, -13, 11, -4] {225/224, 441/440}
[[1, 0, 0, -5, -13], [0, 1, 0, 2, 6], [0, 0, 1, 2, 3]]
comp 17.12658309 rms 1.882869462 bad 2285.583154
generators [1200., 1900.058168, 2783.119618]
[1, -3, -4, 2, 3, -1, 1, 8, -20, 13] {126/125, 385/384}
[[1, 0, 0, -1, 8], [0, 1, 0, -2, 3], [0, 0, 1, 3, -4]]
comp 17.97763590 rms 3.571482050 bad 4894.179827
generators [1200., 1900.444933, 2788.289556]
[3, 0, -3, 1, 4, 1, -10, 11, -10, 17] {441/440, 385/384}
[[1, 1, 0, 3, 5], [0, 3, 0, -1, 4], [0, 0, 1, 0, -1]]
comp 18.38423633 rms 1.217389384 bad 1764.182444
generators [1200., 233.6891156, 2784.876116]
[0, 2, -2, 4, -4, -8, -11, 11, 14, -16] {176/175, 896/891}
[[2, 0, 11, 0, 14], [0, 1, -2, 0, -4], [0, 0, 0, 1, 1]]
comp 20.07262936 rms 2.568435319 bad 4636.382920
generators [600.0000000, 1904.449829, 3372.039360]
[3, 1, 5, -3, 3, 6, -6, -6, 8, 12] {176/175, 540/539}
[[1, 0, 0, 2, -2], [0, 1, 0, 1, 1], [0, 0, 3, -1, 5]]
comp 20.79255579 rms 2.292930734 bad 4520.230946
generators [1200., 1902.851684, 929.9710573]
[1, -1, 1, 6, -10, 4, -10, 17, -7, 2] {441/440, 896/891}
[[1, 0, 0, 10, 17], [0, 1, 0, -6, -10], [0, 0, 1, 1, 1]]
comp 21.23275110 rms 2.274972896 bad 4725.980212
generators [1200., 1903.401073, 2788.404311]
[4, -2, 0, -1, 10, -5, -5, -2, 1, 13] {441/440, 243/242}
[[1, 1, 1, 2, 2], [0, 2, 1, 1, 5], [0, 0, 2, 1, 0]]
comp 22.01175542 rms 1.462086952 bad 3323.608780
generators [1200., 350.4014207, 617.6277206]
[2, -4, 0, -4, 5, -10, 10, -1, 2, -23] {225/224, 243/242}
[[1, 1, 0, -3, 2], [0, 2, 0, 4, 5], [0, 0, 1, 2, 0]]
comp 23.21703942 rms 1.809515516 bad 4699.800337
generators [1200., 350.1386568, 2783.638546]
[4, -2, -6, -1, 3, -3, -5, 23, -19, -2] {385/384, 1375/1372}
[[1, 1, 1, 2, 5], [0, 2, 1, 1, 0], [0, 0, 2, 1, -3]]
comp 25.85062167 rms 1.077522792 bad 3661.035538
generators [1200., 350.6699179, 616.8206966]
[2, -4, 6, 8, -12, 0, -9, 12, 3, -6] {441/440, 8019/8000}
[[2, 0, 0, 9, 12], [0, 1, 0, -4, -6], [0, 0, 1, 2, 3]]
comp 27.40496903 rms .9167078854 bad 3604.161607
generators [600.0000000, 1901.338331, 2786.378136]
[5, -4, -3, -3, 9, -9, 0, 10, -8, -6] {540/539, 1375/1372}
[[1, 0, 0, 0, 2], [0, 1, 3, 3, 0], [0, 0, 5, 4, -3]]
comp 27.81436519 rms .7561992066 bad 3085.383114
generators [1200., 1901.732844, -583.8771683]
[4, 4, 0, -6, -2, -2, -11, 17, 17, -31] {385/384, 9801/9800}
[[2, 1, 0, 7, 8], [0, 2, 0, 3, -1], [0, 0, 1, -1, 0]]
comp 28.20690243 rms 1.049393382 bad 4434.317767
generators [600.0000000, 650.6253937, 2784.681994]
[2, -5, 8, 0, 4, -10, 6, -18, 21, -12] {441/440, 3136/3125}
[[1, 0, 0, -3, -9], [0, 1, 0, 0, 2], [0, 0, 2, 5, 8]]
comp 29.06943484 rms .9765850405 bad 4449.400901
generators [1200., 1901.674054, 1393.524953]
[6, 0, 6, -10, -2, 10, -1, 10, 1, -17] {540/539, 4000/3993}
[[2, 1, 0, 2, 3], [0, 3, 0, 5, -1], [0, 0, 1, 0, 1]]
comp 32.94779996 rms .7610570219 bad 4742.236934
generators [600.0000000, 433.9278373, 2785.854450]
[4, -8, 12, 4, -12, 12, 1, 5, -13, 8] {1375/1372, 6250/6237}
[[4, 0, 0, -1, 5], [0, 1, 0, -1, -3], [0, 0, 1, 2, 3]]
comp 37.88323708 rms .5572687387 bad 4922.462152
generators [300.0000000, 1901.870393, 2785.537590]
[2, 8, -6, -14, 10, -2, -2, 5, 14, -25] {3025/3024, 4375/4374}
[[2, 0, 0, 2, 5], [0, 1, 0, 7, 5], [0, 0, 1, -4, -3]]
comp 38.57526083 rms .1120888160 bad 1035.939660
generators [600.0000000, 1901.942581, 2786.188555]
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