[tuning-math] A 5-limit, "geometric" temperament list

The following is a complete list of all 5-limit temperaments satisfying
the requirements that rms error be less than 15, geometric complexity
less than 40, and the badness calculated from these less than 3000. If
people feel something valuable has been left off (e.g, 135/128, 25/24, or
16875/16384) we could raise the error limit.


81/80   (3)^4/(2)^4/(5) meantone
[[1, 0, -4], [0, 1, 4]]

comp   4.132030727   rms   4.217730828   bad   297.5565312
generators   [1200., 1896.164845]


128/125   (2)^7/(5)^3 augmented
[[3, 5, 7], [0, 1, 0]]

comp   4.828313736   rms   9.677665780   bad   1089.323984
generators   [400.0000000, 91.20185550]


256/243   (2)^8/(3)^5 quintal
[[5, 8, 12], [0, 0, -1]]

comp   5.493061445   rms   12.75974144   bad   2114.877638
generators   [240.0000000, 84.66378778]


250/243   (2)*(5)^3/(3)^5 porcupine
[[1, 2, 3], [0, -3, -5]]

comp   5.948285733   rms   7.975800816   bad   1678.609846
generators   [1200., 162.9960265]


2048/2025   (2)^11/(3)^4/(5)^2 diaschismic
[[2, 3, 5], [0, 1, -2]]

comp   6.271198982   rms   2.612821643   bad   644.4088670
generators   [600.0000000, 105.4465315]


648/625   (2)^3*(3)^4/(5)^4 diminished
[[4, 6, 9], [0, 1, 1]]

comp   6.437751648   rms   11.06006024   bad   2950.938432
generators   [300.0000000, 94.13435693]


3125/3072   (5)^5/(2)^10/(3) diesic (small diesic)
[[1, 0, 2], [0, 5, 1]]

comp   7.741412273   rms   4.569472316   bad   2119.954991
generators   [1200., 379.9679493]


15625/15552   (5)^6/(2)^6/(3)^5 kleismic
[[1, 0, 1], [0, 6, 5]]

comp   9.338935129   rms   1.029625097   bad   838.6315482
generators   [1200., 317.0796753]


32805/32768   (3)^8*(5)/(2)^15 shismic
[[1, 0, 15], [0, 1, -8]]

comp   9.459947973   rms   .1616933186   bad   136.8857747
generators   [1200., 1901.727514]


20000/19683   (2)^5*(5)^4/(3)^9 quadrafifths (minimal diesic)
[[1, 1, 1], [0, 4, 9]]

comp   9.785568434   rms   2.504205191   bad   2346.540676
generators   [1200., 176.2822703]


78732/78125   (2)^2*(3)^9/(5)^7 hemisixths (tiny diesic)
[[1, -1, -1], [0, 7, 9]]

comp   12.19218236   rms   1.157498409   bad   2097.803242
generators   [1200., 442.9792975]


393216/390625   (2)^17*(3)/(5)^8 wuerschmidt
[[1, -1, 2], [0, 8, 1]]

comp   12.54312332   rms   1.071949828   bad   2115.395301
generators   [1200., 387.8196733]


2109375/2097152   (3)^3*(5)^7/(2)^21 orwell
[[1, 0, 3], [0, 7, -3]]

comp   12.77234114   rms   .8004099292   bad   1667.723301
generators   [1200., 271.5895996]


1600000/1594323   (2)^9*(5)^5/(3)^13 amt
[[1, 3, 6], [0, -5, -13]]

comp   13.79419993   rms   .3831037874   bad   1005.555381
generators   [1200., 339.5088256]


6115295232/6103515625   (2)^23*(3)^6/(5)^14 semisuper
[[2, 4, 5], [0, -7, -3]]

comp   21.20762522   rms   .1940180530   bad   1850.624306
generators   [600.0000000, 71.14606343]


1224440064/1220703125   (2)^8*(3)^14/(5)^13 parakleismic
[[1, 5, 6], [0, -13, -14]]

comp   21.32267248   rms   .2766026501   bad   2681.521263
generators   [1200., 315.2509133]


10485760000/10460353203   (2)^24*(5)^4/(3)^21
[[1, 0, -6], [0, 4, 21]]

comp   21.73304916   rms   .1537673823   bad   1578.433204
generators   [1200., 475.5422333]


274877906944/274658203125   (2)^38/(3)^2/(5)^15 hemithird
[[1, 4, 2], [0, -15, 2]]

comp   24.97702150   rms   .6082244804e-1   bad   947.7326423
generators   [1200., 193.1996149]


68719476736000/68630377364883   (2)^39*(5)^3/(3)^29 trichotififths
[[1, 0, -13], [0, 3, 29]]

comp   30.55081228   rms   .5750010064e-1   bad   1639.596150
generators   [1200., 634.0119851]


19073486328125/19042491875328   (5)^19/(2)^14/(3)^19 enneadecal
[[19, 30, 44], [0, 1, 1]]

comp   30.57932033   rms   .1047837215   bad   2996.244873
generators   [63.15789474, 7.292252126]


9010162353515625/9007199254740992   (3)^10*(5)^16/(2)^53
[[2, 1, 6], [0, 8, -5]]

comp   31.25573660   rms   .1772520822e-1   bad   541.2283791
generators   [600.0000000, 162.7418923]


7629394531250/7625597484987   (2)*(5)^18/(3)^27 ennealimmal
[[9, 13, 19], [0, 2, 3]]

comp   33.65327154   rms   .2559250891e-1   bad   975.4269093
generators   [133.3333333, 84.32451333]


50031545098999707/50000000000000000   (3)^35/(2)^16/(5)^17
[[1, -1, -3], [0, 17, 35]]

comp   38.84548584   rms   .2546649929e-1   bad   1492.763207
generators   [1200., 182.4660891]


450359962737049600/450283905890997363   (2)^54*(5)^2/(3)^37 monzismic
[[1, 2, 10], [0, -2, -37]]

comp   39.66560308   rms   .5738429624e-2   bad   358.1254995
generators   [1200., 249.0184479]



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