List of edo-distinct 58et rank two temperaments

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The temperaments listed are 58edo-distinct, meaning that they are all different even if tuned in 58edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator Wedgie Name Complexity Commas
58 19 <<14 1 -31]] 7.0510 6442450944/6103515625
29 10 <<30 -2 -73]] 15.837 9444732965739290427392/8381903171539306640625
58 1 <<16 -3 -42]] 8.828 4398046511104/4119873046875
29 9 <<2 -4 -11]] Srutal 2.121 2048/2025
58 21 <<12 5 -20]] 5.522 254803968/244140625
29 1 <<26 6 -51]] 12.488 1641562064176545792/1490116119384765625
58 17 <<18 -7 -53]] 10.731 9007199254740992/8342742919921875
29 11 <<54 8 -113]] 26.555 [113 8 -54>
58 3 <<10 9 -9]] 4.502 10077696/9765625
29 8 <<34 48 -3]] 17.206 638131544614980078906888/582076609134674072265625
58 23 <<20 -11 -64]] 12.703 18446744073709551616/16894054412841796875
29 2 <<6 46 59]] 14.875 9007199254740992000000/8862938119652501095929
58 15 <<8 13 2]] Unicorn 4.363 1594323/1562500
29 12 <<22 14 -29]] 9.851 2567836929097728/2384185791015625
58 5 <<22 43 17]] 13.625 328256967394537077627/312500
29 7 <<50 16 -91]] 23.481 [91 16 -50>
58 25 <<6 17 13]] Gravity 5.177 129140163/128000000
29 3 <<38 40 -25]] 17.490 407943558924674501581996032/363797880709171295166015625
58 13 <<34 19 -49]] 15.323 654295038711035754184704/582076609134674072265625
29 13 <<10 38 37]] 11.672 1350851717672992089/1342177280000000000
58 7 <<4 21 24]] 6.600 10485760000/10460353203
29 6 <<18 22 -7]] 8.609 4016775629952/3814697265625
58 27 <<26 35 -5]] 12.886 1601009443167990624/1490116119384765625
29 4 <<46 24 -69]] 20.822 [69 24 -46>
58 11 <<2 25 35]] 8.326 858993459200/847288609443
29 14 <<42 32 -47]] 18.755 260789407250723664179754958848/227373675443232059478759765625
58 9 <<28 31 -16]] 13.029 40479843698864750592/37252902984619140625
29 5 <<14 30 15]] 9.338 205891132094649/200000000000000
2 1 <<0 29 46]] 10.202 70368744177664/68630377364883

7-limit temperaments

Period generator Wedgie Name Complexity Commas
58 19 <<14 1 33 -31 13 74]] 8.414 10976/10935 28672/28125
29 10 <<28 2 8 -62 -66 13]] 11.753 2401/2400 401408/390625
58 1 <<16 -3 17 -42 -18 48]] 7.540 1728/1715 28672/28125
29 9 <<2 -4 -16 -11 -31 -26]] 4.290 126/125 2048/2025
58 21 <<12 5 -9 -20 -48 -35]] 6.416 126/125 65536/64827
29 1 <<26 6 24 -51 -35 39]] 10.316 1728/1715 401408/390625
58 17 <<18 -7 1 -53 -49 22]] 8.928 2401/2400 28672/28125
29 11 <<4 -8 26 -22 30 83]] 7.609 2048/2025 19683/19600
58 3 <<10 9 7 -9 -17 -9]] 3.731 126/125 1728/1715
29 8 <<24 10 40 -40 -4 65]] 10.561 31104/30625 118098/117649
58 23 <<20 -11 -15 -64 -80 -4]] 11.806 28672/28125 50421/50000
29 2 <<6 -12 10 -33 -1 57]] 5.925 1728/1715 2048/2025
58 15 <<8 13 23 2 14 17]] 4.847 126/125 10976/10935
29 12 <<22 14 -2 -29 -65 -44]] 9.579 126/125 4194304/4117715
58 5 <<22 43 27 17 -19 -58]] 11.157 2401/2400 177147/175000
29 7 <<8 -16 -6 -44 -32 31]] 7.010 2048/2025 2401/2400
58 25 <<6 17 39 13 45 43]] 8.359 126/125 1605632/1594323
29 3 <<38 40 44 -25 -37 -10]] 14.346 126/125 97955205120/96889010407
58 13 <<24 39 11 6 -50 -84]] 11.703 1728/1715 1594323/1562500
29 13 <<10 -20 -22 -55 -63 5]] 9.999 2048/2025 50421/50000
58 7 <<4 21 -3 24 -16 -66]] 6.420 1728/1715 5120/5103
29 6 <<18 22 30 -7 -3 8]] 7.511 126/125 118098/117649
58 27 <<26 35 53 -5 11 25]] 12.079 126/125 645700815/645657712
29 4 <<12 34 20 26 -2 -49]] 8.457 2401/2400 19683/19600
58 11 <<2 25 13 35 15 -40]] 6.812 2401/2400 5120/5103
29 14 <<16 26 -12 4 -64 -101]] 10.753 31104/30625 65536/64827
58 9 <<28 31 37 -16 -20 -1]] 10.826 126/125 204073344/201768035
29 5 <<14 30 4 15 -33 -75]] 8.670 1728/1715 177147/175000
2 1 <<0 29 29 46 46 -14]] 9.402 5120/5103 50421/50000

11-limit temperaments

Period generator Wedgie Name Complexity Commas
58 19 <<14 1 33 35 -31 13 7 74 78 -16]] 7.910 176/175 243/242 5488/5445
29 10 <<28 2 8 12 -62 -66 -78 13 21 6]] 10.249 176/175 1344/1331 2401/2400
58 1 <<16 -3 17 11 -42 -18 -38 48 36 -28]] 6.539 176/175 540/539 1344/1331
29 9 <<2 -4 -16 -24 -11 -31 -45 -26 -42 -12]] 5.048 126/125 176/175 5488/5445
58 21 <<12 5 -9 1 -20 -48 -40 -35 -15 34]] 5.622 126/125 176/175 1344/1331
29 1 <<26 6 24 36 -51 -35 -33 39 63 18]] 9.209 176/175 540/539 33614/33275
58 17 <<18 -7 1 -13 -53 -49 -83 22 -6 -40]] 8.597 176/175 2401/2400 2560/2541
29 11 <<4 -8 26 10 -22 30 2 83 51 -62]] 6.610 176/175 243/242 896/891
58 3 <<10 9 7 25 -9 -17 5 -9 27 46]] 4.127 126/125 176/175 243/242
29 8 <<24 10 40 2 -40 -4 -80 65 -30 -133]] 10.411 540/539 3072/3025 3168/3125
58 23 <<20 -11 -15 21 -64 -80 -36 -4 87 111]] 10.79 441/440 3072/3025 3388/3375
29 2 <<6 -12 10 -14 -33 -1 -43 57 9 -74]] 5.898 176/175 540/539 896/891
58 15 <<8 13 23 -9 2 14 -42 17 -66 -105]] 6.251 126/125 540/539 896/891
29 12 <<22 14 -2 26 -29 -65 -35 -44 12 80]] 8.473 126/125 176/175 103680/102487
58 5 <<22 43 27 55 17 -19 11 -58 -21 61]] 10.247 243/242 441/440 43923/43750
29 7 <<8 -16 -6 20 -44 -32 4 31 102 77]] 7.436 243/242 441/440 2048/2025
58 25 <<6 17 39 15 13 45 3 43 -24 -93]] 7.341 126/125 243/242 896/891
29 3 <<20 18 14 -8 -18 -34 -82 -18 -81 -71]] 8.475 126/125 1728/1715 2560/2541
58 13 <<24 39 11 31 6 -50 -34 -84 -63 49]] 10.136 441/440 1728/1715 4000/3993
29 13 <<10 -20 -22 -4 -55 -63 -41 5 60 65]] 8.704 441/440 1344/1331 3388/3375
58 7 <<4 21 -3 -19 24 -16 -44 -66 -117 -43]] 7.574 441/440 896/891 1728/1715
29 6 <<18 22 30 16 -7 -3 -37 8 -39 -59]] 6.826 126/125 540/539 1344/1331
58 27 <<32 23 5 51 -38 -82 -30 -53 39 126]] 12.085 126/125 176/175 35831808/35153041
29 4 <<12 34 20 30 26 -2 6 -49 -48 15]] 7.373 243/242 441/440 4000/3993
58 11 <<2 25 13 5 35 15 1 -40 -75 -31]] 6.148 243/242 441/440 896/891
29 14 <<16 26 46 40 4 28 8 34 3 -47]] 8.504 126/125 243/242 5488/5445
58 9 <<28 31 37 41 -16 -20 -32 -1 -12 -13]] 9.390 126/125 540/539 12005/11979
29 5 <<14 30 4 6 15 -33 -39 -75 -90 3]] 7.939 441/440 1344/1331 1728/1715
2 1 <<0 29 29 29 46 46 46 -14 -33 -19]] 8.317 441/440 896/891 3388/3375

13-limit temperaments

Period generator Wedgie Name Complexity Commas
58 19 <<14 1 33 35 51 -31 13 7 29 74 78 115 -16 21 47]] 8.314 176/175 196/195 243/242 364/363
29 10 <<28 2 8 12 44 -62 -66 -78 -34 13 21 95 6 94 108]] 10.002 144/143 176/175 676/675 2401/2400
58 1 <<16 -3 17 11 21 -42 -18 -38 -26 48 36 60 -28 -4 32]] 5.970 144/143 176/175 196/195 364/363
29 9 <<2 -4 -16 -24 -30 -11 -31 -45 -55 -26 -42 -55 -12 -25 -15]] 5.517 126/125 176/175 196/195 364/363
58 21 <<12 5 -9 1 23 -20 -48 -40 -8 -35 -15 35 34 98 76]] 5.758 126/125 144/143 176/175 364/363
29 1 <<26 6 24 36 16 -51 -35 -33 -71 39 63 15 18 -44 -78]] 8.451 144/143 176/175 196/195 2200/2197
58 17 <<18 -7 1 -13 -9 -53 -49 -83 -81 22 -6 5 -40 -29 17]] 7.940 176/175 196/195 364/363 512/507
29 11 <<4 -8 26 10 -2 -22 30 2 -18 83 51 25 -62 -102 -44]] 6.128 144/143 176/175 351/350 676/675
58 3 <<10 9 7 25 -5 -9 -17 5 -45 -9 27 -45 46 -40 -110]] 4.810 126/125 144/143 176/175 196/195
29 8 <<24 10 40 2 46 -40 -4 -80 -16 65 -30 70 -133 -19 152]] 9.854 144/143 196/195 2205/2197 3267/3250
58 23 <<20 -11 -15 21 19 -64 -80 -36 -44 -4 87 85 111 109 -12]] 9.851 144/143 441/440 676/675 847/845
29 2 <<6 -12 10 -14 26 -33 -1 -43 19 57 9 105 -74 36 142]] 6.793 144/143 176/175 196/195 729/728
58 15 <<8 13 23 -9 25 2 14 -42 10 17 -66 10 -105 -15 120]] 5.948 126/125 144/143 196/195 676/675
29 12 <<22 14 -2 26 18 -29 -65 -35 -53 -44 12 -10 80 58 -34]] 7.584 126/125 144/143 176/175 847/845
58 5 <<22 43 27 55 47 17 -19 11 -7 -58 -21 -50 61 32 -41]] 9.188 243/242 351/350 441/440 1188/1183
29 7 <<8 -16 -6 20 -4 -44 -32 4 -36 31 102 50 77 11 -88]] 6.703 144/143 196/195 243/242 2200/2197
58 25 <<6 17 -19 15 -3 13 -47 3 -27 -92 -24 -70 108 62 -66]] 7.020 176/175 243/242 351/350 847/845
29 3 <<20 18 14 50 48 -18 -34 10 2 -18 54 45 92 83 -19]] 7.929 126/125 176/175 243/242 1188/1183
58 13 <<24 39 11 31 17 6 -50 -34 -62 -84 -63 -105 49 7 -56]] 9.414 144/143 351/350 441/440 847/845
29 13 <<10 -20 -22 -4 -34 -55 -63 -41 -91 5 60 -5 65 -14 -103]] 8.755 196/195 352/351 832/825 1001/1000
58 7 <<4 21 -3 39 27 24 -16 48 28 -66 18 -15 120 87 -51]] 7.182 176/175 351/350 676/675 847/845
29 6 <<18 22 30 16 20 -7 -3 -37 -35 8 -39 -35 -59 -55 10]] 6.197 126/125 144/143 196/195 364/363
58 27 <<26 35 53 7 45 -5 11 -79 -25 25 -105 -25 -164 -70 130]] 11.154 126/125 144/143 196/195 114345/114244
29 4 <<12 34 20 30 52 26 -2 6 38 -49 -48 -5 15 72 69]] 7.574 243/242 351/350 441/440 676/675
58 11 <<2 25 13 5 -1 35 15 1 -9 -40 -75 -95 -31 -51 -22]] 5.942 144/143 196/195 243/242 364/363
29 14 <<16 26 46 40 50 4 28 8 20 34 3 20 -47 -30 25]] 7.895 126/125 196/195 364/363 676/675
58 9 <<30 27 21 17 43 -27 -51 -77 -43 -27 -54 0 -25 43 86]] 9.223 126/125 144/143 364/363 1716/1715
29 5 <<14 30 4 6 22 15 -33 -39 -17 -75 -90 -60 3 47 54]] 7.123 144/143 351/350 364/363 441/440
2 1 <<0 29 29 29 29 46 46 46 46 -14 -33 -40 -19 -26 -7]] 7.496 196/195 352/351 364/363 676/675