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 |