List of edo-distinct 12f rank two temperaments
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The temperaments listed are 12edo-distinct, meaning that they are all different even if tuned in 12edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 12f val (<12 19 28 34 42 45|) was chosen as the representative for each class of edo-distinctness.
5-limit temperaments
Number | Wedgie | Name | Complexity | Commas |
1 | <<1 4 4]] | Meantone | 1.231 | 81/80 |
2 | <<2 -4 -11]] | Srutal | 2.121 | 2048/2025 |
3 | <<3 0 -7]] | Augmented | 1.549 | 128/125 |
4 | <<4 4 -3]] | Diminished | 1.826 | 648/625 |
5 | <<5 8 1]] | Ripple | 2.702 | 6561/6250 |
6 | <<6 12 5]] | Wronecki | 3.781 | 531441/500000 |
7-limit temperaments
Number | Wedgie | Name | Complexity | Commas |
1 | <<1 4 -2 4 -6 -16]] | Dominant | 1.466 | 36/35 64/63 |
2 | <<2 -4 -4 -11 -12 2]] | Pajara | 1.953 | 50/49 64/63 |
3 | <<3 0 6 -7 1 14]] | August | 1.655 | 36/35 128/125 |
4 | <<4 4 4 -3 -5 -2]] | Diminished | 1.494 | 36/35 50/49 |
5 | <<5 8 2 1 -11 -18]] | Ripple | 2.454 | 36/35 2560/2401 |
6 | <<6 0 0 -14 -17 0]] | Hexe | 2.689 | 50/49 128/125 |
11-limit temperaments
Number | Wedgie | Name | Complexity | Commas |
1 | <<1 4 -2 6 4 -6 6 -16 0 24]] | Domineering | 1.523 | 36/35 45/44 64/63 |
2 | <<2 -4 -4 0 -11 -12 -7 2 14 14]] | Pajaric | 1.722 | 45/44 50/49 56/55 |
3 | <<3 0 6 6 -7 1 -1 14 14 -4]] | August | 1.506 | 36/35 45/44 56/55 |
4 | <<4 4 4 0 -3 -5 -14 -2 -14 -14]] | Diminished | 1.582 | 36/35 50/49 56/55 |
5 | <<5 8 2 6 1 -11 -8 -18 -14 10]] | Ripple | 2.130 | 36/35 80/77 126/121 |
6 | <<6 0 0 0 -14 -17 -21 0 0 0]] | Hexe | 2.410 | 50/49 56/55 125/121 |
13-limit temperaments
Number | Wedgie | Name | Complexity | Commas |
1 | <<1 4 -2 6 3 4 -6 6 1 -16 0 -8 24 16 -12]] | Dominatrix | 1.367 | 27/26 36/35 45/44 64/63 |
2 | <<2 -4 -4 0 -6 -11 -12 -7 -17 2 14 1 14 -2 -21]] | Pajaric | 1.701 | 40/39 45/44 50/49 56/55 |
3 | <<3 0 6 6 9 -7 1 -1 3 14 14 21 -4 3 9]] | August | 1.536 | 27/26 36/35 45/44 56/55 |
4 | <<4 4 4 0 0 -3 -5 -14 -15 -2 -14 -15 -14 -15 0]] | Diminished | 1.564 | 36/35 40/39 50/49 66/65 |
5 | <<5 8 2 6 3 1 -11 -8 -14 -18 -14 -23 10 1 -12]] | Ripple | 1.996 | 36/35 40/39 66/65 147/143 |
6 | <<6 0 0 0 6 -14 -17 -21 -13 0 0 14 0 17 21]] | Hexe | 2.216 | 50/49 56/55 66/65 105/104 |