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