List of edo-distinct 16et rank two temperaments

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The temperaments listed are 16edo-distinct, meaning that they are all different even if tuned in 16edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator Wedgie Name Complexity Commas
16 7 <<1 -3 -7]] Mavila 1.377 135/128
8 1 <<2 10 11]] 3.113 59049/51200
16 3 <<3 7 4]] Laconic 2.149 2187/2000
4 1 <<4 4 -3]] Diminished 1.826 648/625
16 5 <<5 1 -10]] Magic 2.417 3125/3072
8 3 <<6 -2 -17]] 3.484 140625/131072
16 1 <<7 11 1]] 3.743 177147/156250
2 1 <<8 -8 -31]] 6.008 2562890625/2147483648

7-limit temperaments

Period generator Wedgie Name Complexity Commas
16 7 <<1 -3 5 -7 5 20]] Armodue 1.804 36/35 135/128
8 1 <<2 -6 -6 -14 -15 3]] Bipelog 2.546 50/49 135/128
16 3 <<3 7 -1 4 -10 -22]] Gorgo 2.252 36/35 1029/1024
4 1 <<4 4 4 -3 -5 -2]] Diminished 1.494 36/35 50/49
16 5 <<5 1 9 -10 0 18]] 2.430 36/35 1875/1792
8 3 <<6 -2 -2 -17 -20 1]] Lemba 3.086 50/49 525/512
16 1 <<7 11 3 1 -15 -24]] 3.369 36/35 51200/50421
2 1 <<8 8 -8 -6 -35 -41]] 4.993 648/625 1323/1280

11-limit temperaments

Period generator Wedgie Name Complexity Commas
16 7 <<1 -3 5 -1 -7 5 -5 20 8 -20]] Armodue 1.603 33/32 36/35 45/44
8 1 <<2 -6 -6 -2 -14 -15 -10 3 16 15]] Bipelog 2.211 33/32 45/44 50/49
16 3 <<3 7 -1 -3 4 -10 -15 -22 -31 -5]] 2.320 33/32 36/35 352/343
4 1 <<4 4 4 12 -3 -5 5 -2 14 20]] Demolished 1.831 36/35 45/44 50/49
16 5 <<5 1 9 11 -10 0 0 18 22 0]] 2.303 36/35 45/44 363/343
8 3 <<6 -2 -2 -6 -17 -20 -30 1 -7 -10]] 3.032 50/49 176/175 363/343
16 1 <<7 11 3 9 1 -15 -10 -24 -17 15]] Slurpee 2.916 36/35 121/120 352/343
2 1 <<8 8 8 8 -6 -10 -15 -4 -9 -5]] 2.606 36/35 50/49 363/343

13-limit temperaments

Period generator Wedgie Name Complexity Commas
16 7 <<1 -3 5 -1 3 -7 5 -5 1 20 8 18 -20 -10 14]] Armodue 1.481 27/26 33/32 36/35 45/44
8 1 <<2 -6 -6 -2 -10 -14 -15 -10 -23 3 16 -1 15 -6 -27]] 2.256 33/32 45/44 50/49 78/77
16 3 <<3 7 -1 -3 9 4 -10 -15 3 -22 -31 -5 -5 29 42]] 2.293 27/26 36/35 143/140 275/273
4 1 <<4 4 4 12 12 -3 -5 5 4 -2 14 13 20 19 -3]] 1.829 27/26 36/35 45/44 50/49
16 5 <<5 1 9 11 15 -10 0 0 5 18 22 31 0 9 11]] 2.376 27/26 36/35 78/77 605/588
8 3 <<6 -2 -2 -6 2 -17 -20 -30 -19 1 -7 12 -10 13 29]] 2.725 33/32 50/49 66/65 105/104
16 1 <<7 11 3 9 5 1 -15 -10 -18 -24 -17 -29 15 3 -16]] Slurpee 2.700 36/35 66/65 143/140 352/343
2 1 <<8 8 8 8 8 -6 -10 -15 -17 -4 -9 -11 -5 -7 -2]] 2.354 36/35 50/49 66/65 143/140