List of edo-distinct 26et rank two temperaments

From Xenharmonic Wiki
Jump to: navigation, search

The temperaments listed are 26edo-distinct, meaning that they are all different even if tuned in 26edo. 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
26, 11 <<1 4 4]] Meantone 1.231 81/80
13, 2 <<2 -18 -33]] Phillips 6.882 9685512225/8589934592
26, 5 <<3 -14 -29]] Archaeotherium 5.832 597871125/536870912
13, 1 <<4 -10 -25]] Elvis 4.867 36905625/33554432
26, 3 <<5 -6 -21]] Secund 4.049 2278125/2097152
13, 5 <<6 -2 -17]] Lemba 3.484 140625/131072
26, 9 <<7 2 -13]] Wesley 3.303 78125/73728
13, 6 <<8 6 -9]] Doublewide 3.565 390625/373248
26, 7 <<9 10 -5]] Shibboleth 4.189 1953125/1889568
13, 3 <<10 14 -1]] Fifive 5.041 9765625/9565938
26, 1 <<11 18 3]] Quartonic 6.026 390625000/387420489
13, 4 <<12 22 7]] Unidec 7.088 31381059609/31250000000
2, 1 <<13 0 -30]] Triskaidekic 6.676 1220703125/1073741824

7-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
26, 11 <<1 4 -9 4 -17 -32]] Flattone 2.987 81/80 525/512
13, 2 <<2 8 8 8 7 -4]] Injera 2.205 50/49 81/80
26, 5 <<3 12 -1 12 -10 -36]] Mothra 3.573 81/80 1029/1024
13, 1 <<4 -10 -10 -25 -27 5]] Elvis 4.494 50/49 8505/8192
26, 3 <<5 -6 7 -21 -3 33]] Secund 3.685 405/392 525/512
13, 5 <<6 -2 -2 -17 -20 1]] Lemba 3.086 50/49 525/512
26, 9 <<7 2 15 -13 4 29]] Wesley 3.694 405/392 875/864
13, 6 <<8 6 6 -9 -13 -3]] Doublewide 2.928 50/49 875/864
26, 7 <<9 10 -3 -5 -30 -35]] Superkleismic 4.620 875/864 1029/1024
13, 3 <<10 14 14 -1 -6 -7]] Crepuscular 4.165 50/49 4375/4374
26, 1 <<11 18 5 3 -23 -39]] Quartonic 5.395 1728/1715 4000/3969
13, 4 <<14 4 4 -26 -33 -2]] Dubbla 5.598 50/49 78125/73728
2, 1 <<13 0 13 -30 -16 30]] Triskaidekic 5.617 1728/1715 1875/1792

11-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
26, 11 <<1 4 -9 6 4 -17 6 -32 0 48]] Flattone 2.866 45/44 81/80 385/384
13, 2 <<2 8 8 12 8 7 12 -4 0 6]] Injera 2.153 45/44 50/49 99/98
26, 5 <<3 12 -1 18 12 -10 18 -36 0 54]] Cynder 3.813 45/44 81/80 1029/1024
13, 1 <<4 -10 -10 -2 -25 -27 -17 5 30 29]] Elvis 3.924 45/44 50/49 1344/1331
26, 3 <<5 -6 7 4 -21 -3 -11 33 30 -13]] Secund 3.203 45/44 99/98 385/384
13, 5 <<6 -2 -2 10 -17 -20 -5 1 30 35]] Lemba 3.054 45/44 50/49 385/384
26, 9 <<7 2 15 16 -13 4 1 29 30 -7]] Wesley 3.432 45/44 99/98 875/864
13, 6 <<8 6 6 -4 -9 -13 -34 -3 -30 -32]] Doublewide 3.407 50/49 99/98 875/864
26, 7 <<9 10 -3 2 -5 -30 -28 -35 -30 16]] Superkleismic 4.137 100/99 245/242 385/384
13, 3 <<10 14 14 8 -1 -6 -22 -7 -30 -26]] Crepuscular 3.829 50/49 99/98 1944/1925
26, 1 <<11 18 5 14 3 -23 -16 -39 -30 22]] Quarto 4.675 100/99 245/242 864/847
13, 4 <<14 4 4 6 -26 -33 -39 -2 0 3]] Dubbla 4.917 50/49 125/121 1344/1331
2, 1 <<13 0 13 0 -30 -16 -45 30 0 -45]] Triskaidekic 5.274 99/98 125/121 385/384

13-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
26, 11 <<1 4 -9 6 -4 4 -17 6 -10 -32 0 -24 48 22 -36]] Flattone 2.664 45/44 65/64 78/77 81/80
13, 2 <<2 8 8 12 18 8 7 12 21 -4 0 12 6 21 18]] Injera 2.461 45/44 50/49 78/77 99/98
26, 5 <<3 12 -1 18 14 12 -10 18 11 -36 0 -12 54 43 -18]] Cynder 3.505 45/44 78/77 81/80 640/637
13, 1 <<4 -10 -10 -2 -16 -25 -27 -17 -40 5 30 0 29 -8 -48]] Elvis 3.948 45/44 50/49 78/77 1053/1024
26, 3 <<5 -6 7 4 6 -21 -3 -11 -9 33 30 36 -13 -9 6]] Secundly 2.899 45/44 65/64 78/77 99/98
13, 5 <<6 -2 -2 10 2 -17 -20 -5 -19 1 30 12 35 13 -30]] Lemba 2.745 45/44 50/49 65/64 78/77
26, 9 <<7 2 15 16 24 -13 4 1 12 29 30 48 -7 12 24]] Wesley 3.652 45/44 78/77 99/98 325/324
13, 6 <<8 6 6 22 20 -9 -13 7 2 -3 30 24 41 34 -12]] Cavalier 3.406 45/44 50/49 78/77 325/324
26, 7 <<9 10 -3 2 16 -5 -30 -28 -8 -35 -30 0 16 56 48]] Superkleismic 3.957 100/99 105/104 245/242 1188/1183
13, 3 <<10 14 14 8 12 -1 -6 -22 -18 -7 -30 -24 -26 -18 12]] Crepuscular 3.447 50/49 78/77 99/98 144/143
26, 1 <<11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24]] Quarto 4.328 78/77 100/99 144/143 245/242
13, 4 <<14 4 4 6 22 -26 -33 -39 -17 -2 0 36 3 47 54]] Dubbla 4.770 50/49 105/104 125/121 144/143
2, 1 <<13 0 13 0 0 -30 -16 -45 -48 30 0 0 -45 -48 0]] Triskaidekic 4.943 78/77 99/98 125/121 1200/1183