List of edo-distinct 22et rank two temperaments

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The temperaments listed are 22edo-distinct, meaning that they are all different even if tuned in 22edo. 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
22, 9 <<1 9 12]] Superpyth 2.947 20480/19683
11, 2 <<2 -4 -11]] Srutal 2.121 2048/2025
22, 3 <<3 5 1]] Porcupine 1.663 250/243
11, 1 <<4 14 13]] Comic 4.290 5120000/4782969
22, 7 <<5 1 -10]] Magic 2.417 3072/3125
11, 3 <<16 -10 -53]] Kwazy 10.454 9010162353515625/9007199254740992
22, 5 <<7 -3 -21]] Orson 4.232 2109375/2097152
11, 5 <<8 6 -9]] Doublewide 3.565 390625/373248
22, 1 <<13 7 -19]] Chromo 5.860 1220703125/1146617856
11, 4 <<12 -2 -31]] Wizard 6.558 2197265625/2147483648
2, 1 <<11 11 -8]] Undeka 5.011 48828125/45349632

7-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
22, 9 <<1 9 -2 12 -6 -30]] Superpyth 2.874 64/63 245/243
11, 2 <<2 -4 -4 -11 -12 2]] Pajara 1.953 50/49 64/63
22, 3 <<3 5 -6 1 -18 -28]] Porcupine 2.819 64/63 250/243
11, 1 <<4 14 14 13 11 -7]] Comic 3.815 50/49 2240/2187
22, 7 <<5 1 12 -10 5 25]] Magic 2.937 225/224 245/243
11, 3 <<6 10 10 2 -1 -5]] Hedgehog 2.784 50/49 245/243
22, 5 <<7 -3 8 -21 -7 27]] Orwell 3.685 225/224 1728/1715
11, 5 <<8 6 6 -9 -13 -3]] Doublewide 2.928 50/49 875/864
22, 1 <<9 15 4 3 -19 -33]] Ceratitid 4.482 250/243 1728/1715
11, 4 <<10 2 2 -20 -25 -1]] Astrology 4.127 50/49 3125/3072
2, 1 <<11 11 0 -8 -31 -31]] Undeka 4.941 875/864 3200/3087

11-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
22, 9 <<1 9 -2 -6 12 -6 -13 -30 -45 -10]] Suprapyth 3.011 55/54 64/63 99/98
11, 2 <<2 -4 -4 -12 -11 -12 -26 2 -14 -20]] Pajara 2.543 50/49 64/63 99/98
22, 3 <<3 5 -6 4 1 -18 -4 -28 -8 32]] Porcupine 2.478 55/54 64/63 100/99
11, 1 <<4 -8 -8 -2 -22 -24 -17 4 23 22]] Hemipaj 3.389 50/49 64/63 121/120
22, 7 <<5 1 12 14 -10 5 5 25 29 -2]] Telepathy 2.864 55/54 99/98 176/175
11, 3 <<6 10 10 8 2 -1 -8 -5 -16 -12]] Hedgehog 2.439 50/49 55/54 99/98
22, 5 <<7 -3 8 2 -21 -7 -21 27 15 -22]] Orwell 3.242 99/98 121/120 176/175
11, 5 <<8 6 6 18 -9 -13 1 -3 21 30]] Fleetwood 3.081 50/49 55/54 176/175
22, 1 <<9 15 4 12 3 -19 -12 -33 -24 20]] Ceratitid 3.880 55/54 100/99 5324/5145
11, 4 <<10 2 2 6 -20 -25 -25 -1 7 10]] Astrology 3.575 50/49 121/120 176/175
2, 1 <<11 11 0 0 -8 -31 -38 -31 -38 0]] Undeka 4.657 100/99 352/343 385/384

13-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
22, 9 <<1 9 -2 -6 -9 12 -6 -13 -18 -30 -45 -54 -10 -18 -9]] Suprapyth 3.151 55/54 64/63 65/63 364/363
11, 2 <<2 -4 -4 10 4 -11 -12 9 -1 2 37 24 42 26 -23]] Pajarous 2.481 50/49 55/54 64/63 65/63
22, 3 <<3 5 -6 4 -5 1 -18 -4 -19 -28 -8 -30 32 8 -32]] Porkpie 2.487 55/54 64/63 65/63 100/99
11, 1 <<4 14 14 20 8 13 11 18 -2 -7 -2 -33 8 -29 -46]] Comic 3.391 50/49 65/63 99/98 968/945
22, 7 <<5 1 12 14 -1 -10 5 5 -20 25 29 -6 -2 -47 -55]] Telepathy 2.980 55/54 65/64 91/90 99/98
11, 3 <<6 10 10 8 12 2 -1 -8 -3 -5 -16 -9 -12 -3 12]] Hedgehog 2.196 50/49 55/54 65/63 99/98
22, 5 <<7 -3 8 2 3 -21 -7 -21 -21 27 15 18 -22 -21 3]] Blair 2.911 65/64 78/77 91/90 99/98
11, 5 <<8 6 6 18 16 -9 -13 1 -4 -3 21 15 30 23 -11]] Fleetwood 2.861 50/49 55/54 65/63 176/175
22, 1 <<9 15 4 12 7 3 -19 -12 -22 -33 -24 -39 20 5 -20]] Ceratitid 3.573 55/54 65/63 100/99 352/343
11, 4 <<10 2 2 6 -2 -20 -25 -25 -40 -1 7 -12 10 -13 -29]] Astrology 3.495 50/49 65/64 78/77 121/120
2, 1 <<11 11 0 0 11 -8 -31 -38 -23 -31 -38 -15 0 31 38]] Undeka 4.178 65/63 100/99 169/165 352/343