List of edo-distinct 17c rank two temperaments

From Xenharmonic Wiki
Jump to: navigation, search

The temperaments listed are 17edo-distinct, meaning that they are all different even if tuned in 17edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 17c val (<17 27 40 48 59 63|) was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
17, 7 <<1 4 4]] Meantone 1.231 81/80
17, 5 <<2 -9 -19]] Beatles 3.798 524288/492075
17, 8 <<3 -5 -15]] Progress 2.877 32768/30375
17, 6 <<4 -1 -11]] Smate 2.272 2048/1875
17, 2 <<5 3 -7]] Progression 2.254 3456/3125
17, 4 <<6 7 -3]] Subklei 2.833 17496/15625
17, 1 <<7 11 1]] Slurpee 3.743 177147/156250
17, 3 <<9 2 -18]] Genocchi 4.355 2359296/1953125

7-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
17, 7 <<1 4 -2 4 -6 -16]] Dominant 1.466 36/35 64/63
17, 5 <<2 8 13 8 15 8]] Mohamaq 2.958 81/80 392/375
17, 8 <<3 -5 -6 -15 -18 0]] Progress 2.762 64/63 392/375
17, 6 <<4 -1 9 -11 3 24]] Smate 2.575 36/35 2048/1875
17, 2 <<5 3 7 -7 -3 8]] Progression 1.976 36/35 392/375
17, 4 <<6 7 5 -3 -9 -8]] Subklei 2.340 36/35 1029/1000
17, 1 <<7 11 3 1 -15 -24]] Slurpee 3.369 36/35 51200/50421
17, 3 <<8 -2 1 -22 -21 8]] Hemismate 3.783 256/245 392/375

11-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
17, 7 <<1 4 -2 -6 4 -6 -13 -16 -28 -10]] Dominant 1.864 36/35 56/55 64/63
17, 5 <<2 8 -4 5 8 -12 1 -32 -16 28]] Maqamic 2.569 36/35 64/63 121/120
17, 8 <<3 -5 -6 -1 -15 -18 -12 0 15 18]] Progress 2.399 56/55 64/63 77/75
17, 6 <<4 -1 9 10 -11 3 2 24 27 -3]] Smate 2.443 36/35 56/55 243/242
17, 2 <<5 3 7 4 -7 -3 -11 8 -1 -13]] Progression 1.749 36/35 56/55 77/75
17, 4 <<6 7 5 15 -3 -9 3 -8 11 25]] Subklei 2.459 36/35 77/75 352/343
17, 1 <<7 11 3 9 1 -15 -10 -24 -17 15]] Slurpee 2.916 36/35 121/120 352/343
17, 3 <<8 -2 1 3 -22 -21 -23 8 14 5]] Hemismate 3.279 56/55 77/75 256/245

13-limit temperaments

Period,

generator

Wedgie Name Complexity Commas
17, 7 <<1 4 -2 11 8 4 -6 14 9 -16 12 4 38 30 -13]] Domination 2.061 26/25 36/35 64/63 66/65
17, 5 <<2 8 -4 5 -1 8 -12 1 -9 -32 -16 -32 28 12 -22]] Maqamic 2.402 36/35 64/63 66/65 121/120
17, 8 <<3 -5 -6 -1 -10 -15 -18 -12 -27 0 15 -5 18 -6 -31]] Progressive 2.485 26/25 56/55 64/63 77/75
17, 6 <<4 -1 9 10 -2 -11 3 2 -18 24 27 -1 -3 -39 -44]] Smate 2.520 26/25 36/35 56/55 243/242
17, 2 <<5 3 7 4 6 -7 -3 -11 -9 8 -1 3 -13 -9 6]] Progression 1.563 26/25 36/35 56/55 66/65
17, 4 <<6 7 5 15 14 -3 -9 3 0 -8 11 7 25 21 -7]] Subklei 2.307 26/25 36/35 66/65 352/343
17, 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
17, 3 <<8 -2 1 3 -4 -22 -21 -23 -36 8 14 -2 5 -15 -25]] Hemismate 3.187 26/25 56/55 77/75 256/245