Vulture family

The vulture family of temperaments tempers out the vulture comma, |24 -21 4> = 10485760000/10460353203, a small 5-limit comma of size 4.1998 cents. Aside from vulture itself, the family contains buzzard, considered elsewhere, and condor.

Comma: 10485760000/10460353203

POTE generator: ~320/243 = 475.5426

Map: [<1 0 -6|, <0 4 21|]

EDOs: 5, 48, 53, 164, 217, 270, 323, 2531

Badness: 0.0414

Vulture

The vulture temperament can be described as the 53&217 temperament, tempering out the ragisma, 4375/4374 and the garischisma, [25 -14 0 -1⟩ = 33554432/33480783 aside from the vulture comma. 270edo is a good tuning for this temperament, with generator 107/270, and MOS of 3, 5, 8, 13, 18, 23, 28, 33, 38, 43, 48, or 53 notes are available.

Commas: 4375/4374, 33554432/33480783

POTE generator: ~320/243 = 475.5511

Map: [<1 0 -6 25|, <0 4 21 -56|]

EDOs: 53, 164, 217, 270, 593, 863, 1133

Badness: 0.0370

11-limit

Commas: 4375/4374, 5632/5625, 41503/41472

POTE generator: ~320/243 = 475.5567

Map: [<1 0 -6 25 -33|, <0 4 21 -56 92|]

EDOs: 53, 217, 270

Badness: 0.0319

13-limit

Commas: 676/675, 1001/1000, 4096/4095, 4375/4374

POTE generator: ~320/243 = 475.5572

Map: [<1 0 -6 25 -33 -7|, <0 4 21 -56 92 27|]

EDOs: 53, 217, 270

Badness: 0.0188

17-limit

Commas: 676/675, 936/935, 1001/1000, 1225/1224, 4096/4095

POTE generator: ~112/85 = 475.5617

Map: [<1 0 -6 25 -33 -7 35|, <0 4 21 -56 92 27 -78|]

EDOs: 53, 217, 270, 487, 757g

Badness: 0.0201

19-limit

Commas: 676/675, 936/935, 1001/1000, 1216/1215, 1225/1224, 1540/1539

POTE generator: ~25/19 = 475.5615

Map: [<1 0 -6 25 -33 -7 35 -12|, <0 4 21 -56 92 27 -78 41|]

EDOs: 53, 217, 270, 487, 757g

Badness: 0.0139

Condor

Commas: 10976/10935, 40353607/40000000

POTE generator: ~81/56 = 641.4791

Map: [<1 8 36 29|, <0 -12 -63 -49|]

EDOs: 58, 159, 217, 275

Badness: 0.1547

11-limit

Commas: 441/440, 4000/3993, 10976/10935

POTE generator: ~81/56 = 641.4822

Map: [<1 8 36 29 35|, <0 -12 -63 -49 -59|]

EDOs: 58, 159, 217

Badness: 0.0484

13-limit

Commas: 364/363, 441/440, 676/675, 10976/10935

POTE generator: ~81/56 = 641.4797

Map: [<1 8 36 29 35 47|, <0 -12 -63 -49 -59 -81|]

EDOs: 58, 159, 217

Badness: 0.0255

17-limit

Commas: 364/363, 441/440, 595/594, 676/675, 8624/8619

POTE generator: ~81/56 = 641.4794

Map: [<1 8 36 29 35 47 -5|, <0 -12 -63 -49 -59 -81 17|]

EDOs: 58, 159, 217

Badness: 0.0220