Vulture family

The vulture family of temperaments tempers out the vulture comma, [24 -21 4⟩ = 10485760000/10460353203, a small 5-limit comma of 4.2 cents.

Temperaments discussed elsewhere includes terture.

Vulture

Subgroup: 2.3.5

Comma list: 10485760000/10460353203

Mapping: [⟨1 0 -6], ⟨0 4 21]]

mapping generators: ~2, ~320/243

Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5426

Optimal ET sequence: 53, 164, 217, 270, 323, 2531, 2854b, 3177b, 3500b, 3823b, 4146b, 4469b

Badness: 0.041431

Septimal 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 scales of 3, 5, 8, 13, 18, 23, 28, 33, 38, 43, 48, or 53 notes are available.

Subgroup: 2.3.5.7

Comma list: 4375/4374, 33554432/33480783

Mapping: [⟨1 0 -6 25], ⟨0 4 21 -56]]

Wedgie: ⟨⟨4 21 -56 24 -100 -189]]

Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5511

Optimal ET sequence: 53, 164, 217, 270, 593, 863, 1133

Badness: 0.036985

11-limit

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 5632/5625, 41503/41472

Mapping: [⟨1 0 -6 25 -33], ⟨0 4 21 -56 92]]

Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5567

Optimal ET sequence: 53, 217, 270

Badness: 0.031907

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374

Mapping: [⟨1 0 -6 25 -33 -7], ⟨0 4 21 -56 92 27]]

Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5572

Optimal ET sequence: 53, 217, 270

Badness: 0.018758

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 0 -6 25 -33 -7 35], ⟨0 4 21 -56 92 27 -78]]

Optimal tuning (POTE): ~2 = 1\1, ~112/85 = 475.5617

Optimal ET sequence: 53, 217, 270, 487, 757g

Badness: 0.020103

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

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

Optimal tuning (POTE): ~2 = 1\1, ~25/19 = 475.5615

Optimal ET sequence: 53, 217, 270, 487, 757g

Badness: 0.013850

Semivulture

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4375/4374, 33554432/33480783

Mapping: [⟨2 0 -12 50 41], ⟨0 4 21 -56 -43]]

mapping generators: ~99/70, ~320/243

Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.550

Optimal ET sequence: 106, 164, 270, 916, 1186, 1456

Badness: 0.040799

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374

Mapping: [⟨2 0 -12 50 41 -14], ⟨0 4 21 -56 -43 27]]

Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.553

Optimal ET sequence: 106, 164, 270

Badness: 0.035458

Buzzard

Main article: Buzzard

Buzzard is an alternative lower complexity extension to vulture, but more of a full 13-limit system in its own right. It can be described as 53 & 58. As one might expect, 111edo is a great tuning for it.

Subgroup: 2.3.5.7

Comma list: 1728/1715, 5120/5103

Mapping: [⟨1 0 -6 4], ⟨0 4 21 -3]]

Wedgie: ⟨⟨4 21 -3 24 -16 -66]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.636

Optimal ET sequence: 5, 43c, 48, 53, 111, 164d, 275d

Badness: 0.047963

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 5120/5103

Mapping: [⟨1 0 -6 4 -12], ⟨0 4 21 -3 39]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.700

Optimal ET sequence: 53, 58, 111, 280cd, 391cd

Badness: 0.034484

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 540/539, 676/675

Mapping: [⟨1 0 -6 4 -12 -7], ⟨0 4 21 -3 39 27]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.697

Optimal ET sequence: 53, 58, 111, 280cdf, 391cdf

Badness: 0.018842

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 176/175, 256/255, 351/350, 442/441, 540/539

Mapping: [⟨1 0 -6 4 -12 -7 14], ⟨0 4 21 -3 39 27 -25]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.692

Optimal ET sequence: 53, 58, 111, 321cdfg

Badness: 0.018403

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539

Mapping: [⟨1 0 -6 4 -12 -7 14 -12], ⟨0 4 21 -3 39 27 -25 41]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.679

Optimal ET sequence: 53, 58h, 111

Badness: 0.015649

Buteo

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 2200/2187

Mapping: [⟨1 0 -6 4 9], ⟨0 4 21 -3 -14]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.436

Optimal ET sequence: 5, 48, 53

Badness: 0.060238

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 275/273, 385/384, 572/567

Mapping: [⟨1 0 -6 4 9 -7], ⟨0 4 21 -3 -14 27]]

Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.464

Optimal ET sequence: 5, 48f, 53

Badness: 0.039854

Condor

Subgroup: 2.3.5.7

Comma list: 10976/10935, 40353607/40000000

Mapping: [⟨1 8 36 29], ⟨0 -12 -63 -49]]

Wedgie: ⟨⟨12 63 49 72 44 -63]]

Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4791

Optimal ET sequence: 58, 159, 217

Badness: 0.154715

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 4000/3993, 10976/10935

Mapping: [⟨1 8 36 29 35], ⟨0 -12 -63 -49 -59]]

Optimal tuning (POTE): ~2 = 1\1, 81/56 = 641.4822

Optimal ET sequence: 58, 101cd, 159, 217

Badness: 0.048401

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440, 676/675, 10976/10935

Mapping: [⟨1 8 36 29 35 47], ⟨0 -12 -63 -49 -59 -81]]

Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4797

Optimal ET sequence: 58, 159, 217

Badness: 0.025469

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 8 36 29 35 47 -5], ⟨0 -12 -63 -49 -59 -81 17]]

Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4794

Optimal ET sequence: 58, 159, 217

Badness: 0.021984

Eagle

Subgroup: 2.3.5.7

Comma list: 2401/2400, 10485760000/10460353203

Mapping: [⟨2 4 9 8], ⟨0 -8 -42 -23]]

mapping generators: ~177147/125440, ~28/27

Wedgie: ⟨⟨16 84 46 96 28 -129]]

Optimal tuning (POTE): ~177147/125440 = 1\2, ~28/27 = 62.229

Optimal ET sequence: 58, 154c, 212, 270, 752, 1022, 1292, 2854b

Badness: 0.059498

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800, 19712/19683

Mapping: [⟨2 4 9 8 12], ⟨0 -8 -42 -23 -49]]

Optimal tuning (POTE): ~99/70 = 1\2, ~28/27 = 62.224

Optimal ET sequence: 58, 154ce, 212, 270

Badness: 0.024885

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647

Mapping: [⟨2 4 9 8 12 13], ⟨0 -8 -42 -23 -49 -54]]

Optimal tuning (POTE): ~99/70 = 1\2, ~28/27 = 62.220

Optimal ET sequence: 58, 154cef, 212, 270

Badness: 0.016282

Turkey

Subgroup: 2.3.5.7

Comma list: 4802000/4782969, 5250987/5242880

Mapping: [⟨1 8 36 0], ⟨0 -16 -84 7]]

Wedgie: ⟨⟨16 84 -7 96 -56 -252]]

Optimal tuning (POTE): ~2 = 1\1, ~1715/1296 = 481.120

Optimal ET sequence: 5, 207c, 212, 429

Badness: 0.210964

11-limit

Subgroup: 2.3.5.7.11

Comma list: 19712/19683, 42875/42768, 160083/160000

Mapping: [⟨1 8 36 0 64], ⟨0 -16 -84 7 -151]]

Optimal tuning (POTE): ~2 = 1\1, ~33/25 = 481.120

Optimal ET sequence: 212, 429

Badness: 0.079694

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104

Mapping: [⟨1 8 36 0 64 47], ⟨0 -16 -84 7 -151 -108]]

Optimal tuning (POTE): ~2 = 1\1, ~33/25 = 481.118

Optimal ET sequence: 212, 217, 429

Badness: 0.043787