Vulture family: Difference between revisions

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[[POTE generator]]: ~320/243 = 475.5426
[[POTE generator]]: ~320/243 = 475.5426


{{Val list|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, …, 4146b, 4469 }}
{{Val list|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, 3500b, 3823b, 4146b, 4469b }}


[[Badness]]: 0.041431
[[Badness]]: 0.041431
Line 205: Line 205:


Badness: 0.016282
Badness: 0.016282
== Turkey ==
Subgroup: 2.3.5.7
[[Comma list]]: 4802000/4782969, 5250987/5242880
[[Mapping]]: [{{Val|1 8 36 0}}, {{Val|0 -16 -84 7}}]
{{Multival|legend=1|16 84 -7 96 -56 -252}}
[[POTE generator]]: ~1715/1296 = 481.120
{{Val list|legend=1| 5, 207c, 212, 429 }}
[[Badness]]: 0.210964
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 19712/19683, 42875/42768, 160083/160000
Mapping: [{{Val|1 8 36 0 64}}, {{Val|0 -16 -84 7 -151}}]
POTE generator: ~33/25 = 481.120
Vals: {{Val list| 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: [{{Val|1 8 36 0 64 47}}, {{Val|0 -16 -84 7 -151 -108}}]
POTE generator: ~33/25 = 481.118
Vals: {{Val list| 212, 217, 429 }}
Badness: 0.043787


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 05:11, 26 September 2021

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 buzzard and terture.

Vulture

Subgroup: 2.3.5

Comma: 10485760000/10460353203

Mapping: [⟨1 0 -6], ⟨0 4 21]]

POTE generator: ~320/243 = 475.5426

Template:Val list

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 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 ]]

POTE generator: ~320/243 = 475.5511

Template:Val list

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]]

POTE generator: ~320/243 = 475.5567

Vals: Template:Val list

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]]

POTE generator: ~320/243 = 475.5572

Vals: Template:Val list

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]]

POTE generator: ~112/85 = 475.5617

Vals: Template:Val list

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]]

POTE generator: ~25/19 = 475.5615

Vals: Template:Val list

Badness: 0.013850

Semivulture

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 4 9 -6 -2], ⟨0 -4 -21 56 43]]

POTE generator: ~275/256 = 124.450

Vals: Template:Val list

Badness: 0.040799

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨2 4 9 -6 -2 13], ⟨0 -4 -21 56 43 -27]]

POTE generator: ~275/256 = 124.447

Vals: Template:Val list

Badness: 0.035458

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 ]]

POTE generator: ~81/56 = 641.4791

Template:Val list

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]]

POTE generator: ~81/56 = 641.4822

Vals: Template:Val list

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]]

POTE generator: ~81/56 = 641.4797

Vals: Template:Val list

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]]

POTE generator: ~81/56 = 641.4794

Vals: Template:Val list

Badness: 0.021984

Eagle

Subgroup: 2.3.5.7

Comma list: 2401/2400, 10485760000/10460353203

Mapping: [⟨2 4 9 8], ⟨0 -8 -42 -23]]

Wedgie: ⟨⟨ 16 84 46 96 28 -129 ]]

POTE generator: ~28/27 = 62.229

Template:Val list

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]]

POTE generator: ~28/27 = 62.224

Vals: Template:Val list

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]]

POTE generator: ~28/27 = 62.220

Vals: Template:Val list

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 ]]

POTE generator: ~1715/1296 = 481.120

Template:Val list

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]]

POTE generator: ~33/25 = 481.120

Vals: Template:Val list

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]]

POTE generator: ~33/25 = 481.118

Vals: Template:Val list

Badness: 0.043787

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