Vulture family: Difference between revisions

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The '''vulture family''' of [[temperament]]s [[tempers out]] the [[vulture comma]], ({{monzo| 24 -21 4 }} = 10485760000/10460353203), a small [[5-limit]] comma of 4.2 [[cent]]s. Aside from vulture itself, the family contains [[Hemifamity temperaments#Buzzard|buzzard]], considered elsewhere, and condor.
The '''vulture family''' of [[temperament]]s [[tempers out]] the [[vulture comma]], ({{monzo| 24 -21 4 }} = 10485760000/10460353203), a small [[5-limit]] comma of 4.2 [[cent]]s. Aside from vulture itself, the family contains [[Hemifamity temperaments#Buzzard|buzzard]], considered elsewhere, and condor.
== Vulture ==
Subgroup: 2.3.5


[[Comma]]: 10485760000/10460353203
[[Comma]]: 10485760000/10460353203


POTE generator: ~320/243 = 475.5426
[[Mapping]]: [{{Val|1 0 -6}}, {{Val|0 4 21}}]
 
[[POTE generator]]: ~320/243 = 475.5426
 
{{Val list|legend=1| 5, 48, 53, 164, 217, 270, 323, 2531 }}


Map: [<1 0 -6|, <0 4 21|]
[[Badness]]: 0.041431


{{EDOs|legend=1| 5, 48, 53, 164, 217, 270, 323, 2531 }}
== Septimal vulture ==
The vulture temperament can be described as the 53&217 temperament, tempering out the ragisma, 4375/4374 and the [[garischisma]], {{monzo| 25 -14 0 -1 }} = 33554432/33480783 aside from the vulture comma. [[270edo|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.


Badness: 0.0414
Subgroup: 2.3.5.7


== Vulture ==
[[Comma list]]: 4375/4374, 33554432/33480783
The [[vulture]] temperament can be described as the 53&217 temperament, tempering out the ragisma, 4375/4374 and the [[garischisma]], {{monzo| 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
[[Mapping]]: [{{Val|1 0 -6 25}}, {{Val|0 4 21 -56}}]


POTE generator: ~320/243 = 475.5511
{{Multival|legend=1|4 21 -56 24 -100 -189}}


Map: [<1 0 -6 25|, <0 4 21 -56|]
[[POTE generator]]: ~320/243 = 475.5511


{{EDOs|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}
{{Val list|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}


Badness: 0.0370
[[Badness]]: 0.036985


=== 11-limit ===
=== 11-limit ===
Commas: 4375/4374, 5632/5625, 41503/41472
Subgroup: 2.3.5.7.11
 
Comma list: 4375/4374, 5632/5625, 41503/41472
 
Mapping: [{{Val|1 0 -6 25 -33}}, {{Val|0 4 21 -56 92}}]


POTE generator: ~320/243 = 475.5567
POTE generator: ~320/243 = 475.5567


Map: [<1 0 -6 25 -33|, <0 4 21 -56 92|]
Vals: {{Val list| 53, 217, 270 }}


{{EDOs|legend=1| 53, 217, 270 }}
Badness: 0.031907


Badness: 0.0319
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit ===
Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374
Commas: 676/675, 1001/1000, 4096/4095, 4375/4374
 
Mapping: [{{Val|1 0 -6 25 -33 -7}}, {{Val|0 4 21 -56 92 27}}]


POTE generator: ~320/243 = 475.5572
POTE generator: ~320/243 = 475.5572


Map: [<1 0 -6 25 -33 -7|, <0 4 21 -56 92 27|]
Vals: {{Val list| 53, 217, 270 }}
 
Badness: 0.018758


{{EDOs|legend=1| 53, 217, 270 }}
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0188
Comma list: 676/675, 936/935, 1001/1000, 1225/1224, 4096/4095


=== 17-limit ===
Mapping: [{{Val|1 0 -6 25 -33 -7 35}}, {{Val|0 4 21 -56 92 27 -78}}]
Commas: 676/675, 936/935, 1001/1000, 1225/1224, 4096/4095


POTE generator: ~112/85 = 475.5617
POTE generator: ~112/85 = 475.5617


Map: [<1 0 -6 25 -33 -7 35|, <0 4 21 -56 92 27 -78|]
Vals: {{Val list| 53, 217, 270, 487, 757g }}


{{EDOs|legend=1| 53, 217, 270, 487, 757g }}
Badness: 0.020103


Badness: 0.0201
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


=== 19-limit ===
Comma list: 676/675, 936/935, 1001/1000, 1216/1215, 1225/1224, 1540/1539
Commas: 676/675, 936/935, 1001/1000, 1216/1215, 1225/1224, 1540/1539
 
Mapping: [{{Val|1 0 -6 25 -33 -7 35 -12}}, {{Val|0 4 21 -56 92 27 -78 41}}]


POTE generator: ~25/19 = 475.5615
POTE generator: ~25/19 = 475.5615


Map: [<1 0 -6 25 -33 -7 35 -12|, <0 4 21 -56 92 27 -78 41|]
Vals: {{Val list| 53, 217, 270, 487, 757g }}
 
Badness: 0.013850


{{EDOs|legend=1| 53, 217, 270, 487, 757g }}
== Condor ==
Subgroup: 2.3.5.7


Badness: 0.0139
[[Comma list]]: 10976/10935, 40353607/40000000


== Condor ==
[[Mapping]]: [{{Val|1 8 36 29}}, {{Val|0 -12 -63 -49}}]
Commas: 10976/10935, 40353607/40000000


POTE generator: ~81/56 = 641.4791
{{Multival|legend=1|12 63 49 72 44 -63}}


Map: [<1 8 36 29|, <0 -12 -63 -49|]
[[POTE generator]]: ~81/56 = 641.4791


{{EDOs|legend=1| 58, 159, 217, 275 }}
{{Val list|legend=1| 58, 159, 217, 275 }}


Badness: 0.1547
[[Badness]]: 0.154715


=== 11-limit ===
=== 11-limit ===
Commas: 441/440, 4000/3993, 10976/10935
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 4000/3993, 10976/10935
 
Mapping: [{{Val|1 8 36 29 35}}, {{Val|0 -12 -63 -49 -59}}]


POTE generator: ~81/56 = 641.4822
POTE generator: ~81/56 = 641.4822


Map: [<1 8 36 29 35|, <0 -12 -63 -49 -59|]
Vals: {{Val list| 58, 159, 217 }}
 
Badness: 0.048401


{{EDOs|legend=1| 58, 159, 217 }}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Badness: 0.0484
Comma list: 364/363, 441/440, 676/675, 10976/10935


=== 13-limit ===
Mapping: [{{Val|1 8 36 29 35 47}}, {{Val|0 -12 -63 -49 -59 -81}}]
Commas: 364/363, 441/440, 676/675, 10976/10935


POTE generator: ~81/56 = 641.4797
POTE generator: ~81/56 = 641.4797


Map: [<1 8 36 29 35 47|, <0 -12 -63 -49 -59 -81|]
Vals: {{Val list| 58, 159, 217 }}
 
Badness: 0.025469


{{EDOs|legend=1| 58, 159, 217 }}
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0255
Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619


=== 17-limit ===
Mapping: [{{Val|1 8 36 29 35 47 -5}}, {{Val|0 -12 -63 -49 -59 -81 17}}]
Commas: 364/363, 441/440, 595/594, 676/675, 8624/8619


POTE generator: ~81/56 = 641.4794
POTE generator: ~81/56 = 641.4794


Map: [<1 8 36 29 35 47 -5|, <0 -12 -63 -49 -59 -81 17|]
Vals: {{Val list| 58, 159, 217 }}


{{EDOs|legend=1| 58, 159, 217 }}
Badness: 0.021984
 
Badness: 0.0220


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Vulture]]
[[Category:Vulture]]
{{todo
| review <!-- The EDOs were only formatted not checked for correctness. -->
| cleanup <!-- Do we already have a convention to format maps? -->
}}

Revision as of 03:47, 8 June 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. Aside from vulture itself, the family contains buzzard, considered elsewhere, and condor.

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

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

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