Vulture family: Difference between revisions

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__FORCETOC__
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|temperament]]s [[tempering_out|tempers out]] the [[vulture comma]], |24 -21 4> = 10485760000/10460353203, a small [[5-limit]] comma of size 4.1998 [[cent]]s. Aside from vulture itself, the family contains [[Hemifamity_temperaments#Buzzard|buzzard]], considered elsewhere, and condor.


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


POTE generator: ~320/243 = 475.5426
POTE generator: ~320/243 = 475.5426
Line 8: Line 7:
Map: [<1 0 -6|, <0 4 21|]
Map: [<1 0 -6|, <0 4 21|]


EDOs: [[5edo|5]], [[48edo|48]], [[53edo|53]], [[164edo|164]], [[217edo|217]], [[270edo|270]], [[323edo|323]], [[2531edo|2531]]
{{EDOs|legend=1| 5, 48, 53, 164, 217, 270, 323, 2531 }}


Badness: 0.0414
Badness: 0.0414


=Vulture=
=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]] 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.
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
Commas: 4375/4374, 33554432/33480783
Line 21: Line 20:
Map: [<1 0 -6 25|, <0 4 21 -56|]
Map: [<1 0 -6 25|, <0 4 21 -56|]


EDOs: 53, 164, 217, 270, [[593edo|593]], [[863edo|863]], [[1133edo|1133]]
{{EDOs|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}


Badness: 0.0370
Badness: 0.0370
Line 32: Line 31:
Map: [<1 0 -6 25 -33|, <0 4 21 -56 92|]
Map: [<1 0 -6 25 -33|, <0 4 21 -56 92|]


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


Badness: 0.0319
Badness: 0.0319
Line 43: Line 42:
Map: [<1 0 -6 25 -33 -7|, <0 4 21 -56 92 27|]
Map: [<1 0 -6 25 -33 -7|, <0 4 21 -56 92 27|]


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


Badness: 0.0188
Badness: 0.0188
Line 54: Line 53:
Map: [<1 0 -6 25 -33 -7 35|, <0 4 21 -56 92 27 -78|]
Map: [<1 0 -6 25 -33 -7 35|, <0 4 21 -56 92 27 -78|]


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


Badness: 0.0201
Badness: 0.0201
Line 65: Line 64:
Map: [<1 0 -6 25 -33 -7 35 -12|, <0 4 21 -56 92 27 -78 41|]
Map: [<1 0 -6 25 -33 -7 35 -12|, <0 4 21 -56 92 27 -78 41|]


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


Badness: 0.0139
Badness: 0.0139
Line 76: Line 75:
Map: [<1 8 36 29|, <0 -12 -63 -49|]
Map: [<1 8 36 29|, <0 -12 -63 -49|]


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


Badness: 0.1547
Badness: 0.1547
Line 87: Line 86:
Map: [<1 8 36 29 35|, <0 -12 -63 -49 -59|]
Map: [<1 8 36 29 35|, <0 -12 -63 -49 -59|]


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


Badness: 0.0484
Badness: 0.0484
Line 98: Line 97:
Map: [<1 8 36 29 35 47|, <0 -12 -63 -49 -59 -81|]
Map: [<1 8 36 29 35 47|, <0 -12 -63 -49 -59 -81|]


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


Badness: 0.0255
Badness: 0.0255
Line 109: Line 108:
Map: [<1 8 36 29 35 47 -5|, <0 -12 -63 -49 -59 -81 17|]
Map: [<1 8 36 29 35 47 -5|, <0 -12 -63 -49 -59 -81 17|]


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


Badness: 0.0220
Badness: 0.0220
Line 116: Line 115:
[[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 11:54, 20 December 2020

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.

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

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