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Vulture family: Difference between revisions

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== Vulture ==
== Vulture ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


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


[[Mapping]]: [{{Val|1 0 -6}}, {{Val|0 4 21}}]
[[Mapping]]: [{{val| 1 0 -6 }}, {{val| 0 4 21 }}]


[[POTE generator]]: ~320/243 = 475.5426
Mapping generators: ~2, ~320/243
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~320/243 = 475.5426


{{Val list|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, 3500b, 3823b, 4146b, 4469b }}
{{Val list|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, 3500b, 3823b, 4146b, 4469b }}
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== Septimal vulture ==
== 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.
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 scale]]s of 3, 5, 8, 13, 18, 23, 28, 33, 38, 43, 48, or 53 notes are available.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 33554432/33480783
[[Comma list]]: 4375/4374, 33554432/33480783


[[Mapping]]: [{{Val|1 0 -6 25}}, {{Val|0 4 21 -56}}]
[[Mapping]]: [{{val| 1 0 -6 25 }}, {{val| 0 4 21 -56 }}]


{{Multival|legend=1|4 21 -56 24 -100 -189}}
{{Multival|legend=1| 4 21 -56 24 -100 -189 }}


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


{{Val list|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}
{{Val list|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}
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Mapping: [{{Val|1 0 -6 25 -33}}, {{Val|0 4 21 -56 92}}]
Mapping: [{{Val|1 0 -6 25 -33}}, {{Val|0 4 21 -56 92}}]


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


Optimal GPV sequence: {{Val list| 53, 217, 270 }}
Optimal GPV sequence: {{Val list| 53, 217, 270 }}
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Mapping: [{{Val|1 0 -6 25 -33 -7}}, {{Val|0 4 21 -56 92 27}}]
Mapping: [{{Val|1 0 -6 25 -33 -7}}, {{Val|0 4 21 -56 92 27}}]


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


Optimal GPV sequence: {{Val list| 53, 217, 270 }}
Optimal GPV sequence: {{Val list| 53, 217, 270 }}
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Mapping: [{{Val|1 0 -6 25 -33 -7 35}}, {{Val|0 4 21 -56 92 27 -78}}]
Mapping: [{{Val|1 0 -6 25 -33 -7 35}}, {{Val|0 4 21 -56 92 27 -78}}]


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


Optimal GPV sequence: {{Val list| 53, 217, 270, 487, 757g }}
Optimal GPV sequence: {{Val list| 53, 217, 270, 487, 757g }}
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Comma list: 676/675, 936/935, 1001/1000, 1216/1215, 1225/1224, 1540/1539
Comma list: 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}}]
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
Optimal tuning (POTE): ~2 = 1\1, ~25/19 = 475.5615


Optimal GPV sequence: {{Val list| 53, 217, 270, 487, 757g }}
Optimal GPV sequence: {{Val list| 53, 217, 270, 487, 757g }}
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Mapping: [{{val| 2 4 9 -6 -2 }}, {{val| 0 -4 -21 56 43 }}]
Mapping: [{{val| 2 4 9 -6 -2 }}, {{val| 0 -4 -21 56 43 }}]


POTE generator: ~275/256 = 124.450
Mapping generators: ~99/70, ~320/243
 
Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.550


Optimal GPV sequence: {{Val list| 106, 164, 270, 916, 1186, 1456 }}
Optimal GPV sequence: {{Val list| 106, 164, 270, 916, 1186, 1456 }}
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Mapping: [{{val| 2 4 9 -6 -2 13 }}, {{val| 0 -4 -21 56 43 -27 }}]
Mapping: [{{val| 2 4 9 -6 -2 13 }}, {{val| 0 -4 -21 56 43 -27 }}]


POTE generator: ~275/256 = 124.447
Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.553


Optimal GPV sequence: {{Val list| 106, 164, 270 }}
Optimal GPV sequence: {{Val list| 106, 164, 270 }}
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== Buzzard ==
== Buzzard ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1728/1715, 5120/5103
[[Comma list]]: 1728/1715, 5120/5103
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{{Multival|legend=1| 4 21 -3 24 -16 -66 }}
{{Multival|legend=1| 4 21 -3 24 -16 -66 }}


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


{{Val list|legend=1| 5, 43c, 48, 53, 111, 164d, 275d }}
{{Val list|legend=1| 5, 43c, 48, 53, 111, 164d, 275d }}
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Mapping: [{{val| 1 0 -6 4 -12 }}, {{val| 0 4 21 -3 39 }}]
Mapping: [{{val| 1 0 -6 4 -12 }}, {{val| 0 4 21 -3 39 }}]


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


Optimal GPV sequence: {{Val list| 53, 58, 111, 280cd, 391cd }}
Optimal GPV sequence: {{Val list| 53, 58, 111, 280cd, 391cd }}
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Mapping: [{{val| 1 0 -6 4 -12 -7 }}, {{val| 0 4 21 -3 39 27 }}]
Mapping: [{{val| 1 0 -6 4 -12 -7 }}, {{val| 0 4 21 -3 39 27 }}]


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


Optimal GPV sequence: {{Val list| 53, 58, 111, 280cdf, 391cdf }}
Optimal GPV sequence: {{Val list| 53, 58, 111, 280cdf, 391cdf }}
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Mapping: [{{val| 1 0 -6 4 -12 -7 14 }}, {{val| 0 4 21 -3 39 27 -25 }}]
Mapping: [{{val| 1 0 -6 4 -12 -7 14 }}, {{val| 0 4 21 -3 39 27 -25 }}]


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


Optimal GPV sequence: {{Val list| 53, 58, 111, 321cdfg }}
Optimal GPV sequence: {{Val list| 53, 58, 111, 321cdfg }}
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Mapping: [{{val| 1 0 -6 4 -12 -7 14 -12 }}, {{val| 0 4 21 -3 39 27 -25 41 }}]
Mapping: [{{val| 1 0 -6 4 -12 -7 14 -12 }}, {{val| 0 4 21 -3 39 27 -25 41 }}]


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


Optimal GPV sequence: {{Val list| 53, 58h, 111 }}
Optimal GPV sequence: {{Val list| 53, 58h, 111 }}
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Mapping: [{{val| 1 0 -6 4 9 }}, {{val| 0 4 21 -3 -14 }}]
Mapping: [{{val| 1 0 -6 4 9 }}, {{val| 0 4 21 -3 -14 }}]


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


Optimal GPV sequence: {{Val list| 5, 48, 53 }}
Optimal GPV sequence: {{Val list| 5, 48, 53 }}
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Mapping: [{{val| 1 0 -6 4 9 -7 }}, {{val| 0 4 21 -3 -14 27 }}]
Mapping: [{{val| 1 0 -6 4 9 -7 }}, {{val| 0 4 21 -3 -14 27 }}]


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


Optimal GPV sequence: {{Val list| 5, 48f, 53 }}
Optimal GPV sequence: {{Val list| 5, 48f, 53 }}
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== Condor ==
== Condor ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


[[Mapping]]: [{{Val|1 8 36 29}}, {{Val|0 -12 -63 -49}}]
[[Mapping]]: [{{Val| 1 8 36 29 }}, {{Val| 0 -12 -63 -49 }}]


{{Multival|legend=1|12 63 49 72 44 -63}}
{{Multival|legend=1| 12 63 49 72 44 -63 }}


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


{{Val list|legend=1| 58, 159, 217, 275 }}
{{Val list|legend=1| 58, 159, 217, 275 }}
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Comma list: 441/440, 4000/3993, 10976/10935
Comma list: 441/440, 4000/3993, 10976/10935


Mapping: [{{Val|1 8 36 29 35}}, {{Val|0 -12 -63 -49 -59}}]
Mapping: [{{Val| 1 8 36 29 35 }}, {{Val| 0 -12 -63 -49 -59 }}]


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


Optimal GPV sequence: {{Val list| 58, 101cd, 159, 217 }}
Optimal GPV sequence: {{Val list| 58, 101cd, 159, 217 }}
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Comma list: 364/363, 441/440, 676/675, 10976/10935
Comma list: 364/363, 441/440, 676/675, 10976/10935


Mapping: [{{Val|1 8 36 29 35 47}}, {{Val|0 -12 -63 -49 -59 -81}}]
Mapping: [{{val| 1 8 36 29 35 47 }}, {{val| 0 -12 -63 -49 -59 -81 }}]


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


Optimal GPV sequence: {{Val list| 58, 159, 217 }}
Optimal GPV sequence: {{Val list| 58, 159, 217 }}
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Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619
Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619


Mapping: [{{Val|1 8 36 29 35 47 -5}}, {{Val|0 -12 -63 -49 -59 -81 17}}]
Mapping: [{{val| 1 8 36 29 35 47 -5 }}, {{val| 0 -12 -63 -49 -59 -81 17 }}]


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


Optimal GPV sequence: {{Val list| 58, 159, 217 }}
Optimal GPV sequence: {{Val list| 58, 159, 217 }}
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== Eagle ==
== Eagle ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2401/2400, 10485760000/10460353203
[[Comma list]]: 2401/2400, 10485760000/10460353203
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{{Multival|legend=1|16 84 46 96 28 -129}}
{{Multival|legend=1|16 84 46 96 28 -129}}


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


{{Val list|legend=1| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}
{{Val list|legend=1| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}
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Mapping: [{{val| 2 4 9 8 12 }}, {{val| 0 -8 -42 -23 -49 }}]
Mapping: [{{val| 2 4 9 8 12 }}, {{val| 0 -8 -42 -23 -49 }}]


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


Optimal GPV sequence: {{Val list| 58, 154ce, 212, 270 }}
Optimal GPV sequence: {{Val list| 58, 154ce, 212, 270 }}
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Mapping: [{{val| 2 4 9 8 12 13 }}, {{val| 0 -8 -42 -23 -49 -54 }}]
Mapping: [{{val| 2 4 9 8 12 13 }}, {{val| 0 -8 -42 -23 -49 -54 }}]


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


Optimal GPV sequence: {{Val list| 58, 154cef, 212, 270 }}
Optimal GPV sequence: {{Val list| 58, 154cef, 212, 270 }}
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== Turkey ==
== Turkey ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4802000/4782969, 5250987/5242880
[[Comma list]]: 4802000/4782969, 5250987/5242880


[[Mapping]]: [{{Val|1 8 36 0}}, {{Val|0 -16 -84 7}}]
[[Mapping]]: [{{val| 1 8 36 0 }}, {{val| 0 -16 -84 7 }}]


{{Multival|legend=1|16 84 -7 96 -56 -252}}
{{Multival|legend=1|16 84 -7 96 -56 -252}}


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


{{Val list|legend=1| 5, 207c, 212, 429 }}
{{Val list|legend=1| 5, 207c, 212, 429 }}
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Comma list: 19712/19683, 42875/42768, 160083/160000
Comma list: 19712/19683, 42875/42768, 160083/160000


Mapping: [{{Val|1 8 36 0 64}}, {{Val|0 -16 -84 7 -151}}]
Mapping: [{{val| 1 8 36 0 64 }}, {{val| 0 -16 -84 7 -151 }}]


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


Optimal GPV sequence: {{Val list| 212, 429 }}
Optimal GPV sequence: {{Val list| 212, 429 }}
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Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: [[676/675]], [[1001/1000]], [[19712/19683]], [[31213/31104]]
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}}]
Mapping: [{{val| 1 8 36 0 64 47 }}, {{val| 0 -16 -84 7 -151 -108 }}]


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


Optimal GPV sequence: {{Val list| 212, 217, 429 }}
Optimal GPV sequence: {{Val list| 212, 217, 429 }}
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