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| | {{Val list|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, …, 4146b, 4469 }} | ||
[[Badness]]: 0.041431 | [[Badness]]: 0.041431 | ||
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Comma list: 3025/3024, 4375/4374, 33554432/33480783 | Comma list: 3025/3024, 4375/4374, 33554432/33480783 | ||
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 | POTE generator: ~275/256 = 124.450 | ||
Vals: {{Val list| 106, 164, 270 }} | Vals: {{Val list| 106, 164, 270, 916, 1186, 1456 }} | ||
Badness: 0.040799 | Badness: 0.040799 | ||
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Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374 | Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374 | ||
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 | POTE generator: ~275/256 = 124.447 | ||
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POTE generator: ~81/56 = 641.4822 | POTE generator: ~81/56 = 641.4822 | ||
Vals: {{Val list| 58, 159, 217 }} | Vals: {{Val list| 58, 101cd, 159, 217 }} | ||
Badness: 0.048401 | Badness: 0.048401 | ||
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[[POTE generator]]: ~28/27 = 62.229 | [[POTE generator]]: ~28/27 = 62.229 | ||
{{Val list|legend=1| 58, 212, 270, 752, 1022, 1292, 2854b }} | {{Val list|legend=1| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }} | ||
[[Badness]]: 0.059498 | [[Badness]]: 0.059498 | ||
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POTE generator: ~28/27 = 62.224 | POTE generator: ~28/27 = 62.224 | ||
Vals: {{Val list| 58, 212, 270 }} | Vals: {{Val list| 58, 154ce, 212, 270 }} | ||
Badness: 0.024885 | Badness: 0.024885 | ||
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POTE generator: ~28/27 = 62.220 | POTE generator: ~28/27 = 62.220 | ||
Vals: {{Val list| 58, 212, 270 }} | Vals: {{Val list| 58, 154cef, 212, 270 }} | ||
Badness: 0.016282 | Badness: 0.016282 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Vulture]] | [[Category:Vulture family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | |||
Revision as of 16:53, 10 July 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
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
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
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
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