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Vulture family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Update keys
Line 8: Line 8:
[[Comma list]]: 10485760000/10460353203
[[Comma list]]: 10485760000/10460353203


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


Mapping generators: ~2, ~320/243
: mapping generators: ~2, ~320/243


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~320/243 = 475.5426
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~320/243 = 475.5426
Line 25: Line 25:
[[Comma list]]: 4375/4374, 33554432/33480783
[[Comma list]]: 4375/4374, 33554432/33480783


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


{{Multival|legend=1| 4 21 -56 24 -100 -189 }}
{{Multival|legend=1| 4 21 -56 24 -100 -189 }}
Line 40: Line 40:
Comma list: 4375/4374, 5632/5625, 41503/41472
Comma list: 4375/4374, 5632/5625, 41503/41472


Mapping: [{{val| 1 0 -6 25 -33 }}, {{val| 0 4 21 -56 92 }}]
Mapping: {{mapping| 1 0 -6 25 -33 | 0 4 21 -56 92 }}


Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5567
Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5567
Line 53: Line 53:
Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374
Comma list: 676/675, 1001/1000, 4096/4095, 4375/4374


Mapping: [{{val| 1 0 -6 25 -33 -7 }}, {{val| 0 4 21 -56 92 27 }}]
Mapping: {{mapping| 1 0 -6 25 -33 -7 | 0 4 21 -56 92 27 }}


Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5572
Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 475.5572
Line 66: Line 66:
Comma list: 676/675, 936/935, 1001/1000, 1225/1224, 4096/4095
Comma list: 676/675, 936/935, 1001/1000, 1225/1224, 4096/4095


Mapping: [{{val| 1 0 -6 25 -33 -7 35 }}, {{val| 0 4 21 -56 92 27 -78 }}]
Mapping: {{mapping| 1 0 -6 25 -33 -7 35 | 0 4 21 -56 92 27 -78 }}


Optimal tuning (POTE): ~2 = 1\1, ~112/85 = 475.5617
Optimal tuning (POTE): ~2 = 1\1, ~112/85 = 475.5617
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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: {{mapping| 1 0 -6 25 -33 -7 35 -12 | 0 4 21 -56 92 27 -78 41 }}


Optimal tuning (POTE): ~2 = 1\1, ~25/19 = 475.5615
Optimal tuning (POTE): ~2 = 1\1, ~25/19 = 475.5615
Line 92: Line 92:
Comma list: 3025/3024, 4375/4374, 33554432/33480783
Comma list: 3025/3024, 4375/4374, 33554432/33480783


Mapping: [{{val| 2 0 -12 50 41 }}, {{val| 0 4 21 -56 -43 }}]
Mapping: {{mapping| 2 0 -12 50 41 | 0 4 21 -56 -43 }}


Mapping generators: ~99/70, ~320/243
: mapping generators: ~99/70, ~320/243


Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.550
Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.550
Line 107: Line 107:
Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374
Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374


Mapping: [{{val| 2 0 -12 50 41 -14 }}, {{val| 0 4 21 -56 -43 27 }}]
Mapping: {{mapping| 2 0 -12 50 41 -14 | 0 4 21 -56 -43 27 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.553
Optimal tuning (POTE): ~99/70 = 1\2, ~320/243 = 475.553
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{{Main| Buzzard }}
{{Main| Buzzard }}


''Buzzard'' is an alternative lower complexity extension to vulture, but more of a full 13-limit system in its own right. It can be described as 53 & 58. As one might expect, 111edo is a great tuning for it.  
Buzzard is an alternative lower complexity extension to vulture, but more of a full 13-limit system in its own right. It can be described as 53 & 58. As one might expect, 111edo is a great tuning for it.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 124: Line 124:
[[Comma list]]: 1728/1715, 5120/5103
[[Comma list]]: 1728/1715, 5120/5103


[[Mapping]]: [{{val| 1 0 -6 4 }}, {{val| 0 4 21 -3 }}]
{{Mapping|legend=1| 1 0 -6 4 | 0 4 21 -3 }}


{{Multival|legend=1| 4 21 -3 24 -16 -66 }}
{{Multival|legend=1| 4 21 -3 24 -16 -66 }}
Line 139: Line 139:
Comma list: 176/175, 540/539, 5120/5103
Comma list: 176/175, 540/539, 5120/5103


Mapping: [{{val| 1 0 -6 4 -12 }}, {{val| 0 4 21 -3 39 }}]
Mapping: {{mapping| 1 0 -6 4 -12 | 0 4 21 -3 39 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.700
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.700
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Comma list: 176/175, 351/350, 540/539, 676/675
Comma list: 176/175, 351/350, 540/539, 676/675


Mapping: [{{val| 1 0 -6 4 -12 -7 }}, {{val| 0 4 21 -3 39 27 }}]
Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.697
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.697
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Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539


Mapping: [{{val| 1 0 -6 4 -12 -7 14 }}, {{val| 0 4 21 -3 39 27 -25 }}]
Mapping: {{mapping| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.692
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.692
Line 178: Line 178:
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539


Mapping: [{{val| 1 0 -6 4 -12 -7 14 -12 }}, {{val| 0 4 21 -3 39 27 -25 41 }}]
Mapping: {{mapping| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.679
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.679
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Comma list: 99/98, 385/384, 2200/2187
Comma list: 99/98, 385/384, 2200/2187


Mapping: [{{val| 1 0 -6 4 9 }}, {{val| 0 4 21 -3 -14 }}]
Mapping: {{mapping| 1 0 -6 4 9 | 0 4 21 -3 -14 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.436
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.436
Line 204: Line 204:
Comma list: 99/98, 275/273, 385/384, 572/567
Comma list: 99/98, 275/273, 385/384, 572/567


Mapping: [{{val| 1 0 -6 4 9 -7 }}, {{val| 0 4 21 -3 -14 27 }}]
Mapping: {{mapping| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.464
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.464
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[[Comma list]]: 10976/10935, 40353607/40000000
[[Comma list]]: 10976/10935, 40353607/40000000


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


{{Multival|legend=1| 12 63 49 72 44 -63 }}
{{Multival|legend=1| 12 63 49 72 44 -63 }}
Line 232: Line 232:
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: {{mapping| 1 8 36 29 35 | 0 -12 -63 -49 -59 }}


Optimal tuning (POTE): ~2 = 1\1, 81/56 = 641.4822
Optimal tuning (POTE): ~2 = 1\1, 81/56 = 641.4822
Line 245: Line 245:
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: {{mapping| 1 8 36 29 35 47 | 0 -12 -63 -49 -59 -81 }}


Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4797
Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4797
Line 258: Line 258:
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: {{mapping| 1 8 36 29 35 47 -5 | 0 -12 -63 -49 -59 -81 17 }}


Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4794
Optimal tuning (POTE): ~2 = 1\1, ~81/56 = 641.4794
Line 271: Line 271:
[[Comma list]]: 2401/2400, 10485760000/10460353203
[[Comma list]]: 2401/2400, 10485760000/10460353203


[[Mapping]]: [{{val| 2 4 9 8 }}, {{val| 0 -8 -42 -23 }}]
{{Mapping|legend=1| 2 4 9 8 | 0 -8 -42 -23 }}


Mapping generators: ~177147/125440, ~28/27
: mapping generators: ~177147/125440, ~28/27


{{Multival|legend=1|16 84 46 96 28 -129}}
{{Multival|legend=1|16 84 46 96 28 -129}}
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Comma list: 2401/2400, 9801/9800, 19712/19683
Comma list: 2401/2400, 9801/9800, 19712/19683


Mapping: [{{val| 2 4 9 8 12 }}, {{val| 0 -8 -42 -23 -49 }}]
Mapping: {{mapping| 2 4 9 8 12 | 0 -8 -42 -23 -49 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~28/27 = 62.224
Optimal tuning (POTE): ~99/70 = 1\2, ~28/27 = 62.224
Line 301: Line 301:
Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647
Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647


Mapping: [{{val| 2 4 9 8 12 13 }}, {{val| 0 -8 -42 -23 -49 -54 }}]
Mapping: {{mapping| 2 4 9 8 12 13 | 0 -8 -42 -23 -49 -54 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~28/27 = 62.220
Optimal tuning (POTE): ~99/70 = 1\2, ~28/27 = 62.220
Line 314: Line 314:
[[Comma list]]: 4802000/4782969, 5250987/5242880
[[Comma list]]: 4802000/4782969, 5250987/5242880


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


{{Multival|legend=1|16 84 -7 96 -56 -252}}
{{Multival|legend=1|16 84 -7 96 -56 -252}}
Line 329: Line 329:
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: {{mapping| 1 8 36 0 64 | 0 -16 -84 7 -151 }}


Optimal tuning (POTE): ~2 = 1\1, ~33/25 = 481.120
Optimal tuning (POTE): ~2 = 1\1, ~33/25 = 481.120
Line 342: Line 342:
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: {{mapping| 1 8 36 0 64 47 | 0 -16 -84 7 -151 -108 }}


Optimal tuning (POTE): ~2 = 1\1, ~33/25 = 481.118
Optimal tuning (POTE): ~2 = 1\1, ~33/25 = 481.118
Line 352: Line 352:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Vulture family| ]] <!-- main article -->
[[Category:Vulture family| ]] <!-- main article -->
[[Category:Vulture| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Vulture_family"