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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.
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{{Technical data page}}
The '''vulture family''' of [[temperament]]s [[tempering out|tempers out]] the [[vulture comma]] ({{monzo|legend=1| 24 -21 4 }}, [[ratio]]: 10 485 760 000 / 10 460 353 203), a small [[5-limit]] comma of 4.2 [[cent]]s.  


Temperaments discussed elsewhere includes [[Landscape microtemperaments #Terture|terture]].
Temperaments discussed elsewhere include [[Landscape microtemperaments #Terture|terture]] and [[Buzzardsmic clan #Buzzard|buzzard]]. Considered below are septimal vulture, condor, eagle, and turkey.  


== Vulture ==
== Vulture ==
The generator of the vulture temperament is a grave fourth of [[320/243]], that is, a [[4/3|perfect fourth]] minus a [[81/80|syntonic comma]]. Four of these make a [[3/1|perfect twelfth]]. Its [[ploidacot]] is alpha-tetracot. It is a member of the [[syntonic–diatonic equivalence continuum]] with {{nowrap|''n'' {{=}} 4}}, so it equates a [[256/243|Pythagorean limma]] with a stack of four syntonic commas. It is also in the [[schismic–Mercator equivalence continuum]] with {{nowrap|''n'' {{=}} 4}}, so unless [[53edo]] is used as a tuning, the [[schisma]] is always observed.
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[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]]s:
* [[CTE]]: ~2 = 1200.000, ~320/243 = 475.5351
: [[error map]]: {{val| 0.0000 +0.1855 -0.0758 }}
* [[POTE]]: ~2 = 1200.000, ~320/243 = 475.5426
: error map: {{val| 0.0000 +0.2154 +0.0811 }}


{{Val list|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, 3500b, 3823b, 4146b, 4469b }}
{{Optimal ET sequence|legend=1| 53, 164, 217, 270, 323, 2531, 2854b, 3177b, …, 4469b }}


[[Badness]]: 0.041431
[[Badness]]:
* Smith: 0.041431
* Dirichlet: 0.972


== 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]] 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.
Septimal vulture can be described as the {{nowrap| 53 & 270 }} microtemperament, tempering out the [[ragisma]], 4375/4374 and the [[garischisma]], 33554432/33480783 ({{monzo| 25 -14 0 -1 }}) aside from the vulture comma. [[270edo]] is a good tuning for this temperament, with generator 107\270. The harmonic 7 is found at -14 fifths or {{nowrap| (-14) × 4 {{=}} -56 }} generator steps, so that the smallest [[mos scale]] that includes it is the 58-note one, though for larger scope of harmony, you could try the 111- or 164-note one. For a much simpler mapping of 7 at the cost of higher error, you could try [[#Buzzard|buzzard]].
 
It can be extended to the 11-limit by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]], and to the 13-limit by identifying the hemitwelfth as [[26/15]], tempering out [[676/675]]. Furthermore, the generator of vulture is very close to [[25/19]]; a stack of three generator steps octave-reduced thus represents its fifth complement, [[57/50]]. This corresponds to tempering out [[1216/1215]] with the effect of equating the schisma with [[513/512]] and [[361/360]] in addition to many 11- and 13-limit commas. 270edo remains an excellent tuning in all cases.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 25: Line 42:
[[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 }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000, ~320/243 = 475.5528
: [[error map]]: {{val| 0.0000 +0.2561 +0.2945 +0.2188 }}
* [[POTE]]: ~2 = 1200.0000, ~320/243 = 475.5511
: error map: {{val| 0.0000 +0.2495 +0.2601 +0.3106 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~320/243 = 475.5511
{{Optimal ET sequence|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}


{{Val list|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}
[[Badness]] (Smith): 0.036985
 
[[Badness]]: 0.036985


=== 11-limit ===
=== 11-limit ===
Line 40: Line 59:
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 tunings:
* CTE: ~2 = 1200.0000, ~320/243 = 475.5558
* POTE: ~2 = 1200.0000, ~320/243 = 475.5567


Optimal GPV sequence: {{Val list| 53, 217, 270 }}
{{Optimal ET sequence|legend=0| 53, 217, 270, 2107c, 2377bc }}


Badness: 0.031907
Badness (Smith): 0.031907


==== 13-limit ====
==== 13-limit ====
Line 53: Line 74:
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 tunings:
* CTE: ~2 = 1200.0000, ~320/243 = 475.5566
* POTE: ~2 = 1200.0000, ~320/243 = 475.5572


Optimal GPV sequence: {{Val list| 53, 217, 270 }}
{{Optimal ET sequence|legend=0| 53, 217, 270 }}


Badness: 0.018758
Badness (Smith): 0.018758


==== 17-limit ====
==== 2.3.5.7.11.13.19 subgroup ====
Subgroup: 2.3.5.7.11.13.17
 
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 }}]
 
Optimal tuning (POTE): ~2 = 1\1, ~112/85 = 475.5617
 
Optimal GPV sequence: {{Val list| 53, 217, 270, 487, 757g }}
 
Badness: 0.020103
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 676/675, 936/935, 1001/1000, 1216/1215, 1225/1224, 1540/1539
Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728


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 -12 | 0 4 21 -56 92 27 41 }}


Optimal tuning (POTE): ~2 = 1\1, ~25/19 = 475.5615
Optimal tunings:
* CTE: ~2 = 1200.0000, ~25/19 = 475.5561
* CWE: ~2 = 1200.0000, , ~25/19 = 475.5569


Optimal GPV sequence: {{Val list| 53, 217, 270, 487, 757g }}
{{Optimal ET sequence|legend=0| 53, 217, 270 }}


Badness: 0.013850
Badness (Smith): 0.00704


=== Semivulture ===
=== Semivulture ===
Line 92: Line 104:
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 tunings:
* CTE: ~99/70 = 600.0000, ~320/243 = 475.5523
* POTE: ~99/70 = 600.0000, ~320/243 = 475.5496


Optimal GPV sequence: {{Val list| 106, 164, 270, 916, 1186, 1456 }}
{{Optimal ET sequence|legend=0| 106, 164, 270, 916, 1186, 1456 }}


Badness: 0.040799
Badness (Smith): 0.040799


==== 13-limit ====
==== 13-limit ====
Line 107: Line 121:
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 GPV sequence: {{Val list| 106, 164, 270 }}
 
Badness: 0.035458
 
== Buzzard ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1728/1715, 5120/5103
 
[[Mapping]]: [{{val| 1 0 -6 4 }}, {{val| 0 4 21 -3 }}]
 
{{Multival|legend=1| 4 21 -3 24 -16 -66 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/16 = 475.636
 
{{Val list|legend=1| 5, 43c, 48, 53, 111, 164d, 275d }}
 
[[Badness]]: 0.047963
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 540/539, 5120/5103
 
Mapping: [{{val| 1 0 -6 4 -12 }}, {{val| 0 4 21 -3 39 }}]
 
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.700
 
Optimal GPV sequence: {{Val list| 53, 58, 111, 280cd, 391cd }}
 
Badness: 0.034484
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
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 }}]


Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.697
Optimal tunings:
* CTE: ~99/70 = 600.0000, ~320/243 = 475.5540
* POTE: ~99/70 = 600.0000, ~320/243 = 475.553


Optimal GPV sequence: {{Val list| 53, 58, 111, 280cdf, 391cdf }}
{{Optimal ET sequence|legend=0| 106, 164, 270 }}


Badness: 0.018842
Badness (Smith): 0.035458
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
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 }}]
 
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.692
 
Optimal GPV sequence: {{Val list| 53, 58, 111, 321cdfg }}
 
Badness: 0.018403
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
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 }}]
 
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.679
 
Optimal GPV sequence: {{Val list| 53, 58h, 111 }}
 
Badness: 0.015649
 
=== Buteo ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 385/384, 2200/2187
 
Mapping: [{{val| 1 0 -6 4 9 }}, {{val| 0 4 21 -3 -14 }}]
 
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.436
 
Optimal GPV sequence: {{Val list| 5, 48, 53 }}
 
Badness: 0.060238
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
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 }}]
 
Optimal tuning (POTE): ~2 = 1\1, ~21/16 = 475.464
 
Optimal GPV sequence: {{Val list| 5, 48f, 53 }}
 
Badness: 0.039854


== Condor ==
== Condor ==
Line 213: Line 136:
[[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 }}


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


{{Val list|legend=1| 58, 159, 217 }}
{{Optimal ET sequence|legend=1| 58, 159, 217 }}


[[Badness]]: 0.154715
[[Badness]]: 0.154715
Line 228: Line 149:
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


Optimal GPV sequence: {{Val list| 58, 101cd, 159, 217 }}
{{Optimal ET sequence|legend=1| 58, 101cd, 159, 217 }}


Badness: 0.048401
Badness: 0.048401
Line 241: Line 162:
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


Optimal GPV sequence: {{Val list| 58, 159, 217 }}
{{Optimal ET sequence|legend=1| 58, 159, 217 }}


Badness: 0.025469
Badness: 0.025469
Line 254: Line 175:
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


Optimal GPV sequence: {{Val list| 58, 159, 217 }}
{{Optimal ET sequence|legend=1| 58, 159, 217 }}


Badness: 0.021984
Badness: 0.021984
Line 267: Line 188:
[[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


{{Multival|legend=1|16 84 46 96 28 -129}}
: mapping generators: ~177147/125440, ~28/27


[[Optimal tuning]] ([[POTE]]): ~177147/125440 = 1\2, ~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 }}
{{Optimal ET sequence|legend=1| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}


[[Badness]]: 0.059498
[[Badness]]: 0.059498
Line 284: Line 203:
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


Optimal GPV sequence: {{Val list| 58, 154ce, 212, 270 }}
{{Optimal ET sequence|legend=1| 58, 154ce, 212, 270 }}


Badness: 0.024885
Badness: 0.024885
Line 297: Line 216:
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


Optimal GPV sequence: {{Val list| 58, 154cef, 212, 270 }}
{{Optimal ET sequence|legend=1| 58, 154cef, 212, 270 }}


Badness: 0.016282
Badness: 0.016282
Line 310: Line 229:
[[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}}


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


{{Val list|legend=1| 5, 207c, 212, 429 }}
{{Optimal ET sequence|legend=1| 5, 207c, 212, 429 }}


[[Badness]]: 0.210964
[[Badness]]: 0.210964
Line 325: Line 242:
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


Optimal GPV sequence: {{Val list| 212, 429 }}
{{Optimal ET sequence|legend=1| 212, 429 }}


Badness: 0.079694
Badness: 0.079694
Line 338: Line 255:
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


Optimal GPV sequence: {{Val list| 212, 217, 429 }}
{{Optimal ET sequence|legend=1| 212, 217, 429 }}


Badness: 0.043787
Badness: 0.043787


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Vulture family| ]] <!-- main article -->
[[Category:Vulture family| ]] <!-- main article -->
[[Category:Vulture| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 00:36, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The vulture family of temperaments tempers out the vulture comma (monzo: [24 -21 4⟩, ratio: 10 485 760 000 / 10 460 353 203), a small 5-limit comma of 4.2 cents.

Temperaments discussed elsewhere include terture and buzzard. Considered below are septimal vulture, condor, eagle, and turkey.

Vulture

The generator of the vulture temperament is a grave fourth of 320/243, that is, a perfect fourth minus a syntonic comma. Four of these make a perfect twelfth. Its ploidacot is alpha-tetracot. It is a member of the syntonic–diatonic equivalence continuum with n = 4, so it equates a Pythagorean limma with a stack of four syntonic commas. It is also in the schismic–Mercator equivalence continuum with n = 4, so unless 53edo is used as a tuning, the schisma is always observed.

Subgroup: 2.3.5

Comma list: 10485760000/10460353203

Mapping: [⟨1 0 -6], ⟨0 4 21]]

mapping generators: ~2, ~320/243

Optimal tunings:

  • CTE: ~2 = 1200.000, ~320/243 = 475.5351
error map: ⟨0.0000 +0.1855 -0.0758]
  • POTE: ~2 = 1200.000, ~320/243 = 475.5426
error map: ⟨0.0000 +0.2154 +0.0811]

Optimal ET sequence: 53, 164, 217, 270, 323, 2531, 2854b, 3177b, …, 4469b

Badness:

  • Smith: 0.041431
  • Dirichlet: 0.972

Septimal vulture

Septimal vulture can be described as the 53 & 270 microtemperament, tempering out the ragisma, 4375/4374 and the garischisma, 33554432/33480783 ([25 -14 0 -1⟩) aside from the vulture comma. 270edo is a good tuning for this temperament, with generator 107\270. The harmonic 7 is found at -14 fifths or (-14) × 4 = -56 generator steps, so that the smallest mos scale that includes it is the 58-note one, though for larger scope of harmony, you could try the 111- or 164-note one. For a much simpler mapping of 7 at the cost of higher error, you could try buzzard.

It can be extended to the 11-limit by identifying a stack of four 5/4's as 11/9, tempering out 5632/5625, and to the 13-limit by identifying the hemitwelfth as 26/15, tempering out 676/675. Furthermore, the generator of vulture is very close to 25/19; a stack of three generator steps octave-reduced thus represents its fifth complement, 57/50. This corresponds to tempering out 1216/1215 with the effect of equating the schisma with 513/512 and 361/360 in addition to many 11- and 13-limit commas. 270edo remains an excellent tuning in all cases.

Subgroup: 2.3.5.7

Comma list: 4375/4374, 33554432/33480783

Mapping: [⟨1 0 -6 25], ⟨0 4 21 -56]]

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~320/243 = 475.5528
error map: ⟨0.0000 +0.2561 +0.2945 +0.2188]
  • POTE: ~2 = 1200.0000, ~320/243 = 475.5511
error map: ⟨0.0000 +0.2495 +0.2601 +0.3106]

Optimal ET sequence: 53, 164, 217, 270, 593, 863, 1133

Badness (Smith): 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]]

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~320/243 = 475.5558
  • POTE: ~2 = 1200.0000, ~320/243 = 475.5567

Optimal ET sequence: 53, 217, 270, 2107c, 2377bc

Badness (Smith): 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]]

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~320/243 = 475.5566
  • POTE: ~2 = 1200.0000, ~320/243 = 475.5572

Optimal ET sequence: 53, 217, 270

Badness (Smith): 0.018758

2.3.5.7.11.13.19 subgroup

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728

Mapping: [⟨1 0 -6 25 -33 -7 -12], ⟨0 4 21 -56 92 27 41]]

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~25/19 = 475.5561
  • CWE: ~2 = 1200.0000, , ~25/19 = 475.5569

Optimal ET sequence: 53, 217, 270

Badness (Smith): 0.00704

Semivulture

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4375/4374, 33554432/33480783

Mapping: [⟨2 0 -12 50 41], ⟨0 4 21 -56 -43]]

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

Optimal tunings:

  • CTE: ~99/70 = 600.0000, ~320/243 = 475.5523
  • POTE: ~99/70 = 600.0000, ~320/243 = 475.5496

Optimal ET sequence: 106, 164, 270, 916, 1186, 1456

Badness (Smith): 0.040799

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374

Mapping: [⟨2 0 -12 50 41 -14], ⟨0 4 21 -56 -43 27]]

Optimal tunings:

  • CTE: ~99/70 = 600.0000, ~320/243 = 475.5540
  • POTE: ~99/70 = 600.0000, ~320/243 = 475.553

Optimal ET sequence: 106, 164, 270

Badness (Smith): 0.035458

Condor

Subgroup: 2.3.5.7

Comma list: 10976/10935, 40353607/40000000

Mapping: [⟨1 8 36 29], ⟨0 -12 -63 -49]]

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

Optimal ET sequence: 58, 159, 217

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]]

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

Optimal ET sequence: 58, 101cd, 159, 217

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]]

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

Optimal ET sequence: 58, 159, 217

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]]

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

Optimal ET sequence: 58, 159, 217

Badness: 0.021984

Eagle

Subgroup: 2.3.5.7

Comma list: 2401/2400, 10485760000/10460353203

Mapping: [⟨2 4 9 8], ⟨0 -8 -42 -23]]

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

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

Optimal ET sequence: 58, 154c, 212, 270, 752, 1022, 1292, 2854b

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]]

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

Optimal ET sequence: 58, 154ce, 212, 270

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]]

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

Optimal ET sequence: 58, 154cef, 212, 270

Badness: 0.016282

Turkey

Subgroup: 2.3.5.7

Comma list: 4802000/4782969, 5250987/5242880

Mapping: [⟨1 8 36 0], ⟨0 -16 -84 7]]

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

Optimal ET sequence: 5, 207c, 212, 429

Badness: 0.210964

11-limit

Subgroup: 2.3.5.7.11

Comma list: 19712/19683, 42875/42768, 160083/160000

Mapping: [⟨1 8 36 0 64], ⟨0 -16 -84 7 -151]]

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

Optimal ET sequence: 212, 429

Badness: 0.079694

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104

Mapping: [⟨1 8 36 0 64 47], ⟨0 -16 -84 7 -151 -108]]

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

Optimal ET sequence: 212, 217, 429

Badness: 0.043787

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