Vulture family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5351{{c}}
* [[WE]]: ~2 = 1199.9430{{c}}, ~320/243 = 475.5200{{c}}
: [[error map]]: {{val| -0.057 +0.125 -0.051 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5396{{c}}
: error map: {{val| 0.000 +0.203 +0.018 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5351{{c}}
: [[error map]]: {{val| 0.0000 +0.1855 -0.0758 }}
: [[error map]]: {{val| 0.0000 +0.1855 -0.0758 }}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5426{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5426{{c}}
: error map: {{val| 0.0000 +0.2154 +0.0811 }}
: error map: {{val| 0.0000 +0.2154 +0.0811 }} -->


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


[[Badness]]:
[[Badness]] (Sintel): 0.972
* Smith: 0.041431
* Sintel: 0.972


== Septimal vulture ==
== Septimal vulture ==
Line 45: Line 47:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5528{{c}}
* [[WE]]: ~2 = 1199.9050{{c}}, ~320/243 = 475.5135{{c}}
: [[error map]]: {{val| -0.095 +0.099 +0.039 +0.044 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5515{{c}}
: error map: {{val| 0.000 +0.251 +0.267 +0.292 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5528{{c}}
: [[error map]]: {{val| 0.0000 +0.2561 +0.2945 +0.2188 }}
: [[error map]]: {{val| 0.0000 +0.2561 +0.2945 +0.2188 }}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5511{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~320/243 = 475.5511{{c}}
: error map: {{val| 0.0000 +0.2495 +0.2601 +0.3106 }}
: error map: {{val| 0.0000 +0.2495 +0.2601 +0.3106 }} -->


{{Optimal ET sequence|legend=1| 53, 164, 217, 270, 593, 863, 1133 }}
{{Optimal ET sequence|legend=1| 53, 164, 217, 270, 593, 863, 1133, 1996d }}


[[Badness]] (Smith): 0.036985
[[Badness]] (Sintel): 0.936


=== 11-limit ===
=== 11-limit ===
Line 62: Line 68:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5558{{c}}
* WE: ~2 = 1199.9392{{c}}, ~320/243 = 475.5326{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5567{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5655{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5558{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5567{{c}} -->


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


Badness (Smith): 0.031907
Badness (Sintel): 1.05


==== 13-limit ====
==== 13-limit ====
Line 77: Line 85:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5566{{c}}
* WE: ~2 = 1199.9695{{c}}, ~320/243 = 475.5451{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5572{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5571{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5566{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~320/243 = 475.5572{{c}} -->


{{Optimal ET sequence|legend=0| 53, 217, 270 }}
{{Optimal ET sequence|legend=0| 53, 217, 270 }}


Badness (Smith): 0.018758
Badness (Sintel): 0.775


==== 2.3.5.7.11.13.19 subgroup ====
==== 2.3.5.7.11.13.19 subgroup ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.19


Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728
Comma list: 676/675, 1001/1000, 1216/1215, 1540/1539, 1729/1728
Line 92: Line 102:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5561{{c}}
* WE: ~2 = 1199.9636{{c}}, ~25/19 = 475.5426{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5569{{c}}
<!-- * CTE: ~2 = 1200.0000{{c}}, ~25/19 = 475.5561{{c}} -->


{{Optimal ET sequence|legend=0| 53, 217, 270 }}
{{Optimal ET sequence|legend=0| 53, 217, 270 }}


Badness (Smith): 0.00704
Badness (Sintel): 0.579


=== Semivulture ===
=== Semivulture ===
Line 108: Line 119:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5523{{c}}
* WE: ~99/70 = 599.9594{{c}}, ~320/243 = 475.5174{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5496{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5501{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5523{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5496{{c}} -->


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


Badness (Smith): 0.040799
Badness (Sintel): 1.35


==== 13-limit ====
==== 13-limit ====
Line 123: Line 136:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5540{{c}}
* WE: ~99/70 = 599.9859{{c}}, ~320/243 = 475.5423{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.553{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5536{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.5540{{c}}
* POTE: ~99/70 = 600.0000{{c}}, ~320/243 = 475.553{{c}} -->


{{Optimal ET sequence|legend=0| 106, 164, 270 }}
{{Optimal ET sequence|legend=0| 106, 164, 270 }}


Badness (Smith): 0.035458
Badness (Sintel): 1.47


== Condor ==
== Condor ==
Line 135: Line 150:
[[Comma list]]: 10976/10935, 40353607/40000000
[[Comma list]]: 10976/10935, 40353607/40000000


{{Mapping|legend=1| 1 8 36 29 | 0 -12 -63 -49 }}
{{Mapping|legend=1| 1 -4 -27 -20 | 0 12 63 49 }}
: mapping generators: ~2, ~112/81


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~81/56 = 641.4791{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0142{{c}}, ~112/81 = 558.5276{{c}}
: [[error map]]: {{val| +0.014 +0.319 +0.539 -1.260 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~112/81 = 558.5212{{c}}
: error map: {{val| 0.000 +0.300 +0.523 -1.287 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~112/81 = 558.5209{{c}} -->


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


[[Badness]] (Smith): 0.154715
[[Badness]] (Sintel): 3.92


=== 11-limit ===
=== 11-limit ===
Line 148: Line 169:
Comma list: 441/440, 4000/3993, 10976/10935
Comma list: 441/440, 4000/3993, 10976/10935


Mapping: {{mapping| 1 8 36 29 35 | 0 -12 -63 -49 -59 }}
Mapping: {{mapping| 1 -4 -27 -20 -24 | 0 12 63 49 59 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, 81/56 = 641.4822{{c}}
Optimal tunings:
* WE: ~2 = 1199.9730{{c}}, ~112/81 = 558.5052{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5173{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5178{{c}} -->


{{Optimal ET sequence|legend=0| 58, 101cd, 159, 217 }}
{{Optimal ET sequence|legend=0| 58, 101cd, 159, 217, 376d }}


Badness (Smith): 0.048401
Badness (Sintel): 1.60


=== 13-limit ===
=== 13-limit ===
Line 161: Line 185:
Comma list: 364/363, 441/440, 676/675, 10976/10935
Comma list: 364/363, 441/440, 676/675, 10976/10935


Mapping: {{mapping| 1 8 36 29 35 47 | 0 -12 -63 -49 -59 -81 }}
Mapping: {{mapping| 1 -4 -27 -20 -24 -34 | 0 12 63 49 59 81 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~81/56 = 641.4797{{c}}
Optimal tunings:
* WE: ~2 = 1199.9649{{c}}, ~112/81 = 558.5040{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5197{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~81/56 = 641.4797{{c}} -->


{{Optimal ET sequence|legend=0| 58, 159, 217 }}
{{Optimal ET sequence|legend=0| 58, 159, 217 }}


Badness (Smith): 0.025469
Badness (Sintel): 1.05


=== 17-limit ===
=== 17-limit ===
Line 174: Line 201:
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: {{mapping| 1 8 36 29 35 47 -5 | 0 -12 -63 -49 -59 -81 17 }}
Mapping: {{mapping| 1 -4 -27 -20 -24 -34 12 | 0 12 63 49 59 81 -17 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~81/56 = 641.4794{{c}}
Optimal tunings:
* WE: ~2 = 1199.9594{{c}}, ~112/81 = 558.5017{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5202{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~112/81 = 558.5206{{c}} -->


{{Optimal ET sequence|legend=0| 58, 159, 217 }}
{{Optimal ET sequence|legend=0| 58, 159, 217 }}


Badness (Smith): 0.021984
Badness (Sintel): 1.12


== Eagle ==
== Eagle ==
Line 188: Line 218:


{{Mapping|legend=1| 2 4 9 8 | 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


[[Optimal tuning]] ([[POTE]]): ~177147/125440 = 600.000{{c}}, ~28/27 = 62.229{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~177147/125440 = 599.9818{{c}}, ~28/27 = 62.2266{{c}}
: [[error map]]: {{val| -0.036 +0.159 +0.004 -0.184 }}
* [[CWE]]: ~177147/125440 = 600.0000{{c}}, ~28/27 = 62.2295{{c}}
: error map: {{val| 0.000 +0.209 +0.046 -0.105 }}
<!-- * [[POTE]]: ~177147/125440 = 600.000{{c}}, ~28/27 = 62.229{{c}} -->


{{Optimal ET sequence|legend=1| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}
{{Optimal ET sequence|legend=1| 58, 154c, 212, 270, 752, 1022, 1292, 2854b }}


[[Badness]] (Smith): 0.059498
[[Badness]] (Sintel): 1.51


=== 11-limit ===
=== 11-limit ===
Line 204: Line 238:
Mapping: {{mapping| 2 4 9 8 12 | 0 -8 -42 -23 -49 }}
Mapping: {{mapping| 2 4 9 8 12 | 0 -8 -42 -23 -49 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~28/27 = 62.224{{c}}
Optimal tunings:
* WE: ~99/70 = 599.9796{{c}} ~28/27 = 62.2218{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2251{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~28/27 = 62.224{{c}} -->


{{Optimal ET sequence|legend=0| 58, 154ce, 212, 270 }}
{{Optimal ET sequence|legend=0| 58, 154ce, 212, 270 }}


Badness (Smith): 0.024885
Badness (Sintel): 0.823


=== 13-limit ===
=== 13-limit ===
Line 217: Line 254:
Mapping: {{mapping| 2 4 9 8 12 13 | 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 = 600.000{{c}}, ~28/27 = 62.220{{c}}
Optimal tunings:
* WE: ~99/70 = 599.9763{{c}} ~28/27 = 62.2174{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.2211{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~28/27 = 62.220{{c}} -->


{{Optimal ET sequence|legend=0| 58, 154cef, 212, 270 }}
{{Optimal ET sequence|legend=0| 58, 154cef, 212, 270 }}


Badness (Smith): 0.016282
Badness (Sintel): 0.673


== Turkey ==
== Turkey ==
Line 228: Line 268:
[[Comma list]]: 4802000/4782969, 5250987/5242880
[[Comma list]]: 4802000/4782969, 5250987/5242880


{{Mapping|legend=1| 1 8 36 0 | 0 -16 -84 7 }}
{{Mapping|legend=1| 1 -8 -48 7 | 0 16 84 -7 }}
: mapping generators: ~2, ~3592/1715


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~1715/1296 = 481.120{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1147{{c}}, ~3592/1715 = 718.9483{{c}}
: [[error map]]: {{val| +0.115 +0.300 -0.161 -0.661 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3592/1715 = 718.8806{{c}}
: error map: {{val| 0.000 +0.134 -0.345 -0.990 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~1715/1296 = 481.120{{c}} -->


{{Optimal ET sequence|legend=1| 5, 207c, 212, 429 }}
{{Optimal ET sequence|legend=1| 212, 429, 1070d }}


[[Badness]] (Smith): 0.210964
[[Badness]] (Sintel): 5.34


=== 11-limit ===
=== 11-limit ===
Line 241: Line 287:
Comma list: 19712/19683, 42875/42768, 160083/160000
Comma list: 19712/19683, 42875/42768, 160083/160000


Mapping: {{mapping| 1 8 36 0 64 | 0 -16 -84 7 -151 }}
Mapping: {{mapping| 1 -8 -48 7 -87 | 0 16 84 -7 151 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~33/25 = 481.120{{c}}
Optimal tunings:
* WE: ~2 = 1200.1131{{c}} ~50/33 = 718.9478{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~50/33 = 718.8808{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~50/33 = 728.880{{c}} -->


{{Optimal ET sequence|legend=0| 212, 429 }}
{{Optimal ET sequence|legend=0| 212, 429 }}


Badness (Smith): 0.079694
Badness (Sintel): 2.63


=== 13-limit ===
=== 13-limit ===
Line 254: Line 303:
Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104
Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104


Mapping: {{mapping| 1 8 36 0 64 47 | 0 -16 -84 7 -151 -108 }}
Mapping: {{mapping| 1 -8 -48 7 -87 -61 | 0 16 84 -7 151 108 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~33/25 = 481.118{{c}}
Optimal tunings:
* WE: ~2 = 1200.1324{{c}} ~50/33 = 718.9608{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~50/33 = 718.8825{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~50/33 = 718.882{{c}} -->


{{Optimal ET sequence|legend=0| 212, 217, 429 }}
{{Optimal ET sequence|legend=0| 212, 217, 429 }}


Badness (Smith): 0.043787
Badness (Sintel): 1.81


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 14:17, 28 October 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 that is the amount by which a stack of four syntonic commas falls short of the 256/243 Pythagorean limma. As their defining feature, vulture temperaments split the interval 3/1 into four segments (identified in the 5-limit as 320/243).

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:

  • WE: ~2 = 1199.9430 ¢, ~320/243 = 475.5200 ¢
error map: ⟨-0.057 +0.125 -0.051]
  • CWE: ~2 = 1200.0000 ¢, ~320/243 = 475.5396 ¢
error map: ⟨0.000 +0.203 +0.018]

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

Badness (Sintel): 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:

  • WE: ~2 = 1199.9050 ¢, ~320/243 = 475.5135 ¢
error map: ⟨-0.095 +0.099 +0.039 +0.044]
  • CWE: ~2 = 1200.0000 ¢, ~320/243 = 475.5515 ¢
error map: ⟨0.000 +0.251 +0.267 +0.292]

Optimal ET sequence: 53, 164, 217, 270, 593, 863, 1133, 1996d

Badness (Sintel): 0.936

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:

  • WE: ~2 = 1199.9392 ¢, ~320/243 = 475.5326 ¢
  • CWE: ~2 = 1200.0000 ¢, ~320/243 = 475.5655 ¢

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

Badness (Sintel): 1.05

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:

  • WE: ~2 = 1199.9695 ¢, ~320/243 = 475.5451 ¢
  • CWE: ~2 = 1200.0000 ¢, ~320/243 = 475.5571 ¢

Optimal ET sequence: 53, 217, 270

Badness (Sintel): 0.775

2.3.5.7.11.13.19 subgroup

Subgroup: 2.3.5.7.11.13.19

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:

  • WE: ~2 = 1199.9636 ¢, ~25/19 = 475.5426 ¢
  • CWE: ~2 = 1200.0000 ¢, ~25/19 = 475.5569 ¢

Optimal ET sequence: 53, 217, 270

Badness (Sintel): 0.579

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:

  • WE: ~99/70 = 599.9594 ¢, ~320/243 = 475.5174 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~320/243 = 475.5501 ¢

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

Badness (Sintel): 1.35

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:

  • WE: ~99/70 = 599.9859 ¢, ~320/243 = 475.5423 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~320/243 = 475.5536 ¢

Optimal ET sequence: 106, 164, 270

Badness (Sintel): 1.47

Condor

Subgroup: 2.3.5.7

Comma list: 10976/10935, 40353607/40000000

Mapping: [⟨1 -4 -27 -20], ⟨0 12 63 49]]

mapping generators: ~2, ~112/81

Optimal tunings:

  • WE: ~2 = 1200.0142 ¢, ~112/81 = 558.5276 ¢
error map: ⟨+0.014 +0.319 +0.539 -1.260]
  • CWE: ~2 = 1200.0000 ¢, ~112/81 = 558.5212 ¢
error map: ⟨0.000 +0.300 +0.523 -1.287]

Optimal ET sequence: 58, 159, 217

Badness (Sintel): 3.92

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 4000/3993, 10976/10935

Mapping: [⟨1 -4 -27 -20 -24], ⟨0 12 63 49 59]]

Optimal tunings:

  • WE: ~2 = 1199.9730 ¢, ~112/81 = 558.5052 ¢
  • CWE: ~2 = 1200.0000 ¢, ~112/81 = 558.5173 ¢

Optimal ET sequence: 58, 101cd, 159, 217, 376d

Badness (Sintel): 1.60

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440, 676/675, 10976/10935

Mapping: [⟨1 -4 -27 -20 -24 -34], ⟨0 12 63 49 59 81]]

Optimal tunings:

  • WE: ~2 = 1199.9649 ¢, ~112/81 = 558.5040 ¢
  • CWE: ~2 = 1200.0000 ¢, ~112/81 = 558.5197 ¢

Optimal ET sequence: 58, 159, 217

Badness (Sintel): 1.05

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 364/363, 441/440, 595/594, 676/675, 8624/8619

Mapping: [⟨1 -4 -27 -20 -24 -34 12], ⟨0 12 63 49 59 81 -17]]

Optimal tunings:

  • WE: ~2 = 1199.9594 ¢, ~112/81 = 558.5017 ¢
  • CWE: ~2 = 1200.0000 ¢, ~112/81 = 558.5202 ¢

Optimal ET sequence: 58, 159, 217

Badness (Sintel): 1.12

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 tunings:

  • WE: ~177147/125440 = 599.9818 ¢, ~28/27 = 62.2266 ¢
error map: ⟨-0.036 +0.159 +0.004 -0.184]
  • CWE: ~177147/125440 = 600.0000 ¢, ~28/27 = 62.2295 ¢
error map: ⟨0.000 +0.209 +0.046 -0.105]

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

Badness (Sintel): 1.51

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 tunings:

  • WE: ~99/70 = 599.9796 ¢ ~28/27 = 62.2218 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~28/27 = 62.2251 ¢

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

Badness (Sintel): 0.823

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 tunings:

  • WE: ~99/70 = 599.9763 ¢ ~28/27 = 62.2174 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~28/27 = 62.2211 ¢

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

Badness (Sintel): 0.673

Turkey

Subgroup: 2.3.5.7

Comma list: 4802000/4782969, 5250987/5242880

Mapping: [⟨1 -8 -48 7], ⟨0 16 84 -7]]

mapping generators: ~2, ~3592/1715

Optimal tunings:

  • WE: ~2 = 1200.1147 ¢, ~3592/1715 = 718.9483 ¢
error map: ⟨+0.115 +0.300 -0.161 -0.661]
  • CWE: ~2 = 1200.0000 ¢, ~3592/1715 = 718.8806 ¢
error map: ⟨0.000 +0.134 -0.345 -0.990]

Optimal ET sequence: 212, 429, 1070d

Badness (Sintel): 5.34

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -8 -48 7 -87], ⟨0 16 84 -7 151]]

Optimal tunings:

  • WE: ~2 = 1200.1131 ¢ ~50/33 = 718.9478 ¢
  • CWE: ~2 = 1200.0000 ¢, ~50/33 = 718.8808 ¢

Optimal ET sequence: 212, 429

Badness (Sintel): 2.63

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -8 -48 7 -87 -61], ⟨0 16 84 -7 151 108]]

Optimal tunings:

  • WE: ~2 = 1200.1324 ¢ ~50/33 = 718.9608 ¢
  • CWE: ~2 = 1200.0000 ¢, ~50/33 = 718.8825 ¢

Optimal ET sequence: 212, 217, 429

Badness (Sintel): 1.81

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