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The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo| -2 13 -8 }}.  
{{Technical data page}}
The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo| -2 13 -8 }}. The canonical extension to the 7-limit is by interpreting the generator as a slightly flattened [[~]][[28/27]] so that a flat [[~]][[6/5]] is found at 5 generators, corresponding to tempering [[126/125]], the [[octaphore]] and the [[hemimage comma]].


= Five-limit unicorn =
== Unicorn ==
Subgroup: 2.3.5
By noticing that the generator is very close to [[28/27]] we find the extension to the 7-limit by tempering the [[octaphore]] (which finds [[~]][[9/7]] at 7 gens and [[~]][[4/3]] at 8 gens, hence its name) and [[126/125]] (finding [[~]][[6/5]] at 5 gens). From this we can observe that the most natural extension is by equating adjacent [[superparticular interval]]s, by tempering the [[square-particular]]s between them, leading to its [[S-expression]]-based comma list of {[[676/675|S26]], [[729/728|S27]], [[784/783|S28]], [[841/840|S29]]}, to which experimentation shows we can find a reasonable mapping for prime 43 at -11 gens while all other primes require either quite complex mappings (being significantly positive rather than negative) or require high error or both.
 
[[Subgroup]]: 2.3.5


[[Comma list]]: 1594323/1562500
[[Comma list]]: 1594323/1562500


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -8 -13 }}]
{{Mapping|legend=1| 1 2 3 | 0 -8 -13 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0889¢, ~250/243 =  62.4623¢
* [[CWE]]: ~2 = 1200.0000¢, ~250/243 = 62.4494¢
 
{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}
 
[[Badness]] (Sintel): 3.530
 
== Septimal unicorn ==
{{See also| Octaphore }}
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: [[126/125]], [[10976/10935]]
 
{{Mapping|legend=1| 1 2 3 4 | 0 -8 -13 -23 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6949¢, ~28/27 = 62.2621¢
* [[CWE]]: ~2 = 1200.0000¢, ~28/27 = 62.2996¢
 
{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c, 212c }}
 
[[Badness]] (Sintel): 1.035
 
=== 2.3.5.7.13 subgroup ===
[[Subgroup]]: 2.3.5.7.13
 
[[Comma list]]: [[126/125]], [[196/195]], [[676/675]]
 
{{Mapping|legend=1| 1 2 3 4 5 | 0 -8 -13 -23 -25 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7013¢, ~26/25 = 62.2785¢
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3151¢
 
{{Optimal ET sequence|legend=1| 19, 39df, 58, 77, 212cf }}
 
[[Badness]] (Sintel): 0.590
 
==== 2.3.5.7.13.29 subgroup ====
[[Subgroup]]: 2.3.5.7.13.29
 
[[Comma list]]: [[126/125]], [[196/195]], [[261/260]], [[377/375]]
 
{{Mapping|legend=1| 1 2 3 4 5 6 | 0 -8 -13 -23 -25 -22 }}


[[POTE generator]]: ~250/243 = 62.458
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.7715¢, ~26/25 = 62.2860¢
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3141¢


{{Val list|legend=1| 19, 58, 77, 96, 173, 269 }}
{{Optimal ET sequence|legend=1| 19, 39dfj, 58, 77, 212cf }}


[[Badness]]: 0.150487
[[Badness]] (Sintel): 0.487


= Septimal unicorn =
==== 2.3.5.7.13.29.43 subgroup ====
Subgroup: 2.3.5.7
A notable tuning of unicorn not appearing in the [[optimal ET sequence]] here is [[96edo]] using the 96d val (with a 963[[cent|¢]] [[~]][[7/4]] similar to that of [[meanpop]]), an alternative to [[77edo]] that sacrifices the accuracy of prime 7 in favour of a more accurate [[5/4]] and [[43/32]].


[[Comma list]]: 126/125, 10976/10935
[[Subgroup]]: 2.3.5.7.13.29.43


[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -8 -13 -23 }}]
[[Comma list]]: [[126/125]], [[196/195]], [[216/215]], [[261/260]], [[377/375]]


{{Multival|legend=1| 8 13 23 2 14 17 }}
{{Mapping|legend=1| 1 2 3 4 5 6 6 | 0 -8 -13 -23 -25 -22 -11 }}


[[POTE generator]]: ~28/27 = 62.278
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.6269¢, ~26/25 = 62.2584¢
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3008¢


{{Val list|legend=1| 19, 39d, 58, 77, 135c }}
{{Optimal ET sequence|legend=1| 19, 39dfj, 58, 77, 135c, 212cfn }}


[[Badness]]: 0.040913
[[Badness]] (Sintel): 0.514


== Alicorn ==
=== Alicorn ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 126/125, 540/539, 896/891
Comma list: 126/125, 540/539, 896/891


Mapping: [{{val| 1 2 3 4 3 }}, {{val| 0 -8 -13 -23 9 }}]
Mapping: {{mapping| 1 2 3 4 3 | 0 -8 -13 -23 9 }}


POTE generator: ~28/27 = 62.101
Optimal tunings:  
* WE: ~2 = 1198.6510¢, ~28/27 = 62.0316¢
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.1435¢


Vals: {{Val list| 19, 39d, 58 }}
{{Optimal ET sequence|legend=0| 19, 39d, 58 }}


Badness: 0.039156
Badness (Sintel): 1.294


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 126/125, 144/143, 196/195, 676/675
Comma list: 126/125, 144/143, 196/195, 676/675


Mapping: [{{val| 1 2 3 4 3 5 }}, {{val| 0 -8 -13 -23 9 -25 }}]
Mapping: {{mapping| 1 2 3 4 3 5 | 0 -8 -13 -23 9 -25 }}


POTE generator: ~28/27 = 62.119
Optimal tunings:  
* WE: ~2 = 1198.6298¢, ~26/25 = 62.0480¢
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.1636¢


Vals: {{Val list| 19, 39df, 58 }}
{{Optimal ET sequence|legend=0| 19, 39df, 58 }}


Badness: 0.023667
Badness (Sintel): 0.978


== Camahueto ==
=== Camahueto ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 126/125, 385/384, 10976/10935
Comma list: 126/125, 385/384, 10976/10935


Mapping: [{{val| 1 2 3 4 2 }}, {{val| 0 -8 -13 -23 28 }}]
Mapping: {{mapping| 1 2 3 4 2 | 0 -8 -13 -23 28 }}


POTE generator: ~28/27 = 62.431
Optimal tunings:  
* WE: ~2 = 1200.5186¢, ~28/27 = 62.4576¢
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.4252¢


Vals: {{Val list| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}


Badness: 0.065940
Badness (Sintel): 2.180


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 126/125, 196/195, 385/384, 676/675
Comma list: 126/125, 196/195, 385/384, 676/675


Mapping: [{{val| 1 2 3 4 2 5 }}, {{val| 0 -8 -13 -23 28 -25 }}]
Mapping: {{mapping| 1 2 3 4 2 5 | 0 -8 -13 -23 28 -25 }}


POTE generator: ~28/27 = 62.434
Optimal tunings:  
* WE: ~2 = 1200.5004¢, ~26/25 = 62.4603¢
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.4277¢


Vals: {{Val list| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}


Badness: 0.036155
Badness (Sintel): 1.494


== Qilin ==
=== Qilin ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 126/125, 176/175, 10976/10935
Comma list: 126/125, 176/175, 10976/10935


Mapping: [{{val| 1 2 3 4 6 }}, {{val| 0 -8 -13 -23 -49 }}]
Mapping: {{mapping| 1 2 3 4 6 | 0 -8 -13 -23 -49 }}


POTE generator: ~28/27 = 62.196
Optimal tunings:  
* WE: ~2 = 1199.3865¢, ~28/27 = 62.1645¢
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.2199¢


Vals: {{Val list| 58, 77, 135c, 193c, 328cc }}
{{Optimal ET sequence|legend=0| 58, 77, 135c, 193c, 328cc }}


Badness: 0.041426
Badness (Sintel): 1.370


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 126/125, 176/175, 196/195, 2200/2197
Comma list: 126/125, 176/175, 196/195, 2200/2197


Mapping: [{{val| 1 2 3 4 6 5 }}, {{val| 0 -8 -13 -23 -49 -25 }}]
Mapping: {{mapping| 1 2 3 4 6 5 | 0 -8 -13 -23 -49 -25 }}


POTE generator: ~28/27 = 62.197
Optimal tunings:  
* WE: ~2 = 1199.2874¢, ~26/25 = 62.1601¢
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.2251¢


Vals: {{Val list| 58, 77, 135c, 193cf, 328ccff }}
{{Optimal ET sequence|legend=0| 58, 77, 135c, 193cf, 328ccff }}


Badness: 0.022842
Badness (Sintel): 0.944


== Monocerus ==
=== Monocerus ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 126/125, 243/242, 5488/5445
Comma list: 126/125, 243/242, 5488/5445


Mapping: [{{val| 2 4 6 8 9 }}, {{val| 0 -8 -13 -23 -20 }}]
Mapping: {{mapping| 2 4 6 8 9 | 0 -8 -13 -23 -20 }}


POTE generator: ~28/27 = 62.292
Optimal tunings:  
* WE: ~99/70 = 599.8223¢, ~28/27 = 62.2737¢
* CWE: ~99/70 = 600.0000¢, ~28/27 = 62.3180¢


Vals: {{Val list| 58, 96d, 154, 212ce, 366cce }}
{{Optimal ET sequence|legend=0| 58, 96d, 154, 212ce, 366cce }}


Badness: 0.052757
Badness (Sintel): 1.744


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 126/125, 196/195, 364/363, 676/675
Comma list: 126/125, 196/195, 243/242, 364/363
 
Mapping: {{mapping| 2 4 6 8 9 10 | 0 -8 -13 -23 -20 -25 }}
 
Optimal tunings:
* WE: ~55/39 = 599.8267¢, ~26/25 = 62.2833¢
* CWE: ~55/39 = 600.0000¢, ~26/25 = 62.3262¢
 
{{Optimal ET sequence|legend=0| 58, 96d, 154, 366ccef }}
 
Badness (Sintel): 1.190
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 126/125, 196/195, 221/220, 243/242, 289/288


Mapping: [{{val| 2 4 6 8 9 10 }}, {{val| 0 -8 -13 -23 -20 -25 }}]
Mapping: {{mapping| 2 4 6 8 9 10 9 | 0 -8 -13 -23 -20 -25 -8 }}


POTE generator: ~28/27 = 62.301
Optimal tunings:  
* WE: ~17/12 = 600.0715¢, ~26/25 = 62.3767¢
* CWE: ~17/12 = 600.0000¢, ~26/25 = 62.3605¢


Vals: {{Val list| 58, 96d, 154, 366ccef }}
{{Optimal ET sequence|legend=0| 58, 96d, 154 }}


Badness: 0.028795
Badness (Sintel): 1.237


= Rhinoceros =
== Rhinoceros ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 4375/4374
[[Comma list]]: 49/48, 4375/4374


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -8 -13 -4 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -8 -13 -4 }}
 
{{Multival|legend=1| 8 13 4 2 -16 -27 }}


[[POTE generator]]: ~21/20 = 62.920
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1203.1031¢, ~21/20 = 63.0830¢
* [[CWE]]: ~2 = 1200.0000¢, ~21/20 = 62.6687¢


{{Val list|legend=1| 1c, 19 }}
{{Optimal ET sequence|legend=1| 1c, 19 }}


[[Badness]]: 0.081864
[[Badness]] (Sintel): 2.072


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 100/99, 126/121
Comma list: 49/48, 100/99, 126/121


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -8 -13 -4 -10 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -8 -13 -4 -10 }}


POTE generator: ~21/20 = 62.874
Optimal tunings:  
* WE: ~2 = 1201.1458¢, ~21/20 = 62.9338¢
* CWE: ~2 = 1200.0000¢, ~21/20 = 62.7783¢


Vals: {{Val list| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 19 }}


Badness: 0.059319
Badness (Sintel): 1.961


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 78/77, 100/99, 126/121
Comma list: 49/48, 78/77, 100/99, 126/121


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -8 -13 -4 -10 -6 }}]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -8 -13 -4 -10 -6 }}


POTE generator: ~21/20 = 63.043
Optimal tunings:  
* WE: ~2 = 1202.2047¢, ~21/20 = 63.1591¢
* CWE: ~2 = 1200.0000¢, ~21/20 = 62.8727¢


Vals: {{Val list| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 19 }}


Badness: 0.039343
Badness (Sintel): 1.626


[[Category:Regular temperament theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Unicorn family| ]] <!-- main article -->
[[Category:Unicorn]]
[[Category:Unicorn| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 04:18, 25 April 2026

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 unicorn family tempers out the unicorn comma, 1594323/1562500 = [-2 13 -8⟩. The canonical extension to the 7-limit is by interpreting the generator as a slightly flattened ~28/27 so that a flat ~6/5 is found at 5 generators, corresponding to tempering 126/125, the octaphore and the hemimage comma.

Unicorn

By noticing that the generator is very close to 28/27 we find the extension to the 7-limit by tempering the octaphore (which finds ~9/7 at 7 gens and ~4/3 at 8 gens, hence its name) and 126/125 (finding ~6/5 at 5 gens). From this we can observe that the most natural extension is by equating adjacent superparticular intervals, by tempering the square-particulars between them, leading to its S-expression-based comma list of {S26, S27, S28, S29}, to which experimentation shows we can find a reasonable mapping for prime 43 at -11 gens while all other primes require either quite complex mappings (being significantly positive rather than negative) or require high error or both.

Subgroup: 2.3.5

Comma list: 1594323/1562500

Mapping: [⟨1 2 3], ⟨0 -8 -13]]

Optimal tunings:

  • WE: ~2 = 1200.0889¢, ~250/243 = 62.4623¢
  • CWE: ~2 = 1200.0000¢, ~250/243 = 62.4494¢

Optimal ET sequence: 19, 58, 77, 96, 173, 269

Badness (Sintel): 3.530

Septimal unicorn

See also: Octaphore

Subgroup: 2.3.5.7

Comma list: 126/125, 10976/10935

Mapping: [⟨1 2 3 4], ⟨0 -8 -13 -23]]

Optimal tunings:

  • WE: ~2 = 1199.6949¢, ~28/27 = 62.2621¢
  • CWE: ~2 = 1200.0000¢, ~28/27 = 62.2996¢

Optimal ET sequence: 19, 39d, 58, 77, 135c, 212c

Badness (Sintel): 1.035

2.3.5.7.13 subgroup

Subgroup: 2.3.5.7.13

Comma list: 126/125, 196/195, 676/675

Mapping: [⟨1 2 3 4 5], ⟨0 -8 -13 -23 -25]]

Optimal tunings:

  • WE: ~2 = 1199.7013¢, ~26/25 = 62.2785¢
  • CWE: ~2 = 1200.0000¢, ~26/25 = 62.3151¢

Optimal ET sequence: 19, 39df, 58, 77, 212cf

Badness (Sintel): 0.590

2.3.5.7.13.29 subgroup

Subgroup: 2.3.5.7.13.29

Comma list: 126/125, 196/195, 261/260, 377/375

Mapping: [⟨1 2 3 4 5 6], ⟨0 -8 -13 -23 -25 -22]]

Optimal tunings:

  • WE: ~2 = 1199.7715¢, ~26/25 = 62.2860¢
  • CWE: ~2 = 1200.0000¢, ~26/25 = 62.3141¢

Optimal ET sequence: 19, 39dfj, 58, 77, 212cf

Badness (Sintel): 0.487

2.3.5.7.13.29.43 subgroup

A notable tuning of unicorn not appearing in the optimal ET sequence here is 96edo using the 96d val (with a 963¢ ~7/4 similar to that of meanpop), an alternative to 77edo that sacrifices the accuracy of prime 7 in favour of a more accurate 5/4 and 43/32.

Subgroup: 2.3.5.7.13.29.43

Comma list: 126/125, 196/195, 216/215, 261/260, 377/375

Mapping: [⟨1 2 3 4 5 6 6], ⟨0 -8 -13 -23 -25 -22 -11]]

Optimal tunings:

  • WE: ~2 = 1199.6269¢, ~26/25 = 62.2584¢
  • CWE: ~2 = 1200.0000¢, ~26/25 = 62.3008¢

Optimal ET sequence: 19, 39dfj, 58, 77, 135c, 212cfn

Badness (Sintel): 0.514

Alicorn

Subgroup: 2.3.5.7.11

Comma list: 126/125, 540/539, 896/891

Mapping: [⟨1 2 3 4 3], ⟨0 -8 -13 -23 9]]

Optimal tunings:

  • WE: ~2 = 1198.6510¢, ~28/27 = 62.0316¢
  • CWE: ~2 = 1200.0000¢, ~28/27 = 62.1435¢

Optimal ET sequence: 19, 39d, 58

Badness (Sintel): 1.294

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 144/143, 196/195, 676/675

Mapping: [⟨1 2 3 4 3 5], ⟨0 -8 -13 -23 9 -25]]

Optimal tunings:

  • WE: ~2 = 1198.6298¢, ~26/25 = 62.0480¢
  • CWE: ~2 = 1200.0000¢, ~26/25 = 62.1636¢

Optimal ET sequence: 19, 39df, 58

Badness (Sintel): 0.978

Camahueto

Subgroup: 2.3.5.7.11

Comma list: 126/125, 385/384, 10976/10935

Mapping: [⟨1 2 3 4 2], ⟨0 -8 -13 -23 28]]

Optimal tunings:

  • WE: ~2 = 1200.5186¢, ~28/27 = 62.4576¢
  • CWE: ~2 = 1200.0000¢, ~28/27 = 62.4252¢

Optimal ET sequence: 19, 58e, 77, 96d, 173d

Badness (Sintel): 2.180

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 385/384, 676/675

Mapping: [⟨1 2 3 4 2 5], ⟨0 -8 -13 -23 28 -25]]

Optimal tunings:

  • WE: ~2 = 1200.5004¢, ~26/25 = 62.4603¢
  • CWE: ~2 = 1200.0000¢, ~26/25 = 62.4277¢

Optimal ET sequence: 19, 58e, 77, 96d, 173d

Badness (Sintel): 1.494

Qilin

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 10976/10935

Mapping: [⟨1 2 3 4 6], ⟨0 -8 -13 -23 -49]]

Optimal tunings:

  • WE: ~2 = 1199.3865¢, ~28/27 = 62.1645¢
  • CWE: ~2 = 1200.0000¢, ~28/27 = 62.2199¢

Optimal ET sequence: 58, 77, 135c, 193c, 328cc

Badness (Sintel): 1.370

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 196/195, 2200/2197

Mapping: [⟨1 2 3 4 6 5], ⟨0 -8 -13 -23 -49 -25]]

Optimal tunings:

  • WE: ~2 = 1199.2874¢, ~26/25 = 62.1601¢
  • CWE: ~2 = 1200.0000¢, ~26/25 = 62.2251¢

Optimal ET sequence: 58, 77, 135c, 193cf, 328ccff

Badness (Sintel): 0.944

Monocerus

Subgroup: 2.3.5.7.11

Comma list: 126/125, 243/242, 5488/5445

Mapping: [⟨2 4 6 8 9], ⟨0 -8 -13 -23 -20]]

Optimal tunings:

  • WE: ~99/70 = 599.8223¢, ~28/27 = 62.2737¢
  • CWE: ~99/70 = 600.0000¢, ~28/27 = 62.3180¢

Optimal ET sequence: 58, 96d, 154, 212ce, 366cce

Badness (Sintel): 1.744

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 243/242, 364/363

Mapping: [⟨2 4 6 8 9 10], ⟨0 -8 -13 -23 -20 -25]]

Optimal tunings:

  • WE: ~55/39 = 599.8267¢, ~26/25 = 62.2833¢
  • CWE: ~55/39 = 600.0000¢, ~26/25 = 62.3262¢

Optimal ET sequence: 58, 96d, 154, 366ccef

Badness (Sintel): 1.190

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 126/125, 196/195, 221/220, 243/242, 289/288

Mapping: [⟨2 4 6 8 9 10 9], ⟨0 -8 -13 -23 -20 -25 -8]]

Optimal tunings:

  • WE: ~17/12 = 600.0715¢, ~26/25 = 62.3767¢
  • CWE: ~17/12 = 600.0000¢, ~26/25 = 62.3605¢

Optimal ET sequence: 58, 96d, 154

Badness (Sintel): 1.237

Rhinoceros

Subgroup: 2.3.5.7

Comma list: 49/48, 4375/4374

Mapping: [⟨1 2 3 3], ⟨0 -8 -13 -4]]

Optimal tunings:

  • WE: ~2 = 1203.1031¢, ~21/20 = 63.0830¢
  • CWE: ~2 = 1200.0000¢, ~21/20 = 62.6687¢

Optimal ET sequence: 1c, 19

Badness (Sintel): 2.072

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -8 -13 -4 -10]]

Optimal tunings:

  • WE: ~2 = 1201.1458¢, ~21/20 = 62.9338¢
  • CWE: ~2 = 1200.0000¢, ~21/20 = 62.7783¢

Optimal ET sequence: 1ce, 19

Badness (Sintel): 1.961

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 78/77, 100/99, 126/121

Mapping: [⟨1 2 3 3 4 4], ⟨0 -8 -13 -4 -10 -6]]

Optimal tunings:

  • WE: ~2 = 1202.2047¢, ~21/20 = 63.1591¢
  • CWE: ~2 = 1200.0000¢, ~21/20 = 62.8727¢

Optimal ET sequence: 1ce, 19

Badness (Sintel): 1.626

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