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{{Technical data page}}
{{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]].
The '''unicorn family''' tempers out the [[unicorn comma]] ({{monzo|legend=1| -2 13 -8 }}, [[ratio]]: 1594323/1562500).  


== Unicorn ==
== 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 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
[[Subgroup]]: 2.3.5


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{{Mapping|legend=1| 1 2 3 | 0 -8 -13 }}
{{Mapping|legend=1| 1 2 3 | 0 -8 -13 }}
: mapping generators: ~2, ~250/243


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0889¢, ~250/243 =  62.4623¢
* [[WE]]: ~2 = 1200.0889{{c}}, ~250/243 =  62.4623{{c}}
* [[CWE]]: ~2 = 1200.0000¢, ~250/243 = 62.4494¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~250/243 = 62.4494{{c}}


{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}
{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}
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== Septimal unicorn ==
== Septimal unicorn ==
{{See also| Octaphore }}
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]].


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.
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


{{Mapping|legend=1| 1 2 3 4 | 0 -8 -13 -23 }}
{{Mapping|legend=1| 1 2 3 4 | 0 -8 -13 -23 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.6949¢, ~28/27 = 62.2621¢
* [[WE]]: ~2 = 1199.6949{{c}}, ~28/27 = 62.2621{{c}}
* [[CWE]]: ~2 = 1200.0000¢, ~28/27 = 62.2996¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/27 = 62.2996{{c}}


{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c, 212c }}
{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c, 212c }}
Line 36: Line 38:
[[Badness]] (Sintel): 1.035
[[Badness]] (Sintel): 1.035


=== 2.3.5.7.13 subgroup ===
==== 2.3.5.7.13 subgroup ====
[[Subgroup]]: 2.3.5.7.13
Subgroup: 2.3.5.7.13


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


{{Mapping|legend=1| 1 2 3 4 5 | 0 -8 -13 -23 -25 }}
Subgroup-val mapping: {{mapping| 1 2 3 4 5 | 0 -8 -13 -23 -25 }}


[[Optimal tuning]]s:  
Optimal tunings:  
* [[WE]]: ~2 = 1199.7013¢, ~26/25 = 62.2785¢
* WE: ~2 = 1199.7013{{c}}, ~26/25 = 62.2785{{c}}
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3151¢
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.3151{{c}}


{{Optimal ET sequence|legend=1| 19, 39df, 58, 77, 212cf }}
{{Optimal ET sequence|legend=0| 19, 39df, 58, 77, 212cf }}


[[Badness]] (Sintel): 0.590
Badness (Sintel): 0.590


==== 2.3.5.7.13.29 subgroup ====
==== 2.3.5.7.13.29 subgroup ====
[[Subgroup]]: 2.3.5.7.13.29
Subgroup: 2.3.5.7.13.29


[[Comma list]]: [[126/125]], [[196/195]], [[261/260]], [[377/375]]
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 }}
Subgroup-val mapping: {{mapping| 1 2 3 4 5 6 | 0 -8 -13 -23 -25 -22 }}


[[Optimal tuning]]s:  
Optimal tunings:  
* [[WE]]: ~2 = 1199.7715¢, ~26/25 = 62.2860¢
* [[WE]]: ~2 = 1199.7715{{c}}, ~26/25 = 62.2860{{c}}
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3141¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~26/25 = 62.3141{{c}}


{{Optimal ET sequence|legend=1| 19, 39dfj, 58, 77, 212cf }}
{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 212cf }}


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


==== 2.3.5.7.13.29.43 subgroup ====
==== 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[[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]].
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]].


[[Subgroup]]: 2.3.5.7.13.29.43
Subgroup: 2.3.5.7.13.29.43


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


{{Mapping|legend=1| 1 2 3 4 5 6 6 | 0 -8 -13 -23 -25 -22 -11 }}
Subgroup-val mapping: {{mapping| 1 2 3 4 5 6 6 | 0 -8 -13 -23 -25 -22 -11 }}


[[Optimal tuning]]s:  
Optimal tunings:  
* [[WE]]: ~2 = 1199.6269¢, ~26/25 = 62.2584¢
* WE: ~2 = 1199.6269{{c}}, ~26/25 = 62.2584{{c}}
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3008¢
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.3008{{c}}


{{Optimal ET sequence|legend=1| 19, 39dfj, 58, 77, 135c, 212cfn }}
{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 135c, 212cfn }}


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


=== Alicorn ===
=== Alicorn ===
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Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.6510¢, ~28/27 = 62.0316¢
* WE: ~2 = 1198.6510{{c}}, ~28/27 = 62.0316{{c}}
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.1435¢
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.1435{{c}}


{{Optimal ET sequence|legend=0| 19, 39d, 58 }}
{{Optimal ET sequence|legend=0| 19, 39d, 58 }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.6298¢, ~26/25 = 62.0480¢
* WE: ~2 = 1198.6298{{c}}, ~26/25 = 62.0480{{c}}
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.1636¢
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.1636{{c}}


{{Optimal ET sequence|legend=0| 19, 39df, 58 }}
{{Optimal ET sequence|legend=0| 19, 39df, 58 }}
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Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.5186¢, ~28/27 = 62.4576¢
* WE: ~2 = 1200.5186{{c}}, ~28/27 = 62.4576{{c}}
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.4252¢
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.4252{{c}}


{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}
Line 136: Line 138:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.5004¢, ~26/25 = 62.4603¢
* WE: ~2 = 1200.5004{{c}}, ~26/25 = 62.4603{{c}}
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.4277¢
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.4277{{c}}


{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}
Line 151: Line 153:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.3865¢, ~28/27 = 62.1645¢
* WE: ~2 = 1199.3865{{c}}, ~28/27 = 62.1645{{c}}
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.2199¢
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.2199{{c}}


{{Optimal ET sequence|legend=0| 58, 77, 135c, 193c, 328cc }}
{{Optimal ET sequence|legend=0| 58, 77, 135c, 193c, 328cc }}
Line 166: Line 168:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.2874¢, ~26/25 = 62.1601¢
* WE: ~2 = 1199.2874{{c}}, ~26/25 = 62.1601{{c}}
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.2251¢
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.2251{{c}}


{{Optimal ET sequence|legend=0| 58, 77, 135c, 193cf, 328ccff }}
{{Optimal ET sequence|legend=0| 58, 77, 135c, 193cf, 328ccff }}
Line 181: Line 183:


Optimal tunings:  
Optimal tunings:  
* WE: ~99/70 = 599.8223¢, ~28/27 = 62.2737¢
* WE: ~99/70 = 599.8223{{c}}, ~28/27 = 62.2737{{c}}
* CWE: ~99/70 = 600.0000¢, ~28/27 = 62.3180¢
* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.3180{{c}}


{{Optimal ET sequence|legend=0| 58, 96d, 154, 212ce, 366cce }}
{{Optimal ET sequence|legend=0| 58, 96d, 154, 212ce, 366cce }}
Line 196: Line 198:


Optimal tunings:  
Optimal tunings:  
* WE: ~55/39 = 599.8267¢, ~26/25 = 62.2833¢
* WE: ~55/39 = 599.8267{{c}}, ~26/25 = 62.2833{{c}}
* CWE: ~55/39 = 600.0000¢, ~26/25 = 62.3262¢
* CWE: ~55/39 = 600.0000{{c}}, ~26/25 = 62.3262{{c}}


{{Optimal ET sequence|legend=0| 58, 96d, 154, 366ccef }}
{{Optimal ET sequence|legend=0| 58, 96d, 154, 366ccef }}
Line 211: Line 213:


Optimal tunings:  
Optimal tunings:  
* WE: ~17/12 = 600.0715¢, ~26/25 = 62.3767¢
* WE: ~17/12 = 600.0715{{c}}, ~26/25 = 62.3767{{c}}
* CWE: ~17/12 = 600.0000¢, ~26/25 = 62.3605¢
* CWE: ~17/12 = 600.0000{{c}}, ~26/25 = 62.3605{{c}}


{{Optimal ET sequence|legend=0| 58, 96d, 154 }}
{{Optimal ET sequence|legend=0| 58, 96d, 154 }}
Line 226: Line 228:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1203.1031¢, ~21/20 = 63.0830¢
* [[WE]]: ~2 = 1203.1031{{c}}, ~21/20 = 63.0830{{c}}
* [[CWE]]: ~2 = 1200.0000¢, ~21/20 = 62.6687¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 62.6687{{c}}


{{Optimal ET sequence|legend=1| 1c, 19 }}
{{Optimal ET sequence|legend=1| 1c, 19 }}
Line 241: Line 243:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.1458¢, ~21/20 = 62.9338¢
* WE: ~2 = 1201.1458{{c}}, ~21/20 = 62.9338{{c}}
* CWE: ~2 = 1200.0000¢, ~21/20 = 62.7783¢
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.7783{{c}}


{{Optimal ET sequence|legend=0| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 19 }}
Line 256: Line 258:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1202.2047¢, ~21/20 = 63.1591¢
* WE: ~2 = 1202.2047{{c}}, ~21/20 = 63.1591{{c}}
* CWE: ~2 = 1200.0000¢, ~21/20 = 62.8727¢
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.8727{{c}}


{{Optimal ET sequence|legend=0| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 19 }}
Line 265: Line 267:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Unicorn family| ]] <!-- main article -->
[[Category:Unicorn family| ]] <!-- main article -->
[[Category:Unicorn| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 18:31, 4 August 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 (monzo: [-2 13 -8⟩, ratio: 1594323/1562500).

Unicorn

Subgroup: 2.3.5

Comma list: 1594323/1562500

Mapping: [⟨1 2 3], ⟨0 -8 -13]]

mapping generators: ~2, ~250/243

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

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.

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.

7-limit

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

Subgroup-val 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

Subgroup-val 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

Subgroup-val 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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