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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]] ({{monzo|legend=1| -2 13 -8 }}, [[ratio]]: 1594323/1562500).  


= Five-limit unicorn =
== Unicorn ==
Subgroup: 2.3.5
Unicorn divides the [[4/3|perfect fourth]] into eight equal parts, three for [[10/9]] and five for [[6/5]]. Its [[ploidacot]] is omega-octacot.
 
[[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 }}
: mapping generators: ~2, ~250/243
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0889{{c}}, ~250/243 =  62.4623{{c}}
: [[error map]]: {{val| +0.089 -1.476 +1.943 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~250/243 = 62.4494{{c}}
: error map: {{val| 0.000 -1.550 +1.844 }}
 
{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}
 
[[Badness]] (Sintel): 3.53
 
== Septimal unicorn ==
The canonical extension to the 7-limit is by interpreting the generator as a very slightly flattened [[~]][[28/27]], corresponding to tempering out 126/125, the [[starling comma]], and 10976/10935, the [[hemimage comma]]. As it equates the perfect fourth with a stack of eight 28/27's, it also tempers out the [[octaphore comma]] in the [[2.3.7 subgroup]].


[[POTE generator]]: ~250/243 = 62.458
The hemifourth, reached by four generator steps, can be interpreted as ~[[15/13]]. This gives rise to a natural [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] extension where [[196/195]] and [[676/675]] vanish.  


{{Val list|legend=1| 19, 58, 77, 96, 173, 269 }}
From 10976/10935 = ([[784/783]])<sup>2</sup>⋅([[841/840]]) we obtain an add-29 extension for free, so the generator triples as 28/27~[[29/28]]~[[30/29]], and as 196/195 vanishes already, so does [[729/728]], leading to its [[S-expression]]-based comma list of {[[676/675|S26]], [[729/728|S27]], [[784/783|S28]], [[841/840|S29]]}.


[[Badness]]: 0.150487
Experimentation shows we can find a reasonable mapping for prime 43 at -11 generator steps, tempering out [[216/215]]. All other primes require either quite complex mappings (being significantly positive rather than negative) or require high error or both.


= Septimal unicorn =
In all the subgroups above, the optimum is between [[58edo]] and [[77edo]], though a notable tuning not appearing in the [[optimal ET sequence]]s here is [[96edo]] using the 96d val (with a 963{{c}} [[~]][[7/4]] similar to that of [[meanpop]]), which sacrifices the accuracy of prime 7 in favour of a more accurate 5.
{{see also| Starling temperaments #Unicorn }}


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


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


[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -8 -13 -23 }}]
{{Mapping|legend=1| 1 2 3 4 | 0 -8 -13 -23 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6949{{c}}, ~28/27 = 62.2621{{c}}
: [[error map]]: {{val| -0.305 -0.662 +3.364 -2.074 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/27 = 62.2996{{c}}
: error map: {{val| 0.000 -0.352 +3.792 -1.717 }}
 
{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c, 212c }}


{{Multival|legend=1| 8 13 23 2 14 17 }}
[[Badness]] (Sintel): 1.04


[[POTE generator]]: ~28/27 = 62.278
==== 2.3.5.7.13 subgroup ====
Subgroup: 2.3.5.7.13


{{Val list|legend=1| 19, 39d, 58, 77, 135c }}
Comma list: 126/125, 196/195, 676/675


[[Badness]]: 0.040913
Subgroup-val mapping: {{mapping| 1 2 3 4 5 | 0 -8 -13 -23 -25 }}


== Alicorn ==
Optimal tunings:
* WE: ~2 = 1199.7013{{c}}, ~28/27 = 62.2785{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.3151{{c}}
 
{{Optimal ET sequence|legend=0| 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: {{mapping| 1 2 3 4 5 6 | 0 -8 -13 -23 -25 -22 }}
 
Optimal tunings:
* WE: ~2 = 1199.7715{{c}}, ~28/27 = 62.2860{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.3141{{c}}
 
{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 212cf }}
 
Badness (Sintel): 0.487
 
=== 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{{c}}, ~28/27 = 62.0316{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.1435{{c}}


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


Badness: 0.039156
Badness (Sintel): 1.29


=== 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{{c}}, ~28/27 = 62.0480{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.1636{{c}}


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{{c}}, ~28/27 = 62.4576{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.4252{{c}}


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


Badness: 0.065940
Badness (Sintel): 2.18


=== 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{{c}}, ~28/27 = 62.4603{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.4277{{c}}


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


Badness: 0.036155
Badness (Sintel): 1.49


== 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{{c}}, ~28/27 = 62.1645{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.2199{{c}}


Vals: {{Val list| 58, 77, 135c, 193c, 328cc }}
{{Optimal ET sequence|legend=0| 19e, …, 58, 135c, 193c }}


Badness: 0.041426
Badness (Sintel): 1.37


=== 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{{c}}, ~28/27 = 62.1601{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.2251{{c}}


Vals: {{Val list| 58, 77, 135c, 193cf, 328ccff }}
{{Optimal ET sequence|legend=0| 19e, …, 58, 135c, 193cf }}


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{{c}}, ~28/27 = 62.2737{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.3180{{c}}


Vals: {{Val list| 58, 96d, 154, 212ce, 366cce }}
{{Optimal ET sequence|legend=0| 38d, 58, 96d, 154, 212ce }}


Badness: 0.052757
Badness (Sintel): 1.74


=== 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{{c}}, ~28/27 = 62.2833{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~28/27 = 62.3262{{c}}
 
{{Optimal ET sequence|legend=0| 38df, 58, 96d, 154 }}
 
Badness (Sintel): 1.19
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val| 2 4 6 8 9 10 }}, {{val| 0 -8 -13 -23 -20 -25 }}]
Comma list: 126/125, 196/195, 221/220, 243/242, 289/288


POTE generator: ~28/27 = 62.301
Mapping: {{mapping| 2 4 6 8 9 10 9 | 0 -8 -13 -23 -20 -25 -8 }}


Vals: {{Val list| 58, 96d, 154, 366ccef }}
Optimal tunings:  
* WE: ~17/12 = 600.0715{{c}}, ~28/27 = 62.3767{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~28/27 = 62.3605{{c}}


Badness: 0.028795
{{Optimal ET sequence|legend=0| 38df, 58, 96d, 154 }}


= Rhinoceros =
Badness (Sintel): 1.24
Subgroup: 2.3.5.7
 
== Rhinoceros ==
Rhinoceros tempers out the [[semaphoresma]] and the [[ragisma]], identifying the generator as a [[~]][[21/20]], rather than the [[28/27]] of septimal unicorn. It may be described as the {{nowrap| 19 & 20c }} temperament. [[19edo]] is a good tuning, though [[39edo]] is a possible alternative.
 
[[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 }}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.1031{{c}}, ~21/20 = 63.0830{{c}}
: [[error map]]: {{val| +3.103 -0.412 +2.917 -11.848 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 62.6687{{c}}
: error map: {{val| 0.000 -3.305 -1.007 -19.501 }}


[[POTE generator]]: ~21/20 = 62.920
{{Optimal ET sequence|legend=1| 1c, …, 18bcd, 19 }}


{{Val list|legend=1| 1c, 19 }}
[[Badness]] (Sintel): 2.07


[[Badness]]: 0.081864
=== 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{{c}}, ~21/20 = 62.9338{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.7783{{c}}


Vals: {{Val list| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 18bcd, 19 }}


Badness: 0.059319
Badness (Sintel): 1.96


== 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{{c}}, ~21/20 = 63.1591{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.8727{{c}}


Vals: {{Val list| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 18bcdf, 19 }}


Badness: 0.039343
Badness (Sintel): 1.63


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

Latest revision as of 12:25, 14 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

Unicorn divides the perfect fourth into eight equal parts, three for 10/9 and five for 6/5. Its ploidacot is omega-octacot.

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 ¢
error map: ⟨+0.089 -1.476 +1.943]
  • CWE: ~2 = 1200.0000 ¢, ~250/243 = 62.4494 ¢
error map: ⟨0.000 -1.550 +1.844]

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

Badness (Sintel): 3.53

Septimal unicorn

The canonical extension to the 7-limit is by interpreting the generator as a very slightly flattened ~28/27, corresponding to tempering out 126/125, the starling comma, and 10976/10935, the hemimage comma. As it equates the perfect fourth with a stack of eight 28/27's, it also tempers out the octaphore comma in the 2.3.7 subgroup.

The hemifourth, reached by four generator steps, can be interpreted as ~15/13. This gives rise to a natural 2.3.5.7.13-subgroup extension where 196/195 and 676/675 vanish.

From 10976/10935 = (784/783)2⋅(841/840) we obtain an add-29 extension for free, so the generator triples as 28/27~29/28~30/29, and as 196/195 vanishes already, so does 729/728, leading to its S-expression-based comma list of {S26, S27, S28, S29}.

Experimentation shows we can find a reasonable mapping for prime 43 at -11 generator steps, tempering out 216/215. All other primes require either quite complex mappings (being significantly positive rather than negative) or require high error or both.

In all the subgroups above, the optimum is between 58edo and 77edo, though a notable tuning not appearing in the optimal ET sequences here is 96edo using the 96d val (with a 963 ¢ ~7/4 similar to that of meanpop), which sacrifices the accuracy of prime 7 in favour of a more accurate 5.

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 ¢
error map: ⟨-0.305 -0.662 +3.364 -2.074]
  • CWE: ~2 = 1200.0000 ¢, ~28/27 = 62.2996 ¢
error map: ⟨0.000 -0.352 +3.792 -1.717]

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

Badness (Sintel): 1.04

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 ¢, ~28/27 = 62.2785 ¢
  • CWE: ~2 = 1200.0000 ¢, ~28/27 = 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 ¢, ~28/27 = 62.2860 ¢
  • CWE: ~2 = 1200.0000 ¢, ~28/27 = 62.3141 ¢

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

Badness (Sintel): 0.487

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): 1.29

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 ¢, ~28/27 = 62.0480 ¢
  • CWE: ~2 = 1200.0000 ¢, ~28/27 = 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): 2.18

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 ¢, ~28/27 = 62.4603 ¢
  • CWE: ~2 = 1200.0000 ¢, ~28/27 = 62.4277 ¢

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

Badness (Sintel): 1.49

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: 19e, …, 58, 135c, 193c

Badness (Sintel): 1.37

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 ¢, ~28/27 = 62.1601 ¢
  • CWE: ~2 = 1200.0000 ¢, ~28/27 = 62.2251 ¢

Optimal ET sequence: 19e, …, 58, 135c, 193cf

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: 38d, 58, 96d, 154, 212ce

Badness (Sintel): 1.74

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 ¢, ~28/27 = 62.2833 ¢
  • CWE: ~55/39 = 600.0000 ¢, ~28/27 = 62.3262 ¢

Optimal ET sequence: 38df, 58, 96d, 154

Badness (Sintel): 1.19

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 ¢, ~28/27 = 62.3767 ¢
  • CWE: ~17/12 = 600.0000 ¢, ~28/27 = 62.3605 ¢

Optimal ET sequence: 38df, 58, 96d, 154

Badness (Sintel): 1.24

Rhinoceros

Rhinoceros tempers out the semaphoresma and the ragisma, identifying the generator as a ~21/20, rather than the 28/27 of septimal unicorn. It may be described as the 19 & 20c temperament. 19edo is a good tuning, though 39edo is a possible alternative.

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 ¢
error map: ⟨+3.103 -0.412 +2.917 -11.848]
  • CWE: ~2 = 1200.0000 ¢, ~21/20 = 62.6687 ¢
error map: ⟨0.000 -3.305 -1.007 -19.501]

Optimal ET sequence: 1c, …, 18bcd, 19

Badness (Sintel): 2.07

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, 18bcd, 19

Badness (Sintel): 1.96

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, 18bcdf, 19

Badness (Sintel): 1.63

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