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Unicorn family: Difference between revisions

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m Units; misc. cleanup; - redundant category
Review data for each temp. + intro to rhinoceros
Line 12: Line 12:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0889{{c}}, ~250/243 =  62.4623{{c}}
* [[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}}
* [[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 }}
{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}


[[Badness]] (Sintel): 3.530
[[Badness]] (Sintel): 3.53


== Septimal unicorn ==
== Septimal unicorn ==
Line 32: Line 34:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.6949{{c}}, ~28/27 = 62.2621{{c}}
* [[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}}
* [[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 }}
{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c, 212c }}
Line 46: Line 50:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.7013{{c}}, ~26/25 = 62.2785{{c}}
* WE: ~2 = 1199.7013{{c}}, ~28/27 = 62.2785{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.3151{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.3151{{c}}


{{Optimal ET sequence|legend=0| 19, 39df, 58, 77, 212cf }}
{{Optimal ET sequence|legend=0| 19, 39df, 58, 77, 212cf }}
Line 61: Line 65:


Optimal tunings:  
Optimal tunings:  
* [[WE]]: ~2 = 1199.7715{{c}}, ~26/25 = 62.2860{{c}}
* WE: ~2 = 1199.7715{{c}}, ~28/27 = 62.2860{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~26/25 = 62.3141{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.3141{{c}}


{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 212cf }}
{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 212cf }}
Line 78: Line 82:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.6269{{c}}, ~26/25 = 62.2584{{c}}
* WE: ~2 = 1199.6269{{c}}, ~28/27 = 62.2584{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.3008{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.3008{{c}}


{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 135c, 212cfn }}
{{Optimal ET sequence|legend=0| 19, 39dfj, 58, 77, 135c, 212cfn }}
Line 98: Line 102:
{{Optimal ET sequence|legend=0| 19, 39d, 58 }}
{{Optimal ET sequence|legend=0| 19, 39d, 58 }}


Badness (Sintel): 1.294
Badness (Sintel): 1.29


==== 13-limit ====
==== 13-limit ====
Line 108: Line 112:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.6298{{c}}, ~26/25 = 62.0480{{c}}
* WE: ~2 = 1198.6298{{c}}, ~28/27 = 62.0480{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.1636{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.1636{{c}}


{{Optimal ET sequence|legend=0| 19, 39df, 58 }}
{{Optimal ET sequence|legend=0| 19, 39df, 58 }}
Line 128: Line 132:
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}


Badness (Sintel): 2.180
Badness (Sintel): 2.18


==== 13-limit ====
==== 13-limit ====
Line 138: Line 142:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1200.5004{{c}}, ~26/25 = 62.4603{{c}}
* WE: ~2 = 1200.5004{{c}}, ~28/27 = 62.4603{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.4277{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.4277{{c}}


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


Badness (Sintel): 1.494
Badness (Sintel): 1.49


=== Qilin ===
=== Qilin ===
Line 156: Line 160:
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.2199{{c}}
* 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| 19e, …, 58, 135c, 193c }}


Badness (Sintel): 1.370
Badness (Sintel): 1.37


==== 13-limit ====
==== 13-limit ====
Line 168: Line 172:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.2874{{c}}, ~26/25 = 62.1601{{c}}
* WE: ~2 = 1199.2874{{c}}, ~28/27 = 62.1601{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/25 = 62.2251{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 62.2251{{c}}


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


Badness (Sintel): 0.944
Badness (Sintel): 0.944
Line 186: Line 190:
* CWE: ~99/70 = 600.0000{{c}}, ~28/27 = 62.3180{{c}}
* 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| 38d, 58, 96d, 154, 212ce }}


Badness (Sintel): 1.744
Badness (Sintel): 1.74


==== 13-limit ====
==== 13-limit ====
Line 198: Line 202:


Optimal tunings:  
Optimal tunings:  
* WE: ~55/39 = 599.8267{{c}}, ~26/25 = 62.2833{{c}}
* WE: ~55/39 = 599.8267{{c}}, ~28/27 = 62.2833{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~26/25 = 62.3262{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~28/27 = 62.3262{{c}}


{{Optimal ET sequence|legend=0| 58, 96d, 154, 366ccef }}
{{Optimal ET sequence|legend=0| 38df, 58, 96d, 154 }}


Badness (Sintel): 1.190
Badness (Sintel): 1.19


==== 17-limit ====
==== 17-limit ====
Line 213: Line 217:


Optimal tunings:  
Optimal tunings:  
* WE: ~17/12 = 600.0715{{c}}, ~26/25 = 62.3767{{c}}
* WE: ~17/12 = 600.0715{{c}}, ~28/27 = 62.3767{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~26/25 = 62.3605{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~28/27 = 62.3605{{c}}


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


Badness (Sintel): 1.237
Badness (Sintel): 1.24


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


Line 229: Line 235:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1203.1031{{c}}, ~21/20 = 63.0830{{c}}
* [[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}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 62.6687{{c}}
: error map: {{val| 0.000 -3.305 -1.007 -19.501 }}


{{Optimal ET sequence|legend=1| 1c, 19 }}
{{Optimal ET sequence|legend=1| 1c, …, 18bcd, 19 }}


[[Badness]] (Sintel): 2.072
[[Badness]] (Sintel): 2.07


=== 11-limit ===
=== 11-limit ===
Line 246: Line 254:
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.7783{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.7783{{c}}


{{Optimal ET sequence|legend=0| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 18bcd, 19 }}


Badness (Sintel): 1.961
Badness (Sintel): 1.96


=== 13-limit ===
=== 13-limit ===
Line 261: Line 269:
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.8727{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 62.8727{{c}}


{{Optimal ET sequence|legend=0| 1ce, 19 }}
{{Optimal ET sequence|legend=0| 1ce, 18bcdf, 19 }}


Badness (Sintel): 1.626
Badness (Sintel): 1.63


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Unicorn family| ]] <!-- main article -->
[[Category:Unicorn family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Unicorn_family"