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Unicorn family: Difference between revisions

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Line 11: Line 11:
{{Mapping|legend=1| 1 2 3 | 0 -8 -13 }}
{{Mapping|legend=1| 1 2 3 | 0 -8 -13 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: 2 = 1\1, ~250/243 =  62.441
* [[WE]]: ~2 = 1200.0889¢, ~250/243 =  62.4623¢
* [[POTE]]: 2 = 1\1, ~250/243 = 62.458
* [[CWE]]: ~2 = 1200.0000¢, ~250/243 = 62.4494¢


{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}
{{Optimal ET sequence|legend=1| 19, 58, 77, 96, 173, 269 }}


[[Badness]]:
[[Badness]] (Sintel): 3.530
* Smith: 0.150487
* Dirichlet: 3.530


== Septimal unicorn ==
== Septimal unicorn ==
Line 30: Line 28:
{{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:  
* [[CTE]]: 2 = 1\1, ~28/27 = 62.324
* [[WE]]: ~2 = 1199.6949¢, ~28/27 = 62.2621¢
* [[POTE]]: 2 = 1\1, ~28/27 = 62.278
* [[CWE]]: ~2 = 1200.0000¢, ~28/27 = 62.2996¢


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


Badness:
[[Badness]] (Sintel): 1.035
* Smith: 0.040913
* Dirichlet: 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]], [[351/350]], [[676/675]]
[[Comma list]]: [[126/125]], [[196/195]], [[676/675]]


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


[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~28/27 = 62.339
[[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 }}
{{Optimal ET sequence|legend=1| 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]], [[729/728]], [[784/783]], [[841/840]]
[[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 }}
{{Mapping|legend=1| 1 2 3 4 5 6 | 0 -8 -13 -23 -25 -22 }}


[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~28/27 = 62.334
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7715¢, ~26/25 = 62.2860¢
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3141¢


{{Optimal ET sequence|legend=1| 19, 39dfj, 58, 77, 212cfn }}
{{Optimal ET sequence|legend=1| 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 ====
Line 71: Line 71:
[[Subgroup]]: 2.3.5.7.13.29.43
[[Subgroup]]: 2.3.5.7.13.29.43


[[Comma list]]: [[126/125]], [[729/728]], [[784/783]], [[841/840]], 216/215
[[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 }}
{{Mapping|legend=1| 1 2 3 4 5 6 6 | 0 -8 -13 -23 -25 -22 -11 }}


[[Optimal tuning]] ([[CTE]]): 2 = 1\1, ~28/27 = 62.339
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.6269¢, ~26/25 = 62.2584¢
* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3008¢


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


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


=== Alicorn ===
=== Alicorn ===
Line 88: Line 90:
Mapping: {{mapping| 1 2 3 4 3 | 0 -8 -13 -23 9 }}
Mapping: {{mapping| 1 2 3 4 3 | 0 -8 -13 -23 9 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.101
Optimal tunings:
* WE: ~2 = 1198.6510¢, ~28/27 = 62.0316¢
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.1435¢


{{Optimal ET sequence|legend=1| 19, 39d, 58 }}
{{Optimal ET sequence|legend=0| 19, 39d, 58 }}


Badness: 0.039156
Badness (Sintel): 1.294


==== 13-limit ====
==== 13-limit ====
Line 101: Line 105:
Mapping: {{mapping| 1 2 3 4 3 5 | 0 -8 -13 -23 9 -25 }}
Mapping: {{mapping| 1 2 3 4 3 5 | 0 -8 -13 -23 9 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.119
Optimal tunings:
* WE: ~2 = 1198.6298¢, ~26/25 = 62.0480¢
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.1636¢


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


Badness: 0.023667
Badness (Sintel): 0.978


=== Camahueto ===
=== Camahueto ===
Line 114: Line 120:
Mapping: {{mapping| 1 2 3 4 2 | 0 -8 -13 -23 28 }}
Mapping: {{mapping| 1 2 3 4 2 | 0 -8 -13 -23 28 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.431
Optimal tunings:
* WE: ~2 = 1200.5186¢, ~28/27 = 62.4576¢
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.4252¢


{{Optimal ET sequence|legend=1| 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 ====
Line 127: Line 135:
Mapping: {{mapping| 1 2 3 4 2 5 | 0 -8 -13 -23 28 -25 }}
Mapping: {{mapping| 1 2 3 4 2 5 | 0 -8 -13 -23 28 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.434
Optimal tunings:
* WE: ~2 = 1200.5004¢, ~26/25 = 62.4603¢
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.4277¢


{{Optimal ET sequence|legend=1| 19, 58e, 77, 96d, 173d }}
{{Optimal ET sequence|legend=0| 19, 58e, 77, 96d, 173d }}


Badness: 0.036155
Badness (Sintel): 1.494


=== Qilin ===
=== Qilin ===
Line 140: Line 150:
Mapping: {{mapping| 1 2 3 4 6 | 0 -8 -13 -23 -49 }}
Mapping: {{mapping| 1 2 3 4 6 | 0 -8 -13 -23 -49 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.196
Optimal tunings:
* WE: ~2 = 1199.3865¢, ~28/27 = 62.1645¢
* CWE: ~2 = 1200.0000¢, ~28/27 = 62.2199¢


{{Optimal ET sequence|legend=1| 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 ====
Line 153: Line 165:
Mapping: {{mapping| 1 2 3 4 6 5 | 0 -8 -13 -23 -49 -25 }}
Mapping: {{mapping| 1 2 3 4 6 5 | 0 -8 -13 -23 -49 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.197
Optimal tunings:
* WE: ~2 = 1199.2874¢, ~26/25 = 62.1601¢
* CWE: ~2 = 1200.0000¢, ~26/25 = 62.2251¢


{{Optimal ET sequence|legend=1| 58, 77, 135c, 193cf, 328ccff }}
{{Optimal ET sequence|legend=0| 58, 77, 135c, 193cf, 328ccff }}


Badness: 0.022842
Badness (Sintel): 0.944


=== Monocerus ===
=== Monocerus ===
Line 166: Line 180:
Mapping: {{mapping| 2 4 6 8 9 | 0 -8 -13 -23 -20 }}
Mapping: {{mapping| 2 4 6 8 9 | 0 -8 -13 -23 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.292
Optimal tunings:
* WE: ~99/70 = 599.8223¢, ~28/27 = 62.2737¢
* CWE: ~99/70 = 600.0000¢, ~28/27 = 62.3180¢


{{Optimal ET sequence|legend=1| 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 }}
Mapping: {{mapping| 2 4 6 8 9 10 | 0 -8 -13 -23 -20 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.301
Optimal tunings:
* WE: ~55/39 = 599.8267¢, ~26/25 = 62.2833¢
* CWE: ~55/39 = 600.0000¢, ~26/25 = 62.3262¢


{{Optimal ET sequence|legend=1| 58, 96d, 154, 366ccef }}
{{Optimal ET sequence|legend=0| 58, 96d, 154, 366ccef }}


Badness: 0.028795
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: {{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|legend=0| 58, 96d, 154 }}
 
Badness (Sintel): 1.237


== Rhinoceros ==
== Rhinoceros ==
Line 192: Line 225:
{{Mapping|legend=1| 1 2 3 3 | 0 -8 -13 -4 }}
{{Mapping|legend=1| 1 2 3 3 | 0 -8 -13 -4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 62.920
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.1031¢, ~21/20 = 63.0830¢
* [[CWE]]: ~2 = 1200.0000¢, ~21/20 = 62.6687¢


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


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


=== 11-limit ===
=== 11-limit ===
Line 205: Line 240:
Mapping: {{mapping|  1 2 3 3 4 | 0 -8 -13 -4 -10 }}
Mapping: {{mapping|  1 2 3 3 4 | 0 -8 -13 -4 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 62.874
Optimal tunings:
* WE: ~2 = 1201.1458¢, ~21/20 = 62.9338¢
* CWE: ~2 = 1200.0000¢, ~21/20 = 62.7783¢


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


Badness: 0.059319
Badness (Sintel): 1.961


=== 13-limit ===
=== 13-limit ===
Line 218: Line 255:
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -8 -13 -4 -10 -6 }}
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -8 -13 -4 -10 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 63.043
Optimal tunings:
* WE: ~2 = 1202.2047¢, ~21/20 = 63.1591¢
* CWE: ~2 = 1200.0000¢, ~21/20 = 62.8727¢


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


Badness: 0.039343
Badness (Sintel): 1.626


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