Llywelynsmic clan: Difference between revisions

Units, misc. cleanup
+ badnesses. Adopt WE & CWE tunings
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== Llywelyn a.k.a. shoe ==
== Llywelyn a.k.a. shoe ==
Llywelyn a.k.a. shoe can be described as the {{nowrap| 16 & 21 }} temperament.  
Llywelyn a.k.a. shoe can be described as the {{nowrap| 16 & 21 }} temperament, generated by a flattened [[~]][[8/7]] whole tone, seven of which give the interval class of [[5/1|5]]. Its [[ploidacot]] is alpha-heptaseph.  


[[Subgroup]]: 2.5.7
[[Subgroup]]: 2.5.7
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{{Mapping|legend=2| 1 1 3 | 0 7 -1 }}
{{Mapping|legend=2| 1 1 3 | 0 7 -1 }}
: mapping generators: ~2, ~8/7


{{Mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}
{{Mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}
: mapping generators: ~2, ~8/7


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~8/7 = 226.910{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.1974{{c}}, ~8/7 = 226.7586{{c}}
: [[error map]]: {{val| -0.803 +0.194 +2.008 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.8388{{c}}
: error map: {{val| 0.000 +1.558 +4.335 }}


{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}
[[Badness]] (Sintel): 2.06


=== Overview to extensions ===
=== Overview to extensions ===
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Gencom mapping: {{mapping| 1 0 1 3 1 | 0 0 7 -1 13 }}
Gencom mapping: {{mapping| 1 0 1 3 1 | 0 0 7 -1 13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.114{{c}}
Optimal tunings:
* WE: ~2 = 1199.1784{{c}}, ~8/7 = 226.9582{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0438{{c}}


{{Optimal ET sequence|legend=0| 16, 21, 37, 206cd }}
{{Optimal ET sequence|legend=0| 16, 21, 37, 206cd, 243cd, …, 354ccdd }}
 
Badness (Sintel): 0.651


=== 2.5.7.11.13 subgroup ===
=== 2.5.7.11.13 subgroup ===
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Gencom mapping: {{mapping| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}
Gencom mapping: {{mapping| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.108{{c}}
Optimal tunings:
* WE: ~2 = 1199.1643{{c}}, ~8/7 = 226.9495{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0315{{c}}


{{Optimal ET sequence|legend=0| 16, 21, 37, 206cdf }}
{{Optimal ET sequence|legend=0| 16, 21, 37, 206cdf, 243cdf, …, 354ccddff }}


RMS error: 0.5433 cents
Badness (Sintel): 0.319


=== 2.5.7.11.13.17 subgroup ===
=== 2.5.7.11.13.17 subgroup ===
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Gencom mapping: {{mapping| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}
Gencom mapping: {{mapping| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.242{{c}}
Optimal tunings:
* WE: ~2 = 1199.3162{{c}}, ~8/7 = 227.1125{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.1774{{c}}


{{Optimal ET sequence|legend=0| 16, 21, 37, 95 }}
{{Optimal ET sequence|legend=0| 16, 21, 37, 95 }}
Badness (Sintel): 0.458


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Llywelynsmic clan| ]] <!-- main article -->
[[Category:Llywelynsmic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]