Llywelynsmic clan: Difference between revisions

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-The '''llywelyn clan''' tempers out the no-threes llywelyn comma, {{Monzo|22 0 -1 -7}} = [[4194304/4117715]].
+{{Technical data page}}
+The '''llywelyn clan''' tempers out the no-threes [[llywelyn comma]], {{monzo| 22 0 -1 -7 }} = 4194304/4117715.
-== Llywelyn ==
+Full 7-limit [[extension]]s of llywelyn temperament include:
-Subgroup: 2.5.7
+* [[Gorgo]] (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]
+* [[Ultrapyth]] (+64/63) → [[Archytas clan #Ultrapyth|Archytas clan]]
+* [[Buzzard]] (+1728/1715) → [[Vulture family]]
+* [[Semaja]] (+3125/3087) → [[Porwell temperaments #Semaja|Porwell temperaments]]
+* [[Misneb]] (+225/224) → [[Marvel temperaments #Misneb|Marvel temperaments]]
+* [[Gorgik]] (+2401/2400) → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]
+Discussed below is the 2.5.7 subgroup temperament llywelyn a.k.a. shoe.
+== Llywelyn a.k.a. shoe ==
+Llywelyn a.k.a. shoe can be described as the 16 &amp; 21 temperament, starting with the 2.5.7 subgroup up to the no-3 17-limit.
+[[Subgroup]]: 2.5.7
 [[Comma list]]: 4194304/4117715
-[[Sval]] [[mapping]]: [{{Val| 1 1 3 }}, {{Val| 0 7 -1 }}]
+{{Mapping|legend=2| 1 1 3 | 0 7 -1 }}
+: mapping generators: ~2, ~8/7
-Mapping generators: 2, ~8/7
+{{Mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}
-Gencom mapping: [{{Val| 1 0 1 3 }}, {{Val| 0 0 7 -1 }}]
+: [[Gencom]]: [2 8/7; 4194304/4117715]
-[[Gencom]]: [2 8/7; 4194304/4117715]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 226.910
-[[POTE generator]]: ~8/7 = 226.910
+{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}
-{{Val list|legend=1| 5, 11c, 16, 21, 37 }}
+=== 2.5.7.11 subgroup ===
-====2.5.7.11====
 Subgroup: 2.5.7.11
-[[Comma]]: 176/175, 1310720/1294139
+Comma list: 176/175, 1310720/1294139
+Sval mapping: {{mapping| 1 1 3 1 | 0 7 -1 13 }}
-[[Gencom]]: [2 8/7; 176/175 1310720/1294139]
+Gencom mapping: {{mapping| 1 0 1 3 1 | 0 0 7 -1 13 }}
-[[Gencom|Gencom mapping]]: [{{val|1 0 1 3 1}}, {{val|0 0 7 -1 13}}]
+: gencom: [2 8/7; 176/175 1310720/1294139]
-[[Mapping|Sval mapping]]: [{{val|1 1 3 1}}, {{val|0 7 -1 13}}]
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.114
-[[Tp tuning|POL2 generator]]: ~8/7 = 227.114
+{{Optimal ET sequence|legend=1| 16, 21, 37, 206cd }}
-{{Val list|legend=1| 16, 21, 37 }}
+=== 2.5.7.11.13 subgroup ===
-====2.5.7.11.13====
 Subgroup: 2.5.7.11.13
-[[Comma]]: 176/175, 640/637, 1304576/1294139
+Comma list: 176/175, 640/637, 847/845
-[[Gencom]]: [2 8/7; 176/175 640/637, 1304576/1294139]
+Sval mapping: {{mapping| 1 1 3 1 2 | 0 7 -1 13 9 }}
-[[Gencom|Gencom mapping]]: [{{val|1 0 1 3 1 2}}, {{val|0 0 7 -1 13 9}}]
+Gencom mapping: {{mapping| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}
-[[Mapping|Sval mapping]]: [{{val|1 1 3 1 2}}, {{val|0 7 -1 13 9}}]
+: gencom: [2 8/7; 176/175 640/637, 1304576/1294139]
-[[Tp tuning|POL2 generator]]: ~8/7 = 227.108
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.108
-{{Val list|legend=1| 16, 21, 37 }}
+{{Optimal ET sequence|legend=1| 16, 21, 37, 206cdf }}
-====2.5.7.11.13.17====
+[[Tp tuning #T2 tuning|RMS error]]: 0.5433 cents
-Subgroup: 2.5.7.11
-[[Comma]]: 176/175, 221/200, 640/637, 833/832
+=== 2.5.7.11.13.17 subgroup ===
+Subgroup: 2.5.7.11.13.17
-[[Gencom]]: [2 8/7; 176/175 221/200, 640/637, 833/832]
+Comma list: 176/175, 221/220, 640/637, 847/845
-[[Gencom|Gencom mapping]]: [{{val|1 0 1 3 1 2 2}}, {{val|0 0 7 -1 13 9 11}}]
+Sval mapping: {{mapping| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}
-[[Mapping|Sval mapping]]: [{{val|1 1 3 1 2 2}}, {{val|0 7 -1 13 9 11}}]
+Gencom mapping: {{mapping| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}
-[[Tp tuning|POL2 generator]]: ~8/7 = 227.242
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.242
-{{Val list|legend=1| 16, 21, 37 }}
+{{Optimal ET sequence|legend=1| 16, 21, 37, 95 }}
-=== Extensions ===
-Full 7-limit [[extension]]s of llywelyn temperament include:
-* [[Gorgo]], {36/35, 1029/1024} ([[Gamelismic clan #Gorgo|Gamelismic clan]])
-* [[Ultrapyth]], {64/63, 6860/6561} ([[Archytas clan #Ultrapyth|Archytas clan]])
-* [[Buzzard]], {1728/1715, 5120/5103} ([[Vulture family|Vulture]]/[[Hemifamity temperaments #Buzzard|Hemifamity]])
-* [[Semaja]], {3125/3087, 6144/6125} ([[Porwell temperaments #Semaja|Porwell temperaments]])
-* [[Misneb]], {225/224, 4194304/4117715} ([[Marvel temperaments #Misneb|Marvel temperaments]])
-* [[Gorgik]], {2401/2400, 28672/28125} ([[Breedsmic temperaments #Gorgik|Breedsmic temperaments]])
 [[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Llywelynsmic clan| ]] <!-- main article -->
 [[Category:Rank 2]]