Llywelynsmic clan: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The ''' | The '''llywelynsmic clan''' of [[regular temperament|temperaments]] tempers out the no-threes [[llywelyn comma]] ({{monzo|legend=1| 22 0 -1 -7 }}, [[ratio]]: 4194304/4117715 }}. | ||
== Llywelyn a.k.a. shoe == | == Llywelyn a.k.a. shoe == | ||
Llywelyn a.k.a. shoe can be described as the 16 & | Llywelyn a.k.a. shoe can be described as the {{nowrap| 16 & 21 }} temperament. | ||
[[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 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 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~8/7 = 226.910{{c}} | |||
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }} | |||
[[ | === Overview to extensions === | ||
Full 7-limit [[extension]]s of llywelyn temperament include: | |||
* [[Gorgo]] (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]] | |||
* [[Ultrapyth]] (+64/63) → [[Archytas clan #Ultrapyth|Archytas clan]] | |||
* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan]] | |||
* [[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 immediately below is the canonical 2.5.7.11-subgroup to 2.5.7.11.13.17-subgroup extension. | |||
=== 2.5.7.11 subgroup === | === 2.5.7.11 subgroup === | ||
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Comma list: 176/175, 1310720/1294139 | Comma list: 176/175, 1310720/1294139 | ||
Subgroup-val mapping: {{mapping| 1 1 3 1 | 0 7 -1 13 }} | |||
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 ET sequence|legend=0| 16, 21, 37, 206cd }} | |||
{{Optimal ET sequence|legend= | |||
=== 2.5.7.11.13 subgroup === | === 2.5.7.11.13 subgroup === | ||
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Comma list: 176/175, 640/637, 847/845 | Comma list: 176/175, 640/637, 847/845 | ||
Subgroup-val mapping: {{mapping| 1 1 3 1 2 | 0 7 -1 13 9 }} | |||
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 tuning (POTE): ~2 = | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 16, 21, 37, 206cdf }} | ||
RMS error: 0.5433 cents | |||
=== 2.5.7.11.13.17 subgroup === | === 2.5.7.11.13.17 subgroup === | ||
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Comma list: 176/175, 221/220, 640/637, 847/845 | Comma list: 176/175, 221/220, 640/637, 847/845 | ||
Subgroup-val mapping: {{mapping| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }} | |||
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 = | Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~8/7 = 227.242{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 16, 21, 37, 95 }} | ||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Llywelynsmic clan| ]] <!-- main article --> | [[Category:Llywelynsmic clan| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||