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