Llywelynsmic clan: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
m fix. also gencom is wrong and idk how to calculate it so i removed it for no-3's 17-limit |
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[[Optimal tuning]] ([[POTE]]): ~8/7 = 226.910 | [[Optimal tuning]] ([[POTE]]): ~8/7 = 226.910 | ||
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37 }} | {{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }} | ||
=== 2.5.7.11 subgroup === | === 2.5.7.11 subgroup === | ||
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Optimal tuning (POTE): ~8/7 = 227.114 | Optimal tuning (POTE): ~8/7 = 227.114 | ||
{{Optimal ET sequence|legend=1| 16, 21, 37 }} | {{Optimal ET sequence|legend=1| 16, 21, 37, 206cd }} | ||
=== 2.5.7.11.13 subgroup === | === 2.5.7.11.13 subgroup === | ||
| Line 58: | Line 58: | ||
Optimal tuning (POTE): ~8/7 = 227.108 | Optimal tuning (POTE): ~8/7 = 227.108 | ||
{{Optimal ET sequence|legend=1| 16, 21, 37 }} | {{Optimal ET sequence|legend=1| 16, 21, 37, 206cdf }} | ||
=== 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, | Comma list: 176/175, 640/637, 847/845, 221/220 | ||
Sval mapping: [{{val| 1 1 3 1 2 2 }}, {{val| 0 7 -1 13 9 11 }}] | Sval mapping: [{{val| 1 1 3 1 2 2 }}, {{val| 0 7 -1 13 9 11 }}] | ||
Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 0 7 -1 13 9 11 }}] | Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 0 7 -1 13 9 11 }}] | ||
| Line 73: | Line 71: | ||
Optimal tuning (POTE): ~8/7 = 227.242 | Optimal tuning (POTE): ~8/7 = 227.242 | ||
{{Optimal ET sequence|legend=1| 16, 21, 37 }} | {{Optimal ET sequence|legend=1| 16, 21, 37, 95 }} | ||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Llywelyn clan| ]] <!-- main article --> | [[Category:Llywelyn clan| ]] <!-- main article --> | ||
Revision as of 19:01, 1 August 2024
The llywelyn clan tempers out the no-threes llywelyn comma, [22 0 -1 -7⟩ = 4194304/4117715.
Full 7-limit extensions of llywelyn temperament include:
- Gorgo, {36/35, 1029/1024} → Gamelismic clan
- Ultrapyth, {64/63, 6860/6561} → Archytas clan
- Buzzard, {1728/1715, 5120/5103} → Vulture family / Hemifamity temperaments
- Semaja, {3125/3087, 6144/6125} → Porwell temperaments
- Misneb, {225/224, 4194304/4117715} → Marvel temperaments
- Gorgik, {2401/2400, 28672/28125} → Breedsmic temperaments
Discussed below is the 2.5.7 subgroup temperament llywelyn aka shoe.
Llywelyn aka shoe
Subgroup: 2.5.7
Comma list: 4194304/4117715
Sval mapping: [⟨1 1 3], ⟨0 7 -1]]
Mapping generators: 2, ~8/7
Gencom mapping: [⟨1 0 1 3], ⟨0 0 7 -1]]
Gencom: [2 8/7; 4194304/4117715]
Optimal tuning (POTE): ~8/7 = 226.910
Optimal ET sequence: 5, 11c, 16, 21, 37, 164d
2.5.7.11 subgroup
Subgroup: 2.5.7.11
Comma list: 176/175, 1310720/1294139
Sval mapping: [⟨1 1 3 1], ⟨0 7 -1 13]]
Gencom: [2 8/7; 176/175 1310720/1294139]
Gencom mapping: [⟨1 0 1 3 1], ⟨0 0 7 -1 13]]
Optimal tuning (POTE): ~8/7 = 227.114
Optimal ET sequence: 16, 21, 37, 206cd
2.5.7.11.13 subgroup
Subgroup: 2.5.7.11.13
Comma list: 176/175, 640/637, 847/845
Sval mapping: [⟨1 1 3 1 2], ⟨0 7 -1 13 9]]
Gencom: [2 8/7; 176/175 640/637, 1304576/1294139]
Gencom mapping: [⟨1 0 1 3 1 2], ⟨0 0 7 -1 13 9]]
Optimal tuning (POTE): ~8/7 = 227.108
Optimal ET sequence: 16, 21, 37, 206cdf
2.5.7.11.13.17 subgroup
Subgroup: 2.5.7.11.13.17
Comma list: 176/175, 640/637, 847/845, 221/220
Sval mapping: [⟨1 1 3 1 2 2], ⟨0 7 -1 13 9 11]]
Gencom mapping: [⟨1 0 1 3 1 2 2], ⟨0 0 7 -1 13 9 11]]
Optimal tuning (POTE): ~8/7 = 227.242
Optimal ET sequence: 16, 21, 37, 95