Llywelyn clan
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
- See also: Chromatic pairs #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
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
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
2.5.7.11.13.17 subgroup
Subgroup: 2.5.7.11.13.17
Comma list: 176/175, 221/200, 640/637, 833/832
Sval mapping: [⟨1 1 3 1 2 2], ⟨0 7 -1 13 9 11]]
Gencom: [2 8/7; 176/175 221/200, 640/637, 833/832]
Gencom mapping: [⟨1 0 1 3 1 2 2], ⟨0 0 7 -1 13 9 11]]
Optimal tuning (POTE): ~8/7 = 227.242