Llywelynsmic clan

The llywelyn clan tempers out the no-threes llywelyn comma, [22 0 -1 -7⟩ = 4194304/4117715.

Llywelyn

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]

POTE generator: ~8/7 = 226.910

2.5.7.11

Subgroup: 2.5.7.11

Comma: 176/175, 1310720/1294139

Gencom: [2 8/7; 176/175 1310720/1294139]

Gencom mapping: [⟨1 0 1 3 1], ⟨0 0 7 -1 13]]

Sval mapping: [⟨1 1 3 1], ⟨0 7 -1 13]]

POL2 generator: ~8/7 = 227.114

2.5.7.11.13

Subgroup: 2.5.7.11.13

Comma: 176/175, 640/637, 1304576/1294139

Gencom: [2 8/7; 176/175 640/637, 1304576/1294139]

Gencom mapping: [⟨1 0 1 3 1 2], ⟨0 0 7 -1 13 9]]

Sval mapping: [⟨1 1 3 1 2], ⟨0 7 -1 13 9]]

POL2 generator: ~8/7 = 227.108

2.5.7.11.13.17

Subgroup: 2.5.7.11

Comma: 176/175, 221/200, 640/637, 833/832

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]]

Sval mapping: [⟨1 1 3 1 2 2], ⟨0 7 -1 13 9 11]]

POL2 generator: ~8/7 = 227.242

Extensions

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/Hemifamity)
• Semaja, {3125/3087, 6144/6125} (Porwell temperaments)
• Misneb, {225/224, 4194304/4117715} (Marvel temperaments)
• Gorgik, {2401/2400, 28672/28125} (Breedsmic temperaments)