Llywelynsmic 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

Optimal ET sequence: 16, 21, 37