Llywelynsmic clan

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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) → Gamelismic clan
• Ultrapyth (+64/63) → Archytas clan
• Buzzard (+1728/1715) → Vulture family
• Semaja (+3125/3087) → Porwell temperaments
• Misneb (+225/224) → Marvel temperaments
• Gorgik (+2401/2400) → Breedsmic temperaments

Discussed below is the 2.5.7 subgroup temperament llywelyn a.k.a. shoe.

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

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): ~2 = 1\1, ~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 mapping: [⟨1 0 1 3 1], ⟨0 0 7 -1 13]]

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

Optimal tuning (POTE): ~2 = 1\1, ~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 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): ~2 = 1\1, ~8/7 = 227.108

Optimal ET sequence: 16, 21, 37, 206cdf

RMS error: 0.5433 cents

2.5.7.11.13.17 subgroup

Subgroup: 2.5.7.11.13.17

Comma list: 176/175, 221/220, 640/637, 847/845

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): ~2 = 1\1, ~8/7 = 227.242

Optimal ET sequence: 16, 21, 37, 95