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 llywelynsmic clan of temperaments tempers out the no-threes llywelyn comma (monzo: [22 0 -1 -7⟩, ratio: 4194304/4117715 }}.

Llywelyn a.k.a. shoe

Llywelyn a.k.a. shoe can be described as the 16 & 21 temperament.

Subgroup: 2.5.7

Comma list: 4194304/4117715

Subgroup-val mapping: [⟨1 1 3], ⟨0 7 -1]]

mapping generators: ~2, ~8/7

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

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~8/7 = 226.910 ¢

Optimal ET sequence: 5, 11c, 16, 21, 37, 164d

Overview to extensions

Full 7-limit extensions of llywelyn temperament include:

• Gorgo (+36/35) → Gamelismic clan
• Ultrapyth (+64/63) → Archytas clan
• Buzzard (+1728/1715) → Buzzardsmic clan
• Semaja (+3125/3087) → Porwell temperaments
• Misneb (+225/224) → Marvel temperaments
• Gorgik (+2401/2400) → Breedsmic temperaments

Discussed immediately below is the canonical 2.5.7.11-subgroup to 2.5.7.11.13.17-subgroup extension.

2.5.7.11 subgroup

Subgroup: 2.5.7.11

Comma list: 176/175, 1310720/1294139

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

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

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~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

Subgroup-val 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]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~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

Subgroup-val 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 = 1200.000 ¢, ~8/7 = 227.242 ¢

Optimal ET sequence: 16, 21, 37, 95