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 ¢