Llywelynsmic clan

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

Full 7-limit extensions of llywelyn temperament include:

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

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