Llywelynsmic clan: Difference between revisions

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Cmloegcmluin (talk | contribs)
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Godtone (talk | contribs)
m fix. also gencom is wrong and idk how to calculate it so i removed it for no-3's 17-limit
Line 28: Line 28:
[[Optimal tuning]] ([[POTE]]): ~8/7 = 226.910
[[Optimal tuning]] ([[POTE]]): ~8/7 = 226.910


{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}


=== 2.5.7.11 subgroup ===
=== 2.5.7.11 subgroup ===
Line 43: Line 43:
Optimal tuning (POTE): ~8/7 = 227.114
Optimal tuning (POTE): ~8/7 = 227.114


{{Optimal ET sequence|legend=1| 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 16, 21, 37, 206cd }}


=== 2.5.7.11.13 subgroup ===
=== 2.5.7.11.13 subgroup ===
Line 58: Line 58:
Optimal tuning (POTE): ~8/7 = 227.108
Optimal tuning (POTE): ~8/7 = 227.108


{{Optimal ET sequence|legend=1| 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 16, 21, 37, 206cdf }}


=== 2.5.7.11.13.17 subgroup ===
=== 2.5.7.11.13.17 subgroup ===
Subgroup: 2.5.7.11.13.17
Subgroup: 2.5.7.11.13.17


Comma list: 176/175, 221/200, 640/637, 833/832
Comma list: 176/175, 640/637, 847/845, 221/220


Sval mapping: [{{val| 1 1 3 1 2 2 }}, {{val| 0 7 -1 13 9 11 }}]
Sval mapping: [{{val| 1 1 3 1 2 2 }}, {{val| 0 7 -1 13 9 11 }}]
Gencom: [2 8/7; 176/175 221/200, 640/637, 833/832]


Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 0 7 -1 13 9 11 }}]
Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 0 7 -1 13 9 11 }}]
Line 73: Line 71:
Optimal tuning (POTE): ~8/7 = 227.242
Optimal tuning (POTE): ~8/7 = 227.242


{{Optimal ET sequence|legend=1| 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 16, 21, 37, 95 }}


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Llywelyn clan| ]] <!-- main article -->
[[Category:Llywelyn clan| ]] <!-- main article -->

Revision as of 19:01, 1 August 2024

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 aka shoe.

Llywelyn aka 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 sequence5, 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: [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 sequence16, 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: [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 sequence16, 21, 37, 206cdf

2.5.7.11.13.17 subgroup

Subgroup: 2.5.7.11.13.17

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

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): ~8/7 = 227.242

Optimal ET sequence16, 21, 37, 95