Nuwell family: Difference between revisions
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Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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== Nuwell == | == Nuwell == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 2430/2401 | [[Comma list]]: 2430/2401 | ||
{{Mapping|legend=1| 1 0 3 1 | 0 1 3 2 | 0 0 -4 -1 }} | |||
: mapping generators: ~2, ~3, ~18/7 | |||
{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137 }} | {{Optimal ET sequence|legend=1| 9, 22, 31, 53, 84, 137 }} | ||
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[[Projection pair]]: 5 2401/486 to 2.3.7 | [[Projection pair]]: 5 2401/486 to 2.3.7 | ||
== Big | == Big brother == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 99/98, 121/120 | [[Comma list]]: 99/98, 121/120 | ||
{{Mapping|legend=1| 1 0 3 1 3 | 0 1 3 2 2 | 0 0 -4 -1 -2 }} | |||
{{Optimal ET sequence|legend=1| 8d, 9, 22, 31, 53 }} | {{Optimal ET sequence|legend=1| 8d, 9, 22, 31, 53 }} | ||
| Line 32: | Line 34: | ||
Comma list: 66/65, 99/98, 121/120 | Comma list: 66/65, 99/98, 121/120 | ||
Mapping: | Mapping: {{mapping| 1 0 3 1 3 1 | 0 1 3 2 2 0 | 0 0 -4 -1 -2 2 }} | ||
{{Optimal ET sequence|legend=1| 8d, 9, 22f, 31 }} | {{Optimal ET sequence|legend=1| 8d, 9, 22f, 31 }} | ||
Revision as of 03:03, 7 September 2023
The nuwell family of rank-3 temperaments temper out the nuwell comma, 2430/2401.
Nuwell
Subgroup: 2.3.5.7
Comma list: 2430/2401
Mapping: [⟨1 0 3 1], ⟨0 1 3 2], ⟨0 0 -4 -1]]
- mapping generators: ~2, ~3, ~18/7
Optimal ET sequence: 9, 22, 31, 53, 84, 137
Badness: 0.519 × 10-3
Projection pair: 5 2401/486 to 2.3.7
Big brother
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120
Mapping: [⟨1 0 3 1 3], ⟨0 1 3 2 2], ⟨0 0 -4 -1 -2]]
Optimal ET sequence: 8d, 9, 22, 31, 53
Badness: 0.507 × 10-3
Projection pairs: 5 2401/486 11 98/9 to 2.3.7
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 121/120
Mapping: [⟨1 0 3 1 3 1], ⟨0 1 3 2 2 0], ⟨0 0 -4 -1 -2 2]]
Optimal ET sequence: 8d, 9, 22f, 31