Mint family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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== Mint == | == Mint == | ||
[[Subgroup]]: 2.3.5.7 | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 36/35 | [[Comma list]]: 36/35 | ||
{{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809 | ||
{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }} | {{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }} | ||
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== Nickel == | == Nickel == | ||
[[Subgroup]]: 2.3.5.7.11 | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 36/35, [[45/44]] | [[Comma list]]: 36/35, [[45/44]] | ||
{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801 | ||
{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }} | {{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }} | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: [[27/26]], 36/35, 45/44 | Comma list: [[27/26]], 36/35, 45/44 | ||
Mapping: | Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 685.0048, ~5/4 = 390.2563 | ||
{{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }} | {{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Mint]] | [[Category:Mint family| ]] <!-- main article --> | ||
[[Category:Mint| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] |
Revision as of 05:58, 5 August 2023
The mint family of rank-3 temperaments tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.
Mint
Subgroup: 2.3.5.7
Comma list: 36/35
Mapping: [⟨1 0 0 2], ⟨0 1 0 2], ⟨0 0 1 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809
Optimal ET sequence: 4, 5, 7, 8d, 9, 12
Badness: 0.0637 × 10-3
Nickel
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44
Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 2 2], ⟨0 0 1 -1 1]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801
Optimal ET sequence: 7, 9, 12, 21, 28
Badness: 0.463 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44
Mapping: [⟨1 0 0 2 -2 -1], ⟨0 1 0 2 2 3], ⟨0 0 1 -1 1 0]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 685.0048, ~5/4 = 390.2563
Optimal ET sequence: 7, 9, 12f, 16, 21, 28
Badness: 0.647 × 10-3