Mint family: Difference between revisions
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The '''mint family''' of rank-3 | {{Technical data page}} | ||
The '''mint family''' of [[rank-3 temperament]]s tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]]. | |||
= 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 }} | ||
[[Badness]]: 0.0637 × 10<sup>-3</sup> | [[Badness]]: 0.0637 × 10<sup>-3</sup> | ||
= 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 }} | ||
[[Badness]]: 0.463 × 10<sup>-3</sup> | [[Badness]]: 0.463 × 10<sup>-3</sup> | ||
== 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 }} | ||
Badness: 0.647 × 10<sup>-3</sup> | Badness: 0.647 × 10<sup>-3</sup> | ||
[[Category: | [[Category:Temperament families]] | ||
[[Category: | [[Category:Pages with mostly numerical content]] | ||
[[Category:Mint]] | [[Category:Mint family| ]] <!-- main article --> | ||
[[Category:Mint| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||