Mint family: Difference between revisions
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The '''mint family''' of rank-3 temperaments tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]]. | 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 = | == Mint == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[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 | ||
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[[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 | ||
Revision as of 21:48, 1 June 2021
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]]
POTE generators: ~3/2 = 698.6351, ~5/4 = 404.2809
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]]
POTE generators: ~3/2 = 688.8370, ~5/4 = 391.8801
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]]
POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563
Badness: 0.647 × 10-3