Mint family: Difference between revisions
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m Removing from Category:Regular temperament theory using Cat-a-lot |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]s: ~3/2 = 698.6351, ~5/4 = 404.2809 | [[POTE generator]]s: ~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> | ||
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[[POTE generator]]s: ~3/2 = 688.8370, ~5/4 = 391.8801 | [[POTE generator]]s: ~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> | ||
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POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563 | POTE generators: ~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> | ||
Revision as of 18:09, 7 May 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]]
POTE generators: ~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]]
POTE generators: ~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]]
POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563
Optimal ET sequence: 7, 9, 12f, 16, 21, 28
Badness: 0.647 × 10-3