Mint family: Difference between revisions
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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]]. | 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]]. | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Mint family| ]] <!-- main article --> | [[Category:Mint family| ]] <!-- main article --> | ||
[[Category:Mint| ]] <!-- key article --> | [[Category:Mint| ]] <!-- key article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 00:41, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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