Mint family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''mint family''' of [[rank-3 temperament]] | The '''mint family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|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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{{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }} | {{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 698.6351{{c}}, ~5/4 = 404.2809{{c}} | ||
{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }} | {{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }} | ||
[[Badness]]: 0.0637 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.0637 × 10<sup>-3</sup> | ||
== Nickel | == Nickel == | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 36/35, | [[Comma list]]: 36/35, 45/44 | ||
{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }} | {{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 688.8370{{c}}, ~5/4 = 391.8801{{c}} | ||
{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }} | {{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }} | ||
[[Badness]]: 0.463 × 10<sup>-3</sup> | [[Badness]] (Smith): 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: | Comma list: 27/26, 36/35, 45/44 | ||
Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }} | Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}} | ||
{{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }} | {{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }} | ||
Badness: 0.647 × 10<sup>-3</sup> | Badness (Smith): 0.647 × 10<sup>-3</sup> | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
Revision as of 13:01, 19 November 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 = 1200.0000 ¢, ~3/2 = 698.6351 ¢, ~5/4 = 404.2809 ¢
Optimal ET sequence: 4, 5, 7, 8d, 9, 12
Badness (Smith): 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 = 1200.0000 ¢, ~3/2 = 688.8370 ¢, ~5/4 = 391.8801 ¢
Optimal ET sequence: 7, 9, 12, 21, 28
Badness (Smith): 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 = 1200.0000 ¢, ~3/2 = 685.0048 ¢, ~5/4 = 390.2563 ¢
Optimal ET sequence: 7, 9, 12f, 16, 21, 28
Badness (Smith): 0.647 × 10-3