Mint family: Difference between revisions

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-The mint temperament tempers out [[36/35|36/35]], identifying both [[7/6|7/6]] with [[6/5|6/5]] and [[5/4|5/4]] with [[9/7|9/7]].
+{{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]].
-[[Comma|Comma]]: 36/35
+== Mint  ==
+[[Subgroup]]: 2.3.5.7
-Map: [&lt;1 0 0 2|, &lt;0 1 0 2|, &lt;0 0 1 -1|]
+[[Comma list]]: 36/35
-EDOs: [[4edo|4]], [[5edo|5]], [[7edo|7]], [[9edo|9]], [[12edo|12]]
+{{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }}
-[[Badness|Badness]]: 0.0000637
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809
-==Nickel==
+{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }}
-Commas: 36/35, 45/44
-Map: [&lt;1 0 0 2 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 -1 1|]
+[[Badness]]: 0.0637 × 10<sup>-3</sup>
-EDOs: 7, 9, 12, [[21edo|21]], [[28edo|28]]
+== Nickel  ==
+[[Subgroup]]: 2.3.5.7.11
-Badness: 0.000463
+[[Comma list]]: 36/35, [[45/44]]
-===13-limit===
+{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }}
-Commas: 27/26, 36/35, 45/44
-Map: [&lt;1 0 0 2 -2 -1|, &lt;0 1 0 2 2 3|, &lt;0 0 1 -1 1 0|]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801
-EDOs: 7, 9, [[16edo|16]], 21, 28
+{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }}
-Badness: 0.000647
+[[Badness]]: 0.463 × 10<sup>-3</sup>
-[[Category:Theory]]
+=== 13-limit  ===
-[[Category:Family]]
+Subgroup: 2.3.5.7.11.13
-[[Category:Mint]]
-[[Category:Quartonic]]
+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 }}
+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>
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Mint family| ]] <!-- main article -->
+[[Category:Mint| ]] <!-- key article -->
+[[Category:Rank 3]]