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|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 ==

[[Subgroup]]: 2.3.5.7

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[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 698.6351, ~5/4 = 404.2809

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 698.6351{{c}}, ~5/4 = 404.2809{{c}}

[[Badness]]: 0.0637 × 10-3

[[Badness]] (Smith): 0.0637 × 10-3

== Nickel ==

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 36/35, [[45/44]]

[[Comma list]]: 36/35, 45/44

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 688.8370, ~5/4 = 391.8801

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 688.8370{{c}}, ~5/4 = 391.8801{{c}}

[[Badness]]: 0.463 × 10-3

[[Badness]] (Smith): 0.463 × 10-3

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: [[27/26]], 36/35, 45/44

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 tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}

Badness: 0.647 × 10-3

Badness (Smith): 0.647 × 10-3

[[Category:Temperament families]]

@@ Line 1: / Line 1: @@
 {{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]].
+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
@@ Line 9: / Line 9: @@
 {{Mapping|legend=1| 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 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 }}
-[[Badness]]: 0.0637 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.0637 × 10<sup>-3</sup>
-== Nickel  ==
+== Nickel ==
 [[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 36/35, [[45/44]]
+[[Comma list]]: 36/35, 45/44
 {{Mapping|legend=1| 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 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 }}
-[[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
-Comma list: [[27/26]], 36/35, 45/44
+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 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 }}
-Badness: 0.647 × 10<sup>-3</sup>
+Badness (Smith): 0.647 × 10<sup>-3</sup>
 [[Category:Temperament families]]