Mint family: Difference between revisions

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-The '''mint family''' of rank-3 temperaments tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].
+{{Technical data page}}
+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
 [[Comma list]]: 36/35
-[[Mapping]]: [{{val| 1 0 0 2 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 -1 }}]
+{{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }}
+: mapping generators: ~2, ~3, ~5
-[[POTE generator]]s: ~3/2 = 698.6351, ~5/4 = 404.2809
-{{Val list|legend=1| 4, 5, 7, 8d, 9, 12 }}
-[[Badness]]: 0.0637 × 10<sup>-3</sup>
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1196.3575{{c}}, ~3/2 = 696.5144{{c}}, ~5/4 = 403.0537{{c}}
+: [[error map]]: {{val| -3.643 -9.083 +9.455 +13.864 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}}
+: error map: {{val| 0.000 -6.708 +14.813 +20.543 }}
-= Nickel =
+{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }}
-Subgroup: 2.3.5.7.11
+[[Badness]] (Sintel): 0.281
-[[Comma list]]: 36/35, [[45/44]]
+== Nickel ==
+[[Subgroup]]: 2.3.5.7.11
-[[Mapping]]: [{{val| 1 0 0 2 -2 }}, {{val| 0 1 0 2 2 }}, {{val| 0 0 1 -1 1 }}]
+[[Comma list]]: 36/35, 45/44
-[[POTE generator]]s: ~3/2 = 688.8370, ~5/4 = 391.8801
+{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }}
-{{Val list|legend=1| 7, 9, 12, 21, 28 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1198.7814{{c}}, ~3/2 = 688.1375{{c}}, ~5/4 = 391.4822{{c}}
+: [[error map]]: {{val| -1.219 -15.036 +2.731 +13.530 +14.002 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}}
+: error map: {{val| 0.000 -13.956 +4.914 +15.945 +15.908 }}
-[[Badness]]: 0.463 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }}
-== 13-limit ==
+[[Badness]] (Sintel): 0.557
+=== 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: [{{val| 1 0 0 2 -2 -1 }}, {{val| 0 1 0 2 2 3 }}, {{val| 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 }}
-POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563
+Optimal tunings:
+* WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}}
-{{Val list|legend=1| 7, 9, 12f, 16, 21, 28 }}
+{{Optimal ET sequence|legend=0| 7, 9, 12f, 16, 21, 28, 37b }}
-Badness: 0.647 × 10<sup>-3</sup>
+Badness (Sintel): 0.605
-[[Category:Theory]]
+[[Category:Mint family| ]] <!-- main article -->
-[[Category:Temperament family]]
+[[Category:Temperament families]]
-[[Category:Mint]]
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]