Meantone family: Difference between revisions

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 Badness: 0.036144
+== Superpine ==
+The superpine temperament is generated by 1/3 of a fourth, represented by [[35/32]], which resembles [[porcupine]], but it favors flat fifths instead of sharp ones. Unlike in porcupine, the minor third reached by 2 generators up is strongly neutral-flavored and does not represent [[6/5]]–harmonics other than 3 all require the 15-tone mos to properly utilize. This temperament has an obvious 11-limit interpretation by treating the generator as [[11/10]] as in porcupine, which makes [[11/8]] high-[[complexity]] like the other harmonics, but in the 13-limit 5 generators up closely approximates [[13/8]]. [[43edo]] is a good tuning especially for the higher-limit extensions.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 81/80, 1119744/1071875
+{{Mapping|legend=1| 1 2 4 1 | 0 -3 -12 -13 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~35/32 = 167.279
+{{Optimal ET sequence|legend=1| 7, 36, 43, 79c }}
+[[Badness]]: 0.137
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 81/80, 176/175, 864/847
+Mapping: {{mapping| 1 2 4 1 5 | 0 -3 -12 -13 -11 }}
+Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.407
+Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
+Badness: 0.0576
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 78/77, 81/80, 144/143, 176/175
+Mapping: {{mapping| 1 2 4 1 5 3 | 0 -3 -12 -13 -11 5 }}
+Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 167.427
+Optimal ET sequence: {{Optimal ET sequence| 7, 36, 43 }}
+Badness: 0.0368
 == Lithium ==
@@ Line 2,228: / Line 2,269: @@
 Badness: 0.048829
-== Superpine ==
-The ''superpine'' temperament is generated by 1/3 of a fourth, represented by [[35/32]], which resembles [[porcupine]], but it favors flat fifths instead of sharp ones. Unlike in porcupine, the minor third reached by 2 generators up is strongly neutral-flavored and does not represent [[6/5]]–harmonics other than 3 all require the 15-tone MOS to properly utilize. This temperament has an obvious 11-limit interpretation by treating the generator as [[11/10]] as in porcupine, which makes [[11/8]] high-[[complexity]] like the other harmonics, but in the 13-limit 5 generators up closely approximates [[13/8]]. [[43edo]] is a good tuning especially for the higher-limit extensions.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 81/80, 1119744/1071875
-{{Mapping|1 2 4 1|0 -3 -12 -13}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~35/32 = 167.279
-[[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d, 79c}}
-[[Badness]]: 3.459
-=== 11-limit ===
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 176/175, 81/80, 864/847
-{{Mapping|1 2 4 1 5|0 -3 -12 -13 -11}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/10 = 167.407
-[[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d, 79ce}}
-[[Badness]]: 1.905
-=== 13-limit ===
-[[Subgroup]]: 2.3.5.7.11.13
-[[Comma list]]: 78/77, 144/143, 176/175, 81/80
-{{Mapping|1 2 4 1 5 3|0 -3 -12 -13 -11 5}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/10 = 167.427
-[[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d}}
-[[Badness]]: 1.521
 [[Category:Temperament families]]