Meantone family: Difference between revisions

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== Superpine ==

Suprpine is a temperament generated by 1/3 of a fourth 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. [[43edo]] is ~~an especially~~ good tuning.

Suprpine is a temperament 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.

[[Comma list]]: 81/80, 1119744/1071875

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[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~35/32 = 167.407

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/10 = 167.407

[[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d, 79ce}}

[[Badness]]: 3.459

=== 13-limit ===

[[Comma list]]: 78/77, 144/143, 176/175, 81/80

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/10 = 167.427

[[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d, 79ce}}

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 == Superpine ==
-Suprpine is a temperament generated by 1/3 of a fourth 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. [[43edo]] is an especially good tuning.
+Suprpine is a temperament 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.
 [[Comma list]]: 81/80, 1119744/1071875
@@ Line 2,247: / Line 2,247: @@
 {{Mapping|1 2 4 1|0 -3 -12 -13 -11}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~35/32 = 167.407
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/10 = 167.407
+[[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d, 79ce}}
+[[Badness]]: 3.459
+=== 13-limit ===
+[[Comma list]]: 78/77, 144/143, 176/175, 81/80
+{{Mapping|1 2 4 1|0 -3 -12 -13 -11}}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11/10 = 167.427
 [[Support]]ing [[ET]]s: {{EDOs|7, 43, 36, 50d, 79ce}}