Hemimean clan: Difference between revisions

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-The '''hemimean clan''', tempering out the no-threes hemimean comma [[3136/3125]], contains the temperaments misty and semisept, considered below, as well as [[Meantone family #Septimal meantone|meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Gamelismic clan #Hemithirds|hemithirds]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere.
+The '''hemimean clan''', tempering out the no-threes hemimean comma [[3136/3125]], contains the temperaments hemithirds, misty, and semisept, considered below, as well as [[Meantone family #Septimal meantone|meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere.
 = Didacus =
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 {{Val list|legend=1| 6, 19, 25, 31, 99, 130, 161, 353, 514c }}
+= Hemithirds =
+{{main| Hemithirds }}
+{{see also| Luna family #Hemithirds }}
+Subgroup: 2.3.5.7
+[[Comma list]]: 1029/1024, 3136/3125
+[[Mapping]]: [{{val| 1 4 2 2 }}, {{val| 0 -15 2 5 }}]
+{{Multival|legend=1| 15 -2 -5 -38 -50 -6 }}
+[[POTE generator]]: ~28/25 = 193.244
+[[Minimax tuning]]:
+* [[7-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
+: [[Eigenmonzo]]s: 2, 7/6
+* [[9-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
+: [[Eigenmonzo]]s: 2, 7/6
+{{Val list|legend=1| 31, 87, 118 }}
+Badness: 0.0443
+== 11-limit ==
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 441/440, 3136/3125
+Mapping: [{{val| 1 4 2 2 7 }}, {{val| 0 -15 2 5 -22 }}]
+POTE generator: ~28/25 = 193.227
+Minimax tuning:
+* 11-odd-limit
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
+: Eigenmonzos: 2, 11/7
+{{Val list|legend=1| 31, 87, 118 }}
+Badness: 0.0190
+== 13-limit ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 196/195, 352/351, 385/384, 625/624
+Mapping: [{{val| 1 4 2 2 7 0 }}, {{val| 0 -15 2 5 -22 23 }}]
+POTE generator: ~28/25 = 193.166
+{{Val list|legend=1| 31, 56, 87, 118, 205d }}
+Badness: 0.0217
 = Misty =