Hemfiness temperaments: Difference between revisions

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-'''Hemfiness''' rank-two temperaments temper out the ''hemfiness'' comma, 4096000/4084101 = {{monzo|15 -5 3 -5}} (saquinru-atriyo), the amount by which a stack of three [[5/4]]s and five [[32/21]]s exceed four octaves.
+{{Technical data page}}
+'''Hemfiness''' rank-two temperaments temper out the ''hemfiness'' comma, [[4096000/4084101]] = {{monzo|15 -5 3 -5}} (saquinru-atriyo), the amount by which a stack of three [[5/4]]s and five [[32/21]]s exceed four octaves.
 Temperaments dicussed elsewhere include:
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 [[Mapping]]: [{{val|1 5 5 1}}, {{val|0 -51 -40 27}}]
-[[POTE generator]]: ~8575/8192 = 80.347
+[[Optimal tuning]] ([[POTE]]): ~8575/8192 = 80.347
-{{Optimal ET sequence|legend=1| 15, 194, 209, 224, 463, 687, 1150d }}
+{{Optimal ET sequence|legend=1| 15, …, 194, 209, 224, 463, 687, 1150d }}
 [[Badness]]: 0.178777
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 POTE generator: ~22/21 = 80.347
-{{Optimal ET sequence|legend=1| 15, 194, 209, 224, 463, 1150de }}
+Optimal ET sequence: {{Optimal ET sequence| 15, …, 194, 209, 224, 463, 1150de }}
 Badness: 0.042318
+== Piracy ==
+{{see also|Very high accuracy temperaments #Pirate}}
+Subgroup: 2.3.5.7
+[[Comma list]]: 4096000/4084101, 48828125/48771072
+[[Mapping]]: [{{val|1 -6 0 9}}, {{val|0 49 15 -40}}]
+[[Optimal tuning]] ([[POTE]]): ~4096/3675 = 185.7609
+{{Optimal ET sequence|legend=1| 71, 84, 155, 239, 323, 885, 1208d, 1531d }}
+[[Badness]]: 0.159305
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 6250/6237, 12005/11979, 16384/16335
+Mapping: [{{val|1 -6 0 9 16}}, {{val|0 49 15 -40 -81}}]
+Optimal tuning (POTE): ~49/44 = 185.7671
+Optimal ET sequence: {{Optimal ET sequence| 84, 155, 239, 562e, 801e }}
+Badness: 0.092173
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 2080/2079, 2205/2197, 12005/11979
+Mapping: [{{val|1 -6 0 9 16 2}}, {{val|0 49 15 -40 -81 11}}]
+Optimal tuning (POTE): ~49/44 = 185.7663
+Optimal ET sequence: {{Optimal ET sequence| 84, 155, 239f }}
+Badness: 0.063719
+==== Pirateship ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 364/363, 1716/1715, 4096/4095, 6250/6237
+Mapping: [{{val|1 -6 0 9 16 15}}, {{val|0 49 15 -40 -81 -73}}]
+Optimal tuning (POTE): ~39/35 = 185.7621
+Optimal ET sequence: {{Optimal ET sequence| 84, 155f, 239, 323e }}
+Badness: 0.073523
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Rank 2]]