Octagar temperaments: Difference between revisions

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 Badness: 0.028492
+== Quintupole ==
+The ''quintupole'' temperament tempers out the octagar comma and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents).
+Subgroup: 2.3.5.7
+[[Comma list]]: 4000/3969, 458752/455625
+[[Mapping]]: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]
+{{Multival|legend=1| 5 -16 -34 -37 -68 -34 }}
+[[POTE generator]]: ~135/128 = 99.175
+{{Vals|legend=1| 12, 97, 109, 121 }}
+[[Badness]]: 0.111620
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 896/891, 1375/1372, 4375/4356
+Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]
+POTE generator: ~132/125 = 99.156
+Vals: {{Val list| 12, 109, 121, 351bde, 472bdee }}
+Badness: 0.056501
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 352/351, 364/363, 625/624, 2704/2695
+Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]
+POTE generator: ~55/52 = 99.165
+Vals: {{Val list| 12f, 109, 121 }}
+Badness: 0.038431
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 256/255, 352/351, 364/363, 375/374, 442/441
+Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]
+POTE generator: ~18/17 = 99.172
+Vals: {{Val list| 12f, 109, 121 }}
+Badness: 0.028721
 [[Category:Temperament collection]]
 [[Category:Rank 2]]