Fractional-octave temperaments: Difference between revisions

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 Badness: 0.036267
+==80th-octave temperaments==
+=== Mercury ===
+Defined as 720 & 1600, and named after the 80th element, because a simpler temperament is already named octogintic.
+Subgroup: 2.3.5
+Comma list: {{monzo|-1377 400 320}}
+Mapping: [{{val|80 1 343}}, {{val|0 4 -5}}]
+Mapping generators: {{monzo|-568 165 132}}, {{monzo|142 -41 -33}}
+Optimal tuning (CTE): ~{{monzo|142 -41 -33}} = 471.738
+==== 7-limit ====
+Subgroup: 2.3.5.7
+Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625
+Mapping:[{{val| 80 1 343 -27}}, {{val|0 4 -5 8}}]
+Mapping generators: ~31637227888/31381059609, ~7381125/5619712
+Optimal tuning (CTE): ~7381125/5619712 = 471.734
+==== 11-limit ====
+Subgroup: 2.3.5.7.11
+Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125
+Mapping:[{{val|80 1 343 -27 434}}, {{val|0 4 -5 8 5}}]
+Mapping generators: ~262144/259875, ~2278125/1734656
+Optimal tuning (CTE): ~2278125/1734656 = 471.734
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143
+Mapping: [{{val|80 1 343 -27 434 13}}, {{val|0 4 -5 8 5 9}}]
+Mapping generators: ~77760/77077, ~130/99
+Optimal tuning (CTE): ~130/99 = 471.734
 == 91st-octave temperaments ==