Fractional-octave temperaments: Difference between revisions

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@@ Line 360: / Line 360: @@
 Badness: 0.036267
-==80th-octave temperaments==
+== 80th-octave temperaments ==
 === Mercury ===
-Defined as 720 & 1600, and named after the 80th element, because a simpler temperament is already named octogintic.
+Mercury is described as 720 & 1600, and named after the 80th element, as a simpler temperament is already named octogintic.
-Subgroup: 2.3.5
+[[Subgroup]]: 2.3.5.7
-Comma list: {{monzo|-1377 400 320}}
+[[Comma list]]: {{monzo| -52 17 12 -1 }}, {{monzo| 25 42 -8 -26 }}
-Mapping: [{{val|80 1 343}}, {{val|0 4 -5}}]
+[[Mapping]]: [{{val| 80 1 343 -27 }}, {{val| 0 4 -5 8 }}]
-Mapping generators: {{monzo|-568 165 132}}, {{monzo|142 -41 -33}}
+Mapping generators: ~31637227888/31381059609, ~7381125/5619712
-Optimal tuning (CTE): ~{{monzo|142 -41 -33}} = 471.738
-==== 7-limit ====
-Subgroup: 2.3.5.7
-Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625
+[[Optimal tuning]] ([[CTE]]): ~7381125/5619712 = 471.7339
-Mapping:[{{val| 80 1 343 -27}}, {{val|0 4 -5 8}}]
+{{Val list|legend=1| 720, 1600, 2320, 3920 }}
-Mapping generators: ~31637227888/31381059609, ~7381125/5619712
+[[Badness]]: 1.49
-Optimal tuning (CTE): ~7381125/5619712 = 471.734
 ==== 11-limit ====
 Subgroup: 2.3.5.7.11
-Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125
+Comma list: 9801/9800, 928760463360/928426965851, {{monzo| 49 -13 -14 -1 2 }}
-Mapping:[{{val|80 1 343 -27 434}}, {{val|0 4 -5 8 5}}]
+Mapping: [{{val| 80 1 343 -27 434 }}, {{val| 0 4 -5 8 -5 }}]
-Mapping generators: ~262144/259875, ~2278125/1734656
+Optimal tuning (CTE): ~2278125/1734656 = 471.7342
-Optimal tuning (CTE): ~2278125/1734656 = 471.734
+Optimal GPV sequence: {{Val list| 720, 1600, 2320, 3920 }}
+Badness: 0.178
 ==== 13-limit ====
@@ Line 401: / Line 396: @@
 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: [{{val| 80 1 343 -27 434 13 }}, {{val| 0 4 -5 8 -5 9 }}]
+Optimal tuning (CTE): ~130/99 = 471.7322
-Mapping generators: ~77760/77077, ~130/99
+Optimal GPV sequence: {{Val list| 720, 1600, 2320, 3920 }}
-Optimal tuning (CTE): ~130/99 = 471.734
+Badness: 0.0741
 == 91st-octave temperaments ==