Quartonic family: Difference between revisions

Godtone (talk | contribs)
Biquartonic: add pretty obvious 19-limit extension
Godtone (talk | contribs)
Quartiquart: add pretty obvious 17- and 19-limit extensions
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{{Multival|legend=1| 44 72 100 12 35 30 }}
{{Multival|legend=1| 44 72 100 12 35 30 }}


[[Optimal tuning]] ([[CTE]]): ~25/21 = 1\4, ~250/243 = 45.2411
[[Optimal tuning]] ([[CTE]]): ~25/21 = 1\4, ~250/243 = 45.2411


{{Optimal ET sequence|legend=1| 80, 132d, 212, 292, 504 }}
{{Optimal ET sequence|legend=1| 80, 132d, 212, 292, 504 }}
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Mapping: {{mapping| 4 8 12 15 17 | 0 -11 -18 -25 -21 }}
Mapping: {{mapping| 4 8 12 15 17 | 0 -11 -18 -25 -21 }}


Optimal tuning (CTE): ~25/21 = 1\4, ~77/75 = 45.2303
Optimal tuning (CTE): ~25/21 = 1\4, ~77/75 = 45.2303


Optimal ET sequence: {{Optimal ET sequence| 80, 132de, 212, 292, 504e }}
Optimal ET sequence: {{Optimal ET sequence| 80, 132de, 212, 292, 504e }}
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Mapping: {{mapping| 4 8 12 15 17 16 | 0 -11 -18 -25 -21 -8 }}
Mapping: {{mapping| 4 8 12 15 17 16 | 0 -11 -18 -25 -21 -8 }}


Optimal tuning (CTE): ~25/21 = 1\4, ~77/75 = 45.2243
Optimal tuning (CTE): ~25/21 = 1\4, ~40/39 = 45.2243


Optimal ET sequence: {{Optimal ET sequence| 80, 212, 292f, 504eff }}
Optimal ET sequence: {{Optimal ET sequence| 80, 212, 292f, 504eff }}


Badness: 0.045028
Badness: 0.045028
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 325/324, 1001/1000, 1375/1372, 10648/10647, 289/288
Mapping: {{mapping| 4 8 12 15 17 16 18 | 0 -11 -18 -25 -21 -8 -11 }}
Optimal tuning (CTE): ~25/21 = 1\4, ~40/39 = 45.218
Optimal ET sequence: {{Optimal ET sequence| 52cdeg, 80, 132deg, 212g }}
Badness: 0.033899
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 325/324, 1001/1000, 1375/1372, 10648/10647, 1521/1520
Mapping: {{mapping| 4 8 12 15 17 16 18 20 | 0 -11 -18 -25 -21 -8 -11 20 }}
Optimal tuning (CTE): ~25/21 = 1\4, ~39/38 = 45.210
Optimal ET sequence: {{Optimal ET sequence| 52cdegh, 80, 132degh, 212gh }}
Badness: 0.031462


== Quintiquart ==
== Quintiquart ==