16th-octave temperaments: Difference between revisions

Tristanbay (talk | contribs)
Hilarity: Added optimal et sequences and badnesses (Smith logflat)
Tags: Mobile edit Mobile web edit
Tristanbay (talk | contribs)
Hilarity: Added optimal CTE and CWE tunings
Tags: Mobile edit Mobile web edit
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== Hilarity ==
== Hilarity ==
Hilarity tempers [[40/27]] to 9\16.
Hilarity, the [[80edo|80]] & [[128edo|128]] temperament, tempers [[40/27]] to 9\16.


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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: mapping generators: ~10460353203/10240000000, ~3
: mapping generators: ~10460353203/10240000000, ~3
[[Optimal tuning]]s:
* [[CTE]]: ~10460353203/1024000000 = 1\16, ~3/2 = 703.422
* [[CWE]]: ~10460353203/1024000000 = 1\16, ~3/2 = 703.621


{{Optimal ET sequence|legend=1| 16cc, 32c, 48, 80, 128, 208 }}
{{Optimal ET sequence|legend=1| 16cc, 32c, 48, 80, 128, 208 }}
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: mapping generators: ~392/375, ~3
: mapping generators: ~392/375, ~3
[[Optimal tuning]]s:
* [[CTE]]: ~392/375 = 1\16, ~3/2 = 703.63
* [[CWE]]: ~392/375 = 1\16, ~3/2 = 703.817


{{Optimal ET sequence|legend=1| 32cdd, 48d, 80, 128, 208, 496bd }}
{{Optimal ET sequence|legend=1| 32cdd, 48d, 80, 128, 208, 496bd }}
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: mapping generators: ~392/375, ~3
: mapping generators: ~392/375, ~3
[[Optimal tuning]]s:
* [[CTE]]: ~392/375 = 1\16, ~3/2 = 703.593
* [[CWE]]: ~392/375 = 1\16, ~3/2 = 703.882


{{Optimal ET sequence|legend=1| 48d, 80, 128, 208, 288be, 496bdee }}
{{Optimal ET sequence|legend=1| 48d, 80, 128, 208, 288be, 496bdee }}
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: mapping generators: ~392/375, ~3
: mapping generators: ~392/375, ~3
[[Optimal tuning]]s:
* [[CTE]]: ~392/375 = 1\16, ~3/2 = 703.653
* [[CWE]]: ~392/375 = 1\16, ~3/2 = 703.902


{{Optimal ET sequence|legend=1| 80, 128, 208, 496bdeef }}
{{Optimal ET sequence|legend=1| 80, 128, 208, 496bdeef }}