16th-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|16}} | ||
16edo is an interesting system when it comes to fractional-octave temperaments, as it has no straightforward JI approximation on its own, but some of its multiples do. | 16edo is an interesting system when it comes to fractional-octave temperaments, as it has no straightforward JI approximation on its own, but some of its multiples do. | ||
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[[Badness]]: 3.05 | [[Badness]]: 3.05 | ||
== Hilarity == | |||
Hilarity, the [[80edo|80]] & [[128edo|128]] temperament, tempers [[40/27]] to 9\16. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 39 -48 16 }} | |||
{{Mapping|legend=1| 16 0 -39 | 0 1 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 }} | |||
[[Badness]]: 4.22 | |||
=== 7-limit === | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 179200/177147, 390625/388962 | |||
{{Mapping|legend=1| 16 0 -39 -82 | 0 1 3 5 }} | |||
: mapping generators: ~392/375, ~3 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~392/375 = 1\16, ~3/2 = 703.630 | |||
* [[CWE]]: ~392/375 = 1\16, ~3/2 = 703.817 | |||
{{Optimal ET sequence|legend=1| 32cdd, 48d, 80, 128, 208, 496bd }} | |||
[[Badness]]: 0.302 | |||
=== 11-limit === | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 896/891, 2200/2187, 125000/124509 | |||
{{Mapping|legend=1| 16 0 -39 -82 30 | 0 1 3 5 1 }} | |||
: 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 }} | |||
[[Badness]]: 0.0886 | |||
=== 13-limit === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 325/324, 352/351, 896/891, 540000/539539 | |||
{{Mapping|legend=1| 16 0 -39 -82 30 110 | 0 1 3 5 1 -2 }} | |||
: 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 }} | |||
[[Badness]]: 0.0611 | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||