Schismic–commatic equivalence continuum: Difference between revisions

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POTE -> CTE and CWE since all of these are new items. +intro to sextile. Dirichlet -> smith badness for heptacot until dirichlet is properly documented.
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1\1, ~3/2 = 699.030
* [[CTE]]: ~2 = 1\1, ~3/2 = 699.1680
* [[CWE]]: ~2 = 1\1, ~3/2 = 699.0789


{{Optimal ET sequence|legend=1| 12, …, 79, 91, 103 }}
{{Optimal ET sequence|legend=1| 12, …, 79, 91, 103 }}
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== Sextile ==
== Sextile ==
{{See also| Landscape microtemperaments #Sextile }}
{{See also| Landscape microtemperaments #Sextile }}
The 5-limit version of sextile reaches the interval class of 5 by -6 perfect fifths minus a period of 1/6-octave.


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~4096/3645 = 1\6, ~3/2 = 702.2356
* [[CTE]]: ~4096/3645 = 1\6, ~3/2 = 702.2627 (~4428675/4194304 = 97.7373)
* [[CWE]]: ~4096/3645 = 1\6, ~3/2 = 702.2434 (~4428675/4194304 = 97.7566)


{{Multival|legend=1| 6 -36 -77 }}
{{Multival|legend=1| 6 -36 -77 }}
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== Heptacot ==
== Heptacot ==
Heptacot tempers out the [[heptacot comma]] and divides the fifth into seven equal parts, the most notable example being [[12edo]] (7\12).
Heptacot tempers out the [[heptacot comma]] and divides the fifth into seven equal parts, the most notable example being [[12edo]] (7\12).


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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: 2 = 1\1, ~{{monzo| -37 19 3 }} = 100.309
* [[CTE]]: ~2 = 1\1, ~{{monzo| -37 19 3 }} = 100.3094
* [[CWE]]: ~2 = 1\1, ~{{monzo| -37 19 3 }} = 100.3076


{{Optimal ET sequence|legend=1| 12, …, 287, 299, 311, 323, 981, 1304, 5539bc, 6843bbcc }}
{{Optimal ET sequence|legend=1| 12, …, 287, 299, 311, 323, 981, 1304, 5539bc, 6843bbcc }}


[[Badness]] (Dirichlet): 16.019
[[Badness]]: 0.683


[[Category:12edo]]
[[Category:12edo]]
[[Category:Equivalence continua]]
[[Category:Equivalence continua]]