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Catalog of rank-4 temperaments: Difference between revisions

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Microorganismic and proposed canon extension to 13-limit
Eufalesio (talk | contribs)
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Actually my bad, there are 3 valid extensions to microorganismic so here they are
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== Microorganismic ==
== Microorganismic ==
It splits the septischisma in 3 parts and the pythrabian comma in 5 parts, each of these parts being a tempered [[olympia]]~[[argyria]].
It splits the septischisma in 3 parts and the pythrabian comma in 5 parts, each of these parts being a tempered [[olympia]]~[[argyria]]. It has three valid 13-limit extensions, each of them basically just as accurate, but only koch is a strong extension.


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11
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Notable temperaments not appearing in the optimal ET sequence are {{Edos|8269, 8539, 16808}}.
Notable temperaments not appearing in the optimal ET sequence are {{Edos|8269, 8539, 16808}}.


=== 13-limit ===
=== Leeuwenhoek ===
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: [[67110351/67108864]], [[123201/123200]]
 
[[Mapping]]: {{Mapping|1 0 0 1 7 7|0 2 0 2 −4 −7|0 0 1 0 0 1|0 0 0 3 −5 −1}}
 
[[Optimal tuning|Optimal tunings]]:
 
* [[WE]]: ~2 = 1200.001182{{C}}, ~207515/119808 = 950.977093{{C}}, ~5 = 2786.311871{{C}}, ~539/512 = 88.956523{{C}}
 
: [[error map]]: {{Val|+0.001182 −0.000815 +0.000522 −0.000971 −0.000653 −0.001325}}
 
* [[CWE]]: ~2 = 1200.000000{{C}}, ~207515/119808 =  950.976202{{C}}, ~5 =  2786.312215{{C}}, ~539/512 = 88.956363{{C}}
 
: error map: {{Val|0.000000 −0.002596 −0.001499 −0.004414 −0.004565 −0.005226}}
 
[[Optimal ET sequence]]: {{Edos|15f, 38, 53, 120c, 135f, 188cf, 188, 202f, 217, 270, 742, 1012, 1619, 1889, 2414, 2631, 2684, 4573, 4843, 5585, 8269, 8539, 13112, 16808…}}
 
[[Badness]] (Sintel): 0.349
 
=== Pasteur ===
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: [[67110351/67108864]], [[5767168/5767125]]
 
[[Mapping]]: {{Mapping|1 0 0 7 −3 3|0 1 0 4 −7 −4|0 0 1 0 0 −1|0 0 0 9 −15 −8}}
 
[[Optimal tuning|Optimal tunings]]:
 
* [[WE]]: ~2 = 1200.000392{{C}}, ~3 = 1901.954644{{C}}, ~5 = 2786.314673{{C}}, ~512/455 = 204.332922{{C}}
 
: [[error map]]: {{Val|+0.000392 +0.000035 +0.001743 −0.002847 −0.004657 +0.004426}}
 
* [[CWE]]: ~2 = 1200.000000{{C}}, ~207515/119808 =  950.976202{{C}}, ~5 =  2786.312215{{C}}, ~539/512 = 88.956363{{C}}
 
: error map: {{Val|0.000000 −0.000511 +0.000884 −0.004026 −0.005906 +0.002962}}
 
[[Optimal ET sequence]]: {{Edos|12e, 37b, 41, 53, 94, 176, 217, 270, 581, 851, 1469, 1563, 1739, 1780, 1833, 2009, 2050, 2103, 2320, 2414, 2631, 2684, 5274, 5315, 5585, 8269, 8539, 14124, 16808…}}
 
[[Badness]] (Sintel): 0.924
 
=== Koch ===
[[Subgroup]]: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11.13


Line 1,227: Line 1,269:
[[Optimal ET sequence]]: {{Edos|11c, 15, 38f, 53, 121e, 149e, 202, 217, 270, 783f, 836, 1038, 1106, 1308, 1578, 2414, 2631, 2684, 5315, 5585, 8269, 8539, 14124, 16808…}}
[[Optimal ET sequence]]: {{Edos|11c, 15, 38f, 53, 121e, 149e, 202, 217, 270, 783f, 836, 1038, 1106, 1308, 1578, 2414, 2631, 2684, 5315, 5585, 8269, 8539, 14124, 16808…}}


[[Badness]] (Sintel): 0.387
[[Badness]] (Sintel): 0.912


== Quartismic (117440512/117406179) ==
== Quartismic (117440512/117406179) ==
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