Catalog of rank-4 temperaments: Difference between revisions
→Keenanismic (385/384): - duplicates |
Microorganismic and proposed canon extension to 13-limit |
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Badness (Sintel): 1.69 | Badness (Sintel): 1.69 | ||
== Microorganismic == | |||
It splits the septischisma in 3 parts and the pythrabian comma in 5 parts, each of these parts being a tempered [[olympia]]~[[argyria]]. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: [[67110351/67108864]] | |||
[[Mapping]]: {{Mapping|1 0 0 7 7|0 1 0 1 -2|0 0 1 0 0|0 0 0 3 -5}} | |||
[[Optimal tuning|Optimal tunings]]: | |||
* [[WE]]: ~2 = 1200.001014{{C}}, ~3 = 1901.953889{{C}}, ~5 = 2786.311685{{C}}, ~539/512 = 88.956151{{C}} | |||
: [[error map]]: ⟨+0.001014 −0.000098 0.000000 −0.001537 −0.001401] | |||
* [[CWE]]: ~2 = 1200.000000{{C}}, ~3 = 1901.953627{{C}}, ~5 = 2786.311919{{C}}, ~539/512 = 88.955923{{C}} | |||
: error map: ⟨0.000000 −0.001374 −0.001795 −0.004512 −0.004808] | |||
[[Optimal ET sequence]]: {{Edos|11c, 12e, 15, 26, 38, 41, 53, 68, 94, 161, 176, 202, 217, 255, 270, 566, 742, 836, 1106, 1578, 1848, 2684, 3737, 4007, 4843, 5585, 6421, 6691, 12276, 14960…}} | |||
[[Badness]] (Sintel): 0.387 | |||
Notable temperaments not appearing in the optimal ET sequence are {{Edos|8269, 8539, 16808}}. | |||
=== 13-limit === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: [[67110351/67108864]], [[1990656/1990625]] | |||
[[Mapping]]: {{Mapping|1 0 0 7 7 11|0 1 0 1 -2 3|0 0 1 0 0 -5|0 0 0 3 -5 -6}} | |||
[[Optimal tuning|Optimal tunings]]: | |||
* [[WE]]: ~2 = 1200.001014{{C}}, ~3 = 1901.953889{{C}}, ~5 = 2786.311685{{C}}, ~539/512 = 88.956151{{C}} | |||
: [[error map]]: {{Val|+0.000612 −0.002463 +0.004690 −0.001614 −0.003969 +0.002382}} | |||
* [[CWE]]: ~2 = 1200.000000{{C}}, ~3 = 1901.953627{{C}}, ~5 = 2786.311919{{C}}, ~539/512 = 88.955923{{C}} | |||
: error map: {{Val|0.000000 −0.003186 +0.003468 −0.003438 −0.005995 +0.000566}} | |||
[[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 | |||
== Quartismic (117440512/117406179) == | == Quartismic (117440512/117406179) == | ||