2022edo: Difference between revisions
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{{EDO intro|2022}} | |||
== Theory == | == Theory == | ||
{{ | {{Harmonics in equal|2022}} | ||
2022edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 subgroup. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 19-limit is a reasonable choice. | |||
In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the [-90, -15, 49⟩ comma. | |||
In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank 3 temperament that eliminates the [25,-17,-23,16⟩ comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it's [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val. | In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank 3 temperament that eliminates the [25,-17,-23,16⟩ comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it's [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val. | ||
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In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525. | In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525. | ||
== Regular temperament properties == | |||
Assuming a no-seven 29 limit subgroup, 2.3.5.11.13.17.19. | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{Monzo|3205, -2022}} | |||
|[{{Val|2022 3205}}] | |||
|<nowiki>-0.038534</nowiki> | |||
|0.038533 | |||
|6.493 | |||
|- | |||
|2.3.5 | |||
|[25, -48, 22⟩, [-90, -15, 49⟩ | |||
|[{{Val|2022 3205 4695}}] | |||
| -0.030920 | |||
|0.033254 | |||
|5.603 | |||
|- | |||
|2.3.5.11.13.17.19.23.29 | |||
|2431/2430, 2755/2754, 3520/3519, 142025/141984, | |||
2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875 | |||
|[⟨2022 3205 4695 | |||
6955 7482 8265 | |||
8589 9147 9283]] | |||
| -0.010752 | |||
|0.036910 | |||
|6.219 | |||
|} | |||
== Music == | == Music == | ||