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 == | ||
Revision as of 10:30, 23 April 2022
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.122 | +0.036 | -0.280 | +0.017 | -0.172 | +0.089 | -0.184 | +0.212 | +0.096 | -0.228 |
| Relative (%) | +0.0 | +20.6 | +6.1 | -47.2 | +2.9 | -28.9 | +15.0 | -30.9 | +35.8 | +16.2 | -38.5 | |
| Steps (reduced) |
2022 (0) |
3205 (1183) |
4695 (651) |
5676 (1632) |
6995 (929) |
7482 (1416) |
8265 (177) |
8589 (501) |
9147 (1059) |
9823 (1735) |
10017 (1929) | |
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 supports 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 2.5.11.17.29.41.43.53.61 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.
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [3205, -2022⟩ | [⟨2022 3205]] | -0.038534 | 0.038533 | 6.493 |
| 2.3.5 | [25, -48, 22⟩, [-90, -15, 49⟩ | [⟨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
- Noble Gas by Cinnamon Mavka
Trivia
It is notable that it is the equal division corresponding to the current year, and also that music was composed in it before the wiki page about it was written.