2022edo: Difference between revisions
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== Theory == | == Theory == | ||
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 29-limit is a satisfactory choice. | 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 29-limit is a satisfactory choice. | ||
In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the {{monzo| -90 -15 49 }} comma. | In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo| -90 -15 49 }} comma. | ||
In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank-3 temperament that eliminates the {{monzo| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[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 {{monzo| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[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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If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443. | If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|2022|columns=11}} | {{Harmonics in equal|2022|columns=11}} | ||
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{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
| Line 27: | Line 28: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{monzo| 3205 -2022 }} | ||
| | | {{mapping| 2022 3205 }} | ||
| -0.038534 | | -0.038534 | ||
| 0.038533 | | 0.038533 | ||
| Line 34: | Line 35: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{monzo| 25 -48 22 }}, {{monzo| -90 -15 49 }} | ||
| | | {{mapping| 2022 3205 4695 }} | ||
| -0.030920 | | -0.030920 | ||
| 0.033254 | | 0.033254 | ||
| Line 42: | Line 43: | ||
| 2.3.5.11.13.17.19.23.29 | | 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 | | 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875 | ||
| | | {{mapping| 2022 3205 4695 6955 7482 8265 8589 9147 9283 }} | ||
| -0.010752 | | -0.010752 | ||
| 0.036910 | | 0.036910 | ||
| Line 49: | Line 50: | ||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=IulKlMjxAM8 Noble Gas] | ; [[Eliora]] | ||
* [https://www.youtube.com/watch?v=IulKlMjxAM8 ''Noble Gas''] (2021) | |||
Revision as of 13:44, 15 October 2023
| ← 2021edo | 2022edo | 2023edo → |
Theory
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 29-limit is a satisfactory 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 is 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.
If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.
Prime harmonics
| 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) | |
Regular temperament properties
| 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 (2021)