2022edo: Difference between revisions
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Revision as of 04:40, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
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| ← 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.
| 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 |