2022edo

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2022 equal divisions of the octave (2022edo), or 2022-tone equal temperament (2022tet), 2022 equal temperament (2022et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2022 equal parts of about 0.593 ¢ each.

Theory

Approximation of prime harmonics in 2022edo
Harmonic 2 3 5 7 11 13 17 19 23 29
Error absolute (¢) +0.000 +0.122 +0.036 -0.280 +0.017 -0.172 +0.089 -0.184 +0.212 +0.096
relative (%) +0 +21 +6 -47 +3 -29 +15 -31 +36 +16
Steps
(reduced)
2022
(0)
3205
(1183)
4695
(651)
5676
(1632)
6995
(929)
7482
(1416)
8265
(177)
8589
(501)
9147
(1059)
9823
(1735)

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'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.

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.

Regular temperament properties

Assuming a no-seven 29 limit subgroup, 2.3.5.11.13.17.19.23.29

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

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.