2022edo

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2022 EDO divides the octave into steps of 0.593 cents, that is 593 millicents each.

Theory

Approximation of prime intervals in 2022 EDO
Prime number 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
Error absolute (¢) +0.000 +0.122 +0.036 -0.280 +0.017 -0.172 +0.089 -0.184 +0.212 +0.096 -0.228 +0.288 +0.018 +0.055 -0.225 +0.086 +0.176 +0.029
relative (%) +0 +21 +6 -47 +3 -29 +15 -31 +36 +16 -38 +49 +3 +9 -38 +14 +30 +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) 10534 (424) 10833 (723) 10972 (862) 11231 (1121) 11582 (1472) 11895 (1785) 11992 (1882)

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.

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.

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.