622edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 621edo622edo623edo →
Prime factorization 2 × 311
Step size 1.92926¢
Fifth 364\622 (702.251¢) (→182\311)
Semitones (A1:m2) 60:46 (115.8¢ : 88.75¢)
Consistency limit 7
Distinct consistency limit 7

622 equal divisions of the octave (abbreviated 622edo or 622ed2), also called 622-tone equal temperament (622tet) or 622 equal temperament (622et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 622 equal parts of about 1.929 ¢ each. Each step represents a frequency ratio of 21/622, or the 622nd root of 2.

622edo is enfactored in the 41-limit, having the same tuning as the highly notable 311edo. In that regard, 622edo is a compound of two 311edos that don't intersect, and provides barely anything new apart from most characteristics of what it doubles.

622edo has potential as an add-43 system, correcting the 311edo's mapping for 43, which is the first harmonic not represented consistently by 311edo. Some 43-limit commas it tempers out are 1849/1848, 50000/49923, 59168/59049, 300125/299538, 6837602/6834375, 1048576/1048383.

Prime harmonics

Approximation of prime harmonics in 622edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43
Error absolute (¢) +0.000 +0.296 -0.462 -0.337 +0.451 +0.630 -0.775 -0.407 +0.665 +0.648 +0.945 -0.540 -0.767 -0.264
relative (%) +0 +15 -24 -17 +23 +33 -40 -21 +34 +34 +49 -28 -40 -14
Steps
(reduced)
622
(0)
986
(364)
1444
(200)
1746
(502)
2152
(286)
2302
(436)
2542
(54)
2642
(154)
2814
(326)
3022
(534)
3082
(594)
3240
(130)
3332
(222)
3375
(265)