# 222edo

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 ← 221edo 222edo 223edo →
Prime factorization 2 × 3 × 37
Step size 5.40541¢
Fifth 130\222 (702.703¢) (→65\111)
Semitones (A1:m2) 22:16 (118.9¢ : 86.49¢)
Consistency limit 3
Distinct consistency limit 3

222 equal divisions of the octave (abbreviated 222edo or 222ed2), also called 222-tone equal temperament (222tet) or 222 equal temperament (222et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 222 equal parts of about 5.41 ¢ each. Each step represents a frequency ratio of 21/222, or the 222nd root of 2.

## Theory

222edo is strongly related to 111edo, but they differ on the mappings for 5, 7, and 13. Its 5 is about halfway between its steps; as a result it is inconsistent to the 5-odd-limit. Using the patent val nonetheless, the equal temperament tempers out 2401/2400 and 5120/5103 in the 7-limit, supporting hemififths.

### Prime harmonics

Approximation of prime harmonics in 222edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.75 -2.53 -1.26 +0.03 -2.69 -2.25 -0.22 -1.25 -2.55 +0.91
Relative (%) +0.0 +13.8 -46.8 -23.3 +0.6 -49.8 -41.7 -4.0 -23.1 -47.2 +16.8
Steps
(reduced)
222
(0)
352
(130)
515
(71)
623
(179)
768
(102)
821
(155)
907
(19)
943
(55)
1004
(116)
1078
(190)
1100
(212)