222edo
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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
| ← 221edo | 222edo | 223edo → |
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
| 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) | |