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 | +14 | -47 | -23 | +1 | -50 | -42 | -4 | -23 | -47 | +17 | |
| Steps (reduced) |
222 (0) |
352 (130) |
515 (71) |
623 (179) |
768 (102) |
821 (155) |
907 (19) |
943 (55) |
1004 (116) |
1078 (190) |
1100 (212) | |