888edo
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Prime factorization
23 × 3 × 37
Step size
1.35135¢
Fifth
519\888 (701.351¢) (→173\296)
Semitones (A1:m2)
81:69 (109.5¢ : 93.24¢)
Sharp fifth
520\888 (702.703¢) (→65\111)
Flat fifth
519\888 (701.351¢) (→173\296)
Major 2nd
151\888 (204.054¢)
Consistency limit
3
Distinct consistency limit
3
| ← 887edo | 888edo | 889edo → |
888 equal divisions of the octave (888edo), or 888-tone equal temperament (888tet), 888 equal temperament (888et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 888 equal parts of about 1.35 ¢ each.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.604 | +0.173 | +0.093 | +0.144 | +0.033 | +0.013 | -0.431 | +0.450 | -0.216 | -0.511 |
| relative (%) | -45 | +13 | +7 | +11 | +2 | +1 | -32 | +33 | -16 | -38 | |
| Steps (reduced) |
1407 (519) |
2062 (286) |
2493 (717) |
2815 (151) |
3072 (408) |
3286 (622) |
3469 (805) |
3630 (78) |
3772 (220) |
3900 (348) | |
888edo is excellent in the no-threes 13-limit, and it may possibly have little attention due to its lack of a perfect fifth. The usage of 3/2 is so deeply entrenched into nearly all musical traditions of the world, that temperaments which lack a perfect fifth do not get considered, even if other harmonics are excellently approximated.
888edo tempers out 6656/6655, 105644/105625, 4917248/4915625 and 35153041/35152000 in the no-threes 13 limit.