458edo
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Prime factorization
2 × 229
Step size
2.62009¢
Fifth
268\458 (702.183¢) (→134\229)
Semitones (A1:m2)
44:34 (115.3¢ : 89.08¢)
Consistency limit
3
Distinct consistency limit
3
| ← 457edo | 458edo | 459edo → |
458 equal divisions of the octave (abbreviated 458edo or 458ed2), also called 458-tone equal temperament (458tet) or 458 equal temperament (458et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 458 equal parts of about 2.62 ¢ each. Each step represents a frequency ratio of 21/458, or the 458th root of 2.
458edo is inconsistent to the 5-odd-limit and harmonic 5 is about halfway between its steps. The equal temperament is most notable for tempering out the kleisma, 15625/15552, in the 5-limit and provides the optimal patent val for the 5-limit kleismic temperament.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | +0.23 | -1.16 | +0.61 | -1.10 | +0.52 | -0.15 | +1.18 | +0.55 | +0.12 | -0.06 |
| relative (%) | +0 | +9 | -44 | +23 | -42 | +20 | -6 | +45 | +21 | +4 | -2 | |
| Steps (reduced) |
458 (0) |
726 (268) |
1063 (147) |
1286 (370) |
1584 (210) |
1695 (321) |
1872 (40) |
1946 (114) |
2072 (240) |
2225 (393) |
2269 (437) | |
Subsets and supersets
Since 458 factors into 2 × 229, 458edo contains 2edo and 229edo as subsets.