1258edo
Jump to navigation
Jump to search
Prime factorization
2 × 17 × 37
Step size
0.953895¢
Fifth
736\1258 (702.067¢) (→368\629)
Semitones (A1:m2)
120:94 (114.5¢ : 89.67¢)
Consistency limit
11
Distinct consistency limit
11
| ← 1257edo | 1258edo | 1259edo → |
1258 equal divisions of the octave (abbreviated 1258edo or 1258ed2), also called 1258-tone equal temperament (1258tet) or 1258 equal temperament (1258et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1258 equal parts of about 0.954 ¢ each. Each step represents a frequency ratio of 21/1258, or the 1258th root of 2.
1258edo is consistent in the 11-odd-limit and it is a strong no-7s 19-limit tuning, with errors less than 15%. Despite inconsistency, it provides the optimal patent val for the abigail temperament in the 13-limit.
In 5-limit, it is a tuning for lafa and chlorine, tempering out the septendecima in light of being a multiple of 17.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.112 | +0.014 | +0.331 | +0.033 | -0.146 | -0.027 | +0.102 | +0.343 | -0.324 | -0.361 |
| relative (%) | +0 | +12 | +1 | +35 | +4 | -15 | -3 | +11 | +36 | -34 | -38 | |
| Steps (reduced) |
1258 (0) |
1994 (736) |
2921 (405) |
3532 (1016) |
4352 (578) |
4655 (881) |
5142 (110) |
5344 (312) |
5691 (659) |
6111 (1079) |
6232 (1200) | |