1258edo

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← 1257edo1258edo1259edo →
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

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

Approximation of prime harmonics in 1258edo
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 (%) +0.0 +11.7 +1.4 +34.8 +3.5 -15.3 -2.8 +10.7 +35.9 -34.0 -37.9
Steps
(reduced)
1258
(0)
1994
(736)
2921
(405)
3532
(1016)
4352
(578)
4655
(881)
5142
(110)
5344
(312)
5691
(659)
6111
(1079)
6232
(1200)

Divisors

1258edo has subset edos 1, 2, 17, 34, 37, 74, 629.