# 258edo

 ← 257edo 258edo 259edo →
Prime factorization 2 × 3 × 43
Step size 4.65116¢
Fifth 151\258 (702.326¢)
Semitones (A1:m2) 25:19 (116.3¢ : 88.37¢)
Consistency limit 9
Distinct consistency limit 9

258 equal divisions of the octave (abbreviated 258edo or 258ed2), also called 258-tone equal temperament (258tet) or 258 equal temperament (258et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 258 equal parts of about 4.65 ¢ each. Each step represents a frequency ratio of 21/258, or the 258th root of 2.

The equal temperament tempers out 10976/10935 (hemimage comma), 65625/65536 (horwell comma), and 235298/234375 (triwellisma) in the 7-limit as well as 250047/250000 (landscape comma), 823543/819200 (quince comma), and 1500625/1492992 (uniwiz comma). Using the patent val, it tempers out 441/440, 4375/4356, 16384/16335, and 19712/19683 in the 11-limit; 364/363, 625/624, and 2200/2197 in the 13-limit; 375/374, 595/594, 833/832, 936/935, 2500/2499, 4928/4913 in the 17-limit. It supports cotoneum and mutt.

### Prime harmonics

Approximation of prime harmonics in 258edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.37 -0.27 -1.38 +2.17 +1.33 +2.02 +0.16 -0.37 -1.67 -0.85
Relative (%) +0.0 +8.0 -5.7 -29.8 +46.7 +28.7 +43.5 +3.5 -7.9 -35.9 -18.3
Steps
(reduced)
258
(0)
409
(151)
599
(83)
724
(208)
893
(119)
955
(181)
1055
(23)
1096
(64)
1167
(135)
1253
(221)
1278
(246)

### Subsets and supersets

Since 258 factors into 2 × 3 × 43, 258edo has subset edos 2, 3, 6, 43, 86, and 129, and the equal temperament supports the meridic temperament, which tempers out the 43-15-comma, [168 -43 -43 and the mitonisma, 5250987/5242880.