258edo

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← 257edo258edo259edo →
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.