258edo
| ← 257edo | 258edo | 259edo → |
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
| 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 | +8 | -6 | -30 | +47 | +29 | +43 | +3 | -8 | -36 | -18 | |
| 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.