358edo
| ← 357edo | 358edo | 359edo → |
358 equal divisions of the octave (abbreviated 358edo or 358ed2), also called 358-tone equal temperament (358tet) or 358 equal temperament (358et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 358 equal parts of about 3.35 ¢ each. Each step represents a frequency ratio of 21/358, or the 358th root of 2.
Theory
358edo is consistent to the 7-odd-limit, but the harmonic 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.13 subgroup or even better the 2.9.15.7.13 subgroup.
In the 2.9.5.7.13 subgroup, the equal temperament tempers out 4096/4095, 13720/13689, 59150/59049, 60025/59904, 142884/142805, and 390625/388962.
The patent val supports hypnos in the 11-limit and lee in the 2.3.7 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.40 | -0.84 | -0.11 | +0.56 | -1.60 | +0.81 | +1.12 | -1.04 | +0.81 | -1.51 | -1.46 |
| Relative (%) | -41.7 | -25.0 | -3.3 | +16.7 | -47.7 | +24.3 | +33.3 | -31.2 | +24.2 | -45.0 | -43.5 | |
| Steps (reduced) |
567 (209) |
831 (115) |
1005 (289) |
1135 (61) |
1238 (164) |
1325 (251) |
1399 (325) |
1463 (31) |
1521 (89) |
1572 (140) |
1619 (187) | |
Subset and supersets
358 factors into 2 × 179, with 2edo and 179edo as its subset edos. 716edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1135 -358⟩ | [⟨358 1135]] | -0.0882 | 0.0882 | 2.63 |
| 2.9.5 | [3 -9 11⟩, [-98 17 19⟩ | [⟨358 1135 831]] | +0.0616 | 0.2238 | 6.68 |
| 2.9.5.7 | 390625/388962, 2100875/2097152, 4802000/4782969 | [⟨358 1135 831 1005]] | +0.0561 | 0.1941 | 5.79 |