355edo
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355 equal divisions of the octave (abbreviated 355edo or 355ed2), also called 355-tone equal temperament (355tet) or 355 equal temperament (355et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 355 equal parts of about 3.38 ¢ each. Each step represents a frequency ratio of 21/355, or the 355th root of 2.
| ← 354edo | 355edo | 356edo → |
Theory
355edo is only consistent to the 3-odd-limit since the errors of harmonics 3 and 5 are quite large. It is suitable for the 2.9.5.11.17.19.23.37.41 subgroup. The 2.3.7.13 subgroup is also worth noting.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.14 | -0.96 | +1.31 | -1.09 | -0.33 | +1.16 | +0.18 | -0.17 | -0.05 | -0.92 | +0.46 |
| Relative (%) | +33.8 | -28.4 | +38.9 | -32.3 | -9.8 | +34.4 | +5.4 | -4.9 | -1.4 | -27.3 | +13.6 | |
| Steps (reduced) |
563 (208) |
824 (114) |
997 (287) |
1125 (60) |
1228 (163) |
1314 (249) |
1387 (322) |
1451 (31) |
1508 (88) |
1559 (139) |
1606 (186) | |
Subsets and supersets
Since 355 factors into 5 × 71, 355edo has 5edo and 71edo as its subsets. 710edo, 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 | [-225 71⟩ | [⟨355 1125]] | +0.1724 | 0.1724 | 5.10 |
| 2.9.5 | [-57 7 15⟩, [-37 19 -10⟩ | [⟨355 1125 824]] | +0.2530 | 0.1812 | 5.36 |