381edo
| ← 380edo | 381edo | 382edo → |
381 equal divisions of the octave (abbreviated 381edo or 381ed2), also called 381-tone equal temperament (381tet) or 381 equal temperament (381et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 381 equal parts of about 3.15 ¢ each. Each step represents a frequency ratio of 21/381, or the 381st root of 2.
381edo is consistent to the 13-odd-limit with a sharp tendency. The equal temperament tempers out the vulture comma, [24 -21 4⟩, in the 5-limit and 6144/6125 (porwell comma) and 250047/250000 (landscape comma) in the 7-limit. It provides the optimal patent val for the porwell planar temperament tempering out 6144/6125, and nessafof, the 99 & 282 temperament tempering out it and the landscape comma 250047/250000.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.41 | +1.09 | +1.25 | -0.14 | +0.42 | -1.02 | -1.45 | -1.50 | +0.34 | +1.42 |
| Relative (%) | +0.0 | +12.9 | +34.5 | +39.8 | -4.3 | +13.2 | -32.3 | -46.0 | -47.7 | +10.9 | +45.1 | |
| Steps (reduced) |
381 (0) |
604 (223) |
885 (123) |
1070 (308) |
1318 (175) |
1410 (267) |
1557 (33) |
1618 (94) |
1723 (199) |
1851 (327) |
1888 (364) | |
Subsets and supersets
Since 381 factors into 3 × 127, 381edo contains 3edo and 127edo as subsets.