381edo

← 380edo

381edo

382edo →

Prime factorization	3 × 127
Step size	3.14961 ¢
Fifth	223\381 (702.362 ¢)
Semitones (A1:m2)	37:28 (116.5 ¢ : 88.19 ¢)
Consistency limit	13
Distinct consistency limit	13

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 2^1/381, or the 381st root of 2.

381edo is consistent to the 13-odd-limit with a sharp tendency. It 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

Approximation of prime harmonics in 381edo

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.