1395edo

← 1394edo

1395edo

1396edo →

Prime factorization	32 × 5 × 31
Step size	0.860215¢
Fifth	816\1395 (701.935¢) (→272\465)
Semitones (A1:m2)	132:105 (113.5¢ : 90.32¢)
Consistency limit	21
Distinct consistency limit	21
Special properties	zeta peak zeta peak integer zeta integral zeta gap

1395 equal divisions of the octave (abbreviated 1395edo or 1395ed2), also called 1395-tone equal temperament (1395tet) or 1395 equal temperament (1395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1395 equal parts of about 0.86 ¢ each. Each step represents a frequency ratio of 2^1/1395, or the 1395th root of 2.

1395edo is a strong higher-limit system, being a zeta peak, peak integer, integral and gap edo. The patent val is the first one after 311 with a lower 37-limit relative error, though it is only consistent through the 21-odd-limit, due to harmonic 23 being all of 0.3 cents flat. A comma basis for the 19-limit is {2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

Prime harmonics

Approximation of prime harmonics in 1395edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47
Error	absolute (¢)	+0.000	-0.020	-0.077	-0.224	+0.080	-0.098	-0.009	+0.121	-0.317	+0.100	-0.089	-0.161	+0.185	+0.310	+0.300
	relative (%)	+0	-2	-9	-26	+9	-11	-1	+14	-37	+12	-10	-19	+21	+36	+35
Steps (reduced)		1395 (0)	2211 (816)	3239 (449)	3916 (1126)	4826 (641)	5162 (977)	5702 (122)	5926 (346)	6310 (730)	6777 (1197)	6911 (1331)	7267 (292)	7474 (499)	7570 (595)	7749 (774)

Subsets and supersets

Since 1395 factors into 3² × 5 × 31, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.