352edo

← 351edo

352edo

353edo →

Prime factorization	25 × 11
Step size	3.40909¢
Fifth	206\352 (702.273¢) (→103\176)
Semitones (A1:m2)	34:26 (115.9¢ : 88.64¢)
Consistency limit	7
Distinct consistency limit	7

352 equal divisions of the octave (abbreviated 352edo or 352ed2), also called 352-tone equal temperament (352tet) or 352 equal temperament (352et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 352 equal parts of about 3.41 ¢ each. Each step represents a frequency ratio of 2^1/352, or the 352nd root of 2.

Theory

352edo is consistent to the 7-odd-limit. Using the patent val, the equal temperament tempers out 2401/2400, 15625/15552, 390625/388962, and 33554432/33480783 in the 7-limit; 3025/3024, 4375/4356, 14700/14641, 19712/19683, 41503/41472, and 131072/130977 in the 11-limit. It supports newt, world calendar, septiruthenic, enki and fortune.

Prime harmonics

Approximation of prime harmonics in 352edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.32	-1.09	-0.64	+0.95	+1.52	+0.73	-0.92	-1.00	-0.03	+0.42
	Relative (%)	+0.0	+9.3	-31.9	-18.9	+28.0	+44.5	+21.3	-27.0	-29.4	-0.9	+12.3
Steps (reduced)		352 (0)	558 (206)	817 (113)	988 (284)	1218 (162)	1303 (247)	1439 (31)	1495 (87)	1592 (184)	1710 (302)	1744 (336)

Subsets and supersets

352 factors into 2⁵ × 11, with subset edos 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	15625/15552, [95 -57 -2⟩	[⟨352 558 817]]	+0.0891	0.2801	8.22
2.3.5.7	2401/2400, 15625/15552, 33554432/33480783	[⟨352 558 817 988]]	+0.1242	0.2500	7.33

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	35\352	119.32	15/14	Septidiasemi
1	65\352	221.59	8388608/7381125	Fortune
1	93\352	317.05	6/5	Hanson
1	103\352	351.14	49/40	Newt
4	93\352 (5\352)	317.05 (17.05)	6/5 (126/125)	Quadritikleismic
4	117\352 (29\352)	398.86 (98.86)	34/27 (18/17)	World calendar

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct