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

Theory

352et is consistent to the 7-odd-limit. Using the patent val, it tempers out 156250000/155649627, 33554432/33480783, 359661568/358722675 and 2401/2400 in the 7-limit; 214990848/214358881, 78121827/77948684, 100663296/100656875, 10333575/10307264, 2097152/2096325, 1366875/1362944, 125000/124509, 536870912/535869675, 151263/151250, 104857600/104825259, 131072/130977, 1265625/1261568, 200704/200475, 5788125/5767168, 19712/19683, 1479016/1476225, 3025/3024, 41503/41472, 532400/531441 and 67110351/67108864 in the 11-limit. It supports 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. 2112edo, which sextuples it, gives a good correction to the harmonic 11.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[279 -176⟩	[⟨352 558]]	-0.1002	0.1002	2.94
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, 359661568/358722675	[⟨352 558 817 988]]	+0.1242	0.2500	7.33

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	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

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