332edo

← 331edo

332edo

333edo →

Prime factorization	22 × 83
Step size	3.61446¢
Fifth	194\332 (701.205¢) (→97\166)
Semitones (A1:m2)	30:26 (108.4¢ : 93.98¢)
Consistency limit	7
Distinct consistency limit	7

332 equal divisions of the octave (abbreviated 332edo or 332ed2), also called 332-tone equal temperament (332tet) or 332 equal temperament (332et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 332 equal parts of about 3.61 ¢ each. Each step represents a frequency ratio of 2^1/332, or the 332nd root of 2.

Theory

332edo is consistent to the 7-odd-limit. The equal temperament tempers out 2401/2400, 19683/19600, 118098/117649, and 29360128/29296875 in the 7-limit. It provides the optimal patent val for 11-, 13-, and 17-limit sedia.

Prime harmonics

Approximation of prime harmonics in 332edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.75	+0.43	-0.15	+1.69	+1.64	-0.14	-1.13	+0.64	+0.54	+0.75
	Relative (%)	+0.0	-20.8	+12.0	-4.2	+46.9	+45.4	-3.8	-31.2	+17.7	+15.0	+20.7
Steps (reduced)		332 (0)	526 (194)	771 (107)	932 (268)	1149 (153)	1229 (233)	1357 (29)	1410 (82)	1502 (174)	1613 (285)	1645 (317)

Subsets and supersets

Since 332 factors into 2² × 83, 332edo has subset edos 2, 4, 83, and 166.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	[-13 17 -6⟩, [-53 10 16⟩	[⟨332 526 771]]	0.0955	0.2778	7.69
2.3.5.7	2401/2400, 19683/19600, 29360128/29296875	[⟨332 526 771 932]]	0.0851	0.2412	6.67

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	33\332	119.28	15/14	Septidiasemi
1	75\332	271.08	1024/875	Quasiorwell
1	127\332	459.04	125/96	Majvam
1	143\332	516.87	27/20	Gravity
2	143\332 (23\332)	516.87 (83.13)	27/20 (21/20)	Harry
2	45\332	162.65	1125/1024	Kwazy

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