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

Theory

332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and 2401/2400 in the 7-limit. It provides the optimal patent val for majvamoid and sedia.

Prime harmonics

Approximation of prime harmonics in 12edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-2.0	+13.7	+31.2	+48.7	-40.5	-5.0	+2.5	-28.3	-29.6	-45.0
	Relative (%)	+0.0	-2.0	+13.7	+31.2	+48.7	-40.5	-5.0	+2.5	-28.3	-29.6	-45.0
Steps (reduced)		12 (0)	19 (7)	28 (4)	34 (10)	42 (6)	44 (8)	49 (1)	51 (3)	54 (6)	58 (10)	59 (11)

Subsets and supersets

332 factors into 2² × 83, with subset edos 2, 4, 83, and 166.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-263 166⟩	[⟨332 526]]	0.2367	0.2367	6.55
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