432edo

← 431edo

432edo

433edo →

Prime factorization	24 × 33
Step size	2.77778 ¢
Fifth	253\432 (702.778 ¢)
Semitones (A1:m2)	43:31 (119.4 ¢ : 86.11 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

432et tempers out 283115520/282475249, 703125/702464, 102760448/102515625 and 40353607/40310784 in the 7-limit. It provides the optimal patent val for the maja temperament.

Odd harmonics

Approximation of odd harmonics in 432edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.82	-0.20	+0.62	-1.13	-1.32	+1.14	+0.62	+0.60	-0.29	-1.34	-0.50
	Relative (%)	+29.6	-7.3	+22.3	-40.8	-47.4	+41.0	+22.3	+21.6	-10.5	-48.1	-17.9
Steps (reduced)		685 (253)	1003 (139)	1213 (349)	1369 (73)	1494 (198)	1599 (303)	1688 (392)	1766 (38)	1835 (107)	1897 (169)	1954 (226)

Subsets and supersets

432 is a highly factorable number. It factors into 2⁴ × 3³, with subset edos 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, and 216.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[685 -432⟩	[⟨432 685]]	-0.2596	0.2595	9.34
2.3.5	[41 -20 -4⟩, [-3 -23 17⟩	[⟨432 685 1003]]	-0.1440	0.2676	9.63
2.3.5.7	5120/5103, 703125/702464, 6565234375/6530347008	[⟨432 685 1003 1213]]	-0.1631	0.2341	8.43

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	163\432	452.78	125/96	Maja
4	179\432 (37\432)	497.22 (102.78)	4/3	Undim

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