# 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

432 equal divisions of the octave (abbreviated 432edo or 432ed2), also called 432-tone equal temperament (432tet) or 432 equal temperament (432et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 432 equal parts of about 2.78 ¢ each. Each step represents a frequency ratio of 21/432, or the 432nd root of 2.

## Theory

432edo has a reasonable approximation to the 7-limit, where the equal temperament tempers out 5120/5103, 703125/702464, 40353607/40310784, 102760448/102515625, and 283115520/282475249. It supports and provides a good tuning for the 5-limit 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, factoring into 24 × 33, so 432edo has 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