# 324edo

 ← 323edo 324edo 325edo →
Prime factorization 22 × 34
Step size 3.7037¢
Fifth 190\324 (703.704¢) (→95\162)
Semitones (A1:m2) 34:22 (125.9¢ : 81.48¢)
Dual sharp fifth 190\324 (703.704¢) (→95\162)
Dual flat fifth 189\324 (700¢) (→7\12)
Dual major 2nd 55\324 (203.704¢)
Consistency limit 3
Distinct consistency limit 3

324 equal divisions of the octave (abbreviated 324edo or 324ed2), also called 324-tone equal temperament (324tet) or 324 equal temperament (324et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 324 equal parts of about 3.7 ¢ each. Each step represents a frequency ratio of 21/324, or the 324th root of 2.

324edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps, making it a dual-fifth system, with the flat fifth being the 700-cent fifth coming from 12edo, and the sharp fifth coming from 162edo.

It is nonetheless an excellent 2.9.15.21.11.13 subgroup tuning.

### Odd harmonics

Approximation of odd harmonics in 324edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.75 -1.13 +1.54 -0.21 +0.53 +0.21 +0.62 -1.25 -1.22 -0.41 +1.36
Relative (%) +47.2 -30.5 +41.7 -5.6 +14.4 +5.8 +16.7 -33.8 -32.9 -11.1 +36.6
Steps
(reduced)
514
(190)
752
(104)
910
(262)
1027
(55)
1121
(149)
1199
(227)
1266
(294)
1324
(28)
1376
(80)
1423
(127)
1466
(170)

### Subsets and supersets

Since 324 factors into 22 × 34, 324edo has subset edos 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, and 162. 648edo, which doubles it, gives a possible correction to its harmonic 3.