# 327edo

 ← 326edo 327edo 328edo →
Prime factorization 3 × 109
Step size 3.66972¢
Fifth 191\327 (700.917¢)
Semitones (A1:m2) 29:26 (106.4¢ : 95.41¢)
Consistency limit 7
Distinct consistency limit 7

327 equal divisions of the octave (abbreviated 327edo or 327ed2), also called 327-tone equal temperament (327tet) or 327 equal temperament (327et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 327 equal parts of about 3.67 ¢ each. Each step represents a frequency ratio of 21/327, or the 327th root of 2.

## Theory

327edo is consistent to the 7-odd-limit, though it has a reasonable approximation to the full 13-limit in its patent val. The equal temperament tempers out the semicomma in the 5-limit; 16875/16807, 19683/19600, 250047/250000, and 2100875/2097152 in the 7-limit; 540/539, 1375/1372, 3025/3024, 8019/8000, 35937/35840, 46656/46585, 102487/102400, 137781/137500, and 160083/160000 in the 11-limit; and 625/624, 1575/1573, 1716/1715, 2200/2197, 4225/4224, and 10648/10647 in the 13-limit. It supports mirkat, pnict, and the subgroup temperament petrtri.

### Odd harmonics

Approximation of odd harmonics in 327edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.04 -0.99 -0.02 +1.59 -0.86 -0.16 +1.64 +1.47 -0.27 -1.06 -0.75
Relative (%) -28.3 -27.0 -0.5 +43.5 -23.4 -4.4 +44.7 +40.0 -7.2 -28.8 -20.5
Steps
(reduced)
518
(191)
759
(105)
918
(264)
1037
(56)
1131
(150)
1210
(229)
1278
(297)
1337
(29)
1389
(81)
1436
(128)
1479
(171)

### Subsets and supersets

Since 327 factors into 3 × 109, 327edo has 3edo and 109edo as its subsets.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-518 327 [327 518]] 0.3273 0.3274 8.92
2.3.5 2109375/2097152, [-20 39 -18 [327 518 759]] 0.3608 0.2715 7.40
2.3.5.7 16875/16807, 19683/19600, 2100875/2097152 [327 518 759 918]] 0.2722 0.2807 7.65
2.3.5.7.11 540/539, 1375/1372, 8019/8000, 2100875/2097152 [327 518 759 918 1131]] 0.2674 0.2512 6.85
2.3.5.7.11.13 540/539, 625/624, 1575/1573, 2200/2197, 8019/8000 [327 518 759 918 1131 1210]] 0.2301 0.2441 6.65

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 74\327 271.56 75/64 Orson
3 44\327 161.47 192/175 Pnict
3 50\327 183.49 10/9 Mirkat

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