327edo

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← 326edo327edo328edo →
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 327-tone equal temperament (327tet), 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 of 327edo represents a frequency ratio of 21/327, or the 327th root of 2.

Theory

327et tempers out 283115520/282475249, 156250000/155649627, 16875/16807, 19683/19600, 95703125/95551488, 250047/250000 and 2100875/2097152 in the 7-limit; 95703125/95664294, 56723625/56689952, 55296000/55240493, 20155392/20131375, 46656/46585, 2734375/2725888, 104162436/103984375, 226492416/226474325, 540/539, 9765625/9732096, 137781/137500, 5767168/5764801, 85937500/85766121, 1375/1372, 8019/8000, 134775333/134217728, 47265625/47258883, 3025/3024, 160083/160000, 35937/35840, 202397184/201768035, 102487/102400, 20614528/20588575, 805255/802816, 1771561/1769472 and 526153617/524288000 in the 11-limit. It supports 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 -27 -1 +43 -23 -4 +45 +40 -7 -29 -20
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

327 factors into 3 × 109, with 3edo and 109edo as its subset EDOs.

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 19683/19600, 16875/16807, 2109375/2097152 [327 518 759 918]] 0.2722 0.2807 7.65
2.3.5.7.11 540/539, 3025/3024, 8019/8000, 5788125/5767168 [327 518 759 918 1131]] 0.2674 0.2512 6.85
2.3.5.7.11.13 540/539, 625/624, 3025/3024, 8019/8000, 4225/4224 [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
(reduced)*
Cents
(reduced)*
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