352edo

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← 351edo352edo353edo →
Prime factorization 25 × 11
Step size 3.40909¢
Fifth 206\352 (702.273¢) (→103\176)
Semitones (A1:m2) 34:26 (115.9¢ : 88.64¢)
Consistency limit 7
Distinct consistency limit 7

352 equal divisions of the octave (abbreviated 352edo), or 352-tone equal temperament (352tet), 352 equal temperament (352et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 352 equal parts of about 3.41 ¢ each. Each step of 352edo represents a frequency ratio of 21/352, or the 352nd root of 2.

Theory

352edo is consistent to the 7-odd-limit. Using the patent val, the equal temperament tempers out 2401/2400, 15625/15552, 390625/388962, and 33554432/33480783 in the 7-limit; 3025/3024, 4375/4356, 14700/14641, 19712/19683, 41503/41472, and 131072/130977 in the 11-limit. It supports newt, world calendar, septiruthenic, enki and fortune.

Prime harmonics

Approximation of prime harmonics in 352edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 +0.32 -1.09 -0.64 +0.95 +1.52 +0.73 -0.92 -1.00 -0.03 +0.42
relative (%) +0 +9 -32 -19 +28 +45 +21 -27 -29 -1 +12
Steps
(reduced)
352
(0)
558
(206)
817
(113)
988
(284)
1218
(162)
1303
(247)
1439
(31)
1495
(87)
1592
(184)
1710
(302)
1744
(336)

Subsets and supersets

352 factors into 25 × 11, with subset edos 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5 15625/15552, [95 -57 -2 [352 558 817]] +0.0891 0.2801 8.22
2.3.5.7 2401/2400, 15625/15552, 33554432/33480783 [352 558 817 988]] +0.1242 0.2500 7.33

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 35\352 119.32 15/14 Septidiasemi
1 65\352 221.59 8388608/7381125 Fortune
1 93\352 317.05 6/5 Hanson
1 103\352 351.14 49/40 Newt
4 93\352
(5\352)
317.05
(17.05)
6/5
(126/125)
Quadritikleismic
4 117\352
(29\352)
398.86
(98.86)
34/27
(18/17)
World calendar

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