# 351edo

 ← 350edo 351edo 352edo →
Prime factorization 33 × 13
Step size 3.4188¢
Fifth 205\351 (700.855¢)
Semitones (A1:m2) 31:28 (106¢ : 95.73¢)
Consistency limit 7
Distinct consistency limit 7

351 equal divisions of the octave (abbreviated 351edo or 351ed2), also called 351-tone equal temperament (351tet) or 351 equal temperament (351et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 351 equal parts of about 3.42 ¢ each. Each step represents a frequency ratio of 21/351, or the 351st root of 2.

## Theory

351et is consistent to the 7-odd-limit with a reasonable approximation to the 11-limit. The equal temperament tempers out 19683/19600, 65625/65536, and 235298/234375 in the 7-limit; 441/440, 24057/24010, 35937/35840, 41503/41472, 43923/43904, and 46656/46585 in the 11-limit. It supports snape.

### Odd harmonics

Approximation of odd harmonics in 351edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.10 +0.01 -1.30 +1.22 -0.89 +0.50 -1.09 +1.03 -0.08 +1.01 +0.79
Relative (%) -32.2 +0.3 -38.2 +35.6 -26.0 +14.6 -31.9 +30.1 -2.3 +29.7 +23.0
Steps
(reduced)
556
(205)
815
(113)
985
(283)
1113
(60)
1214
(161)
1299
(246)
1371
(318)
1435
(31)
1491
(87)
1542
(138)
1588
(184)

### Subsets and supersets

351 factors into 33 × 13 with subset edos 3, 9, 13, 27, 39, and 117.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-556 351 [351 556]] 0.3471 0.3472 10.16
2.3.5 [-36 11 8, [-11 26 -13 [351 556 815]] 0.2298 0.3284 9.61
2.3.5.7 19683/19600, 65625/65536, 235298/234375 [351 556 815 985]] 0.2885 0.3021 8.84
2.3.5.7.11 441/440, 19683/19600, 35937/35840, 65625/65536 [351 556 815 985 1214]] 0.2823 0.2705 7.91

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 116\351 396.58 98304/78125 Squarschmidt

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