# 349edo

 ← 348edo 349edo 350edo →
Prime factorization 349 (prime)
Step size 3.4384¢
Fifth 204\349 (701.433¢)
Semitones (A1:m2) 32:27 (110¢ : 92.84¢)
Consistency limit 5
Distinct consistency limit 5

349 equal divisions of the octave (abbreviated 349edo or 349ed2), also called 349-tone equal temperament (349tet) or 349 equal temperament (349et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 349 equal parts of about 3.44 ¢ each. Each step represents a frequency ratio of 21/349, or the 349th root of 2.

## Theory

349edo is only consistent to the 5-odd-limit. Omitting the harmonic 7, it is consistent to the 13-odd-limit with a flat tendency. In the 2.3.5.11.13 subgroup, the equal temperament tempers out 625/624, 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072 and 166375/165888.

### Odd harmonics

Approximation of odd harmonics in 349edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.52 -1.21 +0.80 -1.04 -1.17 -1.56 +1.70 +1.63 +1.63 +0.28 +0.95
Relative (%) -15.2 -35.3 +23.3 -30.4 -34.2 -45.3 +49.5 +47.5 +47.3 +8.1 +27.7
Steps
(reduced)
553
(204)
810
(112)
980
(282)
1106
(59)
1207
(160)
1291
(244)
1364
(317)
1427
(31)
1483
(87)
1533
(137)
1579
(183)

### Subsets and supersets

349edo is the 70th prime edo. 1047edo, which triples it, gives a good correction to the harmonic 7.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-553 349 [349 553]] 0.1648 0.1648 4.79
2.3.5 2109375/2097152, [-31 43 -16 [349 553 810]] 0.2841 0.2158 6.28
2.3.5.11 166375/165888, 1366875/1362944, 1953125/1948617 [349 553 810 1207]] 0.2980 0.1884 5.48
2.3.5.11.13 625/624, 17303/17280, 41067/40960, 216513/216320 [349 553 810 1207 1291]] 0.3227 0.1756 5.11

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 79\349 271.63 75/64 Orson

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

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