# 337edo

 ← 336edo 337edo 338edo →
Prime factorization 337 (prime)
Step size 3.56083¢
Fifth 197\337 (701.484¢)
Semitones (A1:m2) 31:26 (110.4¢ : 92.58¢)
Consistency limit 9
Distinct consistency limit 9

337 equal divisions of the octave (abbreviated 337edo or 337ed2), also called 337-tone equal temperament (337tet) or 337 equal temperament (337et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 337 equal parts of about 3.56 ¢ each. Each step represents a frequency ratio of 21/337, or the 337th root of 2.

## Theory

337edo is consistent to the 9-odd-limit, but the error of harmonic 5 is quite large. If the harmonic is used at all, it tends very flat. The equal temperament tempers out 16875/16807, 420175/419904, and 5250987/5242880 in the 7-limit. It supports tokko and sqrtphi.

### Odd harmonics

Approximation of odd harmonics in 337edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.47 -1.74 -0.28 -0.94 +0.61 -0.17 +1.35 -1.69 +1.60 -0.75 -1.57
Relative (%) -13.2 -49.0 -7.9 -26.5 +17.2 -4.8 +37.8 -47.5 +44.8 -21.1 -44.0
Steps
(reduced)
534
(197)
782
(108)
946
(272)
1068
(57)
1166
(155)
1247
(236)
1317
(306)
1377
(29)
1432
(84)
1480
(132)
1524
(176)

### Subsets and supersets

337edo is the 68th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-534 337 [337 534]] 0.1487 0.1487 4.18
2.3.5 15625/15552, [-88 57 -1 [337 534 782]] 0.3495 0.3089 8.67
2.3.5.7 15625/15552, 16875/16807, 7381125/7340032 [337 534 782 946]] 0.2870 0.2886 8.10

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 67\337 238.58 147/128 Tokko
1 89\337 316.91 6/5 Hanson
1 117\337 416.62 14/11 Sqrtphi (337, 11-limit)

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

Francium