# 3498edo

 ← 3497edo 3498edo 3499edo →
Prime factorization 2 × 3 × 11 × 53
Step size 0.343053¢
Fifth 2046\3498 (701.887¢) (→31\53)
Semitones (A1:m2) 330:264 (113.2¢ : 90.57¢)
Consistency limit 25
Distinct consistency limit 25

3498 equal divisions of the octave (abbreviated 3498edo or 3498ed2), also called 3498-tone equal temperament (3498tet) or 3498 equal temperament (3498et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3498 equal parts of about 0.343 ¢ each. Each step represents a frequency ratio of 21/3498, or the 3498th root of 2.

3498edo is consistent in the 25-odd-limit, and it is a good 19-limit tuning. Except for harmonic 17, it is a mostly flat system. In the 7-limit, it is enfactored, with the same tuning as 1749edo, and corrects its mappings for 11 and 19.

3498edo notably contains 53edo, tempering out the Mercator's comma, and also 106edo and 159edo.

### Prime harmonics

Approximation of prime harmonics in 3498edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.068 -0.036 -0.044 -0.031 -0.047 +0.019 -0.086 -0.144 -0.075 +0.076
Relative (%) +0.0 -19.9 -10.4 -12.8 -9.2 -13.8 +5.5 -25.0 -42.0 -21.8 +22.1
Steps
(reduced)
3498
(0)
5544
(2046)
8122
(1126)
9820
(2824)
12101
(1607)
12944
(2450)
14298
(306)
14859
(867)
15823
(1831)
16993
(3001)
17330
(3338)

### Subsets and supersets

Since 3498edo factors as 2 × 3 × 11 × 53, it has subset edos 1, 2, 3, 6, 11, 22, 33, 53, 66, 106, 159, 318, 583, 1166, 1749.