3498edo

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← 3497edo3498edo3499edo →
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 3498-tone equal temperament (3498tet), 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 of 3498edo 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 -20 -10 -13 -9 -14 +5 -25 -42 -22 +22
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.