# 2190edo

 ← 2189edo 2190edo 2191edo →
Prime factorization 2 × 3 × 5 × 73
Step size 0.547945¢
Fifth 1281\2190 (701.918¢) (→427\730)
Semitones (A1:m2) 207:165 (113.4¢ : 90.41¢)
Consistency limit 15
Distinct consistency limit 15

2190 equal divisions of the octave (abbreviated 2190edo or 2190ed2), also called 2190-tone equal temperament (2190tet) or 2190 equal temperament (2190et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2190 equal parts of about 0.548 ¢ each. Each step represents a frequency ratio of 21/2190, or the 2190th root of 2.

2190edo is is a very strong 13-limit system; no smaller division has a smaller 13-limit relative error, and nothing beats it until 2684. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

### Prime harmonics

Approximation of prime harmonics in 2190edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.037 -0.012 -0.059 -0.085 +0.020 +0.250 +0.021 +0.219 +0.012 +0.170
Relative (%) +0.0 -6.8 -2.3 -10.7 -15.5 +3.7 +45.6 +3.9 +39.9 +2.2 +31.0
Steps
(reduced)
2190
(0)
3471
(1281)
5085
(705)
6148
(1768)
7576
(1006)
8104
(1534)
8952
(192)
9303
(543)
9907
(1147)
10639
(1879)
10850
(2090)

### Subsets and supersets

2190 factors into 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, 730.

4380edo, which doubles 2190edo, provides a good correction to the harmonics 17 and 23.