# 15900edo

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 ← 15899edo 15900edo 15901edo →
Prime factorization 22 × 3 × 52 × 53
Step size 0.0754717¢
Fifth 9301\15900 (701.962¢)
Semitones (A1:m2) 1507:1195 (113.7¢ : 90.19¢)
Consistency limit 23
Distinct consistency limit 23

The 15900 equal divisions of the octave, or the 15900-tone equal temperament (15900tet), 15900 equal temperament (15900et) when viewed from a regular temperament perspective, divides the octave into 15900 equal parts of about 0.075 cents each.

## Theory

15900edo tempers out the magnetisma in the 2.3.29.43 subgroup. It is consistent in the 23-odd-limit and has 10% or less errors on prime harmonics 3, 7, 11, 13, 19, 29, 41, 47, 53, 59, 71.

### Divisors

15900edo has subset EDOs 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 53, 60, 75, 100, 106, 150, 159, 212, 265, 300, 318, 530, 636, 795, 1060, 1325, 1590, 2650, 3180, 3975, 5300, 7950.

A single step of 15900edo is the relative cent of 159edo.

### Prime harmonics

Approximation of prime harmonics in 15900edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 +0.0073 +0.0259 +0.0043 +0.0028 +0.0006 +0.0257 -0.0036 +0.0275 +0.0077 +0.0210
Relative (%) +0.0 +9.6 +34.3 +5.7 +3.7 +0.8 +34.1 -4.7 +36.5 +10.2 +27.9
Steps
(reduced)
15900
(0)
25201
(9301)
36919
(5119)
44637
(12837)
55005
(7305)
58837
(11137)
64991
(1391)
67542
(3942)
71925
(8325)
77242
(13642)
78772
(15172)