5902edo

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← 5901edo5902edo5903edo →
Prime factorization 2 × 13 × 227
Step size 0.203321¢ 
Fifth 3452\5902 (701.864¢) (→1726\2951)
Semitones (A1:m2) 556:446 (113¢ : 90.68¢)
Dual sharp fifth 3453\5902 (702.067¢)
Dual flat fifth 3452\5902 (701.864¢) (→1726\2951)
Dual major 2nd 1003\5902 (203.931¢)
Consistency limit 7
Distinct consistency limit 7

5902 equal divisions of the octave (abbreviated 5902edo or 5902ed2), also called 5902-tone equal temperament (5902tet) or 5902 equal temperament (5902et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5902 equal parts of about 0.203 ¢ each. Each step represents a frequency ratio of 21/5902, or the 5902nd root of 2.

5902 is notable for an extremely good approximation of the 2.5.7 subgroup. It also has a very accurate representation of the 13th harmonic, inherited from 227edo which is a convergent.

Odd harmonics

Approximation of odd harmonics in 5902edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.0912 -0.0040 -0.0018 +0.0209 +0.0884 +0.0010 -0.0952 -0.0418 -0.0545 -0.0930 -0.0127
Relative (%) -44.9 -2.0 -0.9 +10.3 +43.5 +0.5 -46.8 -20.6 -26.8 -45.7 -6.3
Steps
(reduced)
9354
(3452)
13704
(1900)
16569
(4765)
18709
(1003)
20418
(2712)
21840
(4134)
23058
(5352)
24124
(516)
25071
(1463)
25923
(2315)
26698
(3090)
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