5902edo
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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
← 5901edo | 5902edo | 5903edo → |
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
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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