21489edo
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Prime factorization
3 × 13 × 19 × 29
Step size
0.0558425¢
Fifth
12570\21489 (701.941¢) (→4190\7163)
Semitones (A1:m2)
2034:1617 (113.6¢ : 90.3¢)
Consistency limit
7
Distinct consistency limit
7
| ← 21488edo | 21489edo | 21490edo → |
21489 equal divisions of the octave (abbreviated 21489edo or 21489ed2), also called 21489-tone equal temperament (21489tet) or 21489 equal temperament (21489et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 21489 equal parts of about 0.0558 ¢ each. Each step represents a frequency ratio of 21/21489, or the 21489th root of 2.
21489edo can be used as a polymicrotonal system, being the lowest common multiple of 19edo, 29edo and 39edo, and also containing 13edo as a subset too.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0000 | -0.0145 | +0.0049 | -0.0140 | +0.0153 | +0.0140 | -0.0273 | +0.0160 | +0.0099 | -0.0086 | +0.0154 |
| relative (%) | +0 | -26 | +9 | -25 | +27 | +25 | -49 | +29 | +18 | -15 | +28 | |
| Steps (reduced) |
21489 (0) |
34059 (12570) |
49896 (6918) |
60327 (17349) |
74340 (9873) |
79519 (15052) |
87835 (1879) |
91284 (5328) |
97207 (11251) |
104393 (18437) |
106461 (20505) | |
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