21489edo

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← 21488edo21489edo21490edo →
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

21489 equal divisions of the octave (abbreviated 21489edo), or 21489-tone equal temperament (21489tet), 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 of 21489edo 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

Approximation of prime harmonics in 21489edo
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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