253389edo

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← 253388edo253389edo253390edo →
Prime factorization 3 × 84463
Step size 0.0047358¢
Fifth 148223\253389 (701.955¢)
Semitones (A1:m2) 24005:19052 (113.7¢ : 90.23¢)
Consistency limit 59
Distinct consistency limit 59

253389 equal divisions of the octave (abbreviated 253389edo), or 253389-tone equal temperament (253389tet), 253389 equal temperament (253389et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 253389 equal parts of about 0.00474 ¢ each. Each step of 253389edo represents a frequency ratio of 21/253389, or the 253389th root of 2.

253389edo is distinctly consistent to the 59-odd-limit, and indeed is the first edo to achieve it. For that reason, it might attract considerable attention from those who are not put off by extremely small step sizes.

Prime harmonics

Approximation of prime harmonics in 253389edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00000 -0.00030 -0.00018 +0.00068 +0.00039 +0.00133 -0.00058 -0.00050 +0.00076 +0.00025 +0.00072
relative (%) +0 -6 -4 +14 +8 +28 -12 -10 +16 +5 +15
Steps
(reduced)
253389
(0)
401612
(148223)
588351
(81573)
711353
(204575)
876582
(116415)
937651
(177484)
1035718
(22162)
1076378
(62822)
1146221
(132665)
1230959
(217403)
1255339
(241783)