258008edo

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← 258007edo258008edo258009edo →
Prime factorization 23 × 32251
Step size 0.00465102¢ 
Fifth 150925\258008 (701.955¢)
Semitones (A1:m2) 24443:19399 (113.7¢ : 90.23¢)
Consistency limit 35
Distinct consistency limit 35

258008 equal divisions of the octave (abbreviated 258008edo or 258008ed2), also called 258008-tone equal temperament (258008tet) or 258008 equal temperament (258008et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 258008 equal parts of about 0.00465 ¢ each. Each step represents a frequency ratio of 21/258008, or the 258008th root of 2.

It is notable as a high-limit tuning system and is especially strong in the 13-limit, although it's also somewhat impractical given the vast density of notes. It is the first non-trivial EDO to be consistent in the 36-odd-prime-sum-limit.


Approximation of prime harmonics in 258008edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37
Error Absolute (¢) +0.00000 -0.00002 -0.00011 -0.00013 -0.00015 -0.00024 -0.00052 -0.00131 -0.00081 +0.00018 -0.00131 +0.00166
Relative (%) +0.0 -0.5 -2.4 -2.9 -3.3 -5.1 -11.3 -28.2 -17.3 +3.9 -28.2 +35.6
Steps
(reduced)
258008
(0)
408933
(150925)
599076
(83060)
724320
(208304)
892561
(118537)
954743
(180719)
1054598
(22566)
1095999
(63967)
1167115
(135083)
1253398
(221366)
1278222
(246190)
1344081
(54041)