258008edo
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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
| ← 258007edo | 258008edo | 258009edo → |
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.
| 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) | |