10428edo
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Prime factorization
22 × 3 × 11 × 79
Step size
0.115075¢
Fifth
6100\10428 (701.956¢) (→1525\2607)
Semitones (A1:m2)
988:784 (113.7¢ : 90.22¢)
Consistency limit
21
Distinct consistency limit
21
| ← 10427edo | 10428edo | 10429edo → |
10428 equal divisions of the octave (abbreviated 10428edo or 10428ed2), also called 10428-tone equal temperament (10428tet) or 10428 equal temperament (10428et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 10428 equal parts of about 0.115 ¢ each. Each step represents a frequency ratio of 21/10428, or the 10428th root of 2.
10428edo is consistent in the 21-odd-limit, though with a large error on the 19th harmonic. An alternate mapping to consider is 2.3.5.7.11.13.17.29 subgroup, that is add-29 17-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0013 | -0.0076 | -0.0112 | +0.0054 | -0.0213 | -0.0072 | -0.0447 | +0.0341 | -0.0030 | -0.0413 |
| Relative (%) | +0.0 | +1.1 | -6.6 | -9.7 | +4.7 | -18.5 | -6.3 | -38.8 | +29.6 | -2.6 | -35.9 | |
| Steps (reduced) |
10428 (0) |
16528 (6100) |
24213 (3357) |
29275 (8419) |
36075 (4791) |
38588 (7304) |
42624 (912) |
44297 (2585) |
47172 (5460) |
50659 (8947) |
51662 (9950) | |
Subsets and supersets
Since 10428 factors as 22 × 3 × 11 × 79, it has nontrivial subset edos 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 79, 132, 158, 237, 316, 474, 869, 948, 1738, 2607, 3476, 5214.