User:Overthink/10257edo
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Prime factorization
3 × 13 × 263
Step size
0.116993 ¢
Fifth
6000\10257 (701.96 ¢) (→ 2000\3419)
Semitones (A1:m2)
972:771 (113.7 ¢ : 90.2 ¢)
Consistency limit
25
Distinct consistency limit
25
| ← 10256edo | 10257edo | 10258edo → |
10257 equal divisions of the octave (abbreviated 10257edo or 10257ed2), also called 10257-tone equal temperament (10257tet) or 10257 equal temperament (10257et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 10257 equal parts of about 0.117 ¢ each. Each step represents a frequency ratio of 21/10257, or the 10257th root of 2.
Theory
10257edo is consistent to the 25-odd-limit, and nearly consistent to the 59-odd-limit; the only inconsistencies being (27/22, 44/27), (27/26, 52/27), (41/27, 54/41), (47/27, 54/47), (55/54, 108/55), all of which include odd 27.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0046 | -0.0019 | -0.0046 | -0.0456 | -0.0480 | -0.0124 | +0.0009 | -0.0205 | -0.0364 | -0.0224 |
| Relative (%) | +0.0 | +4.0 | -1.6 | -3.9 | -39.0 | -41.0 | -10.6 | +0.7 | -17.5 | -31.1 | -19.2 | |
| Steps (reduced) |
10257 (0) |
16257 (6000) |
23816 (3302) |
28795 (8281) |
35483 (4712) |
37955 (7184) |
41925 (897) |
43571 (2543) |
46398 (5370) |
49828 (8800) |
50815 (9787) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0425 | -0.0481 | -0.0231 | -0.0489 | -0.0328 | -0.0316 | +0.0500 | +0.0144 | +0.0051 | -0.0036 | +0.0141 |
| Relative (%) | -36.3 | -41.1 | -19.8 | -41.8 | -28.0 | -27.0 | +42.7 | +12.3 | +4.4 | -3.1 | +12.1 | |
| Steps (reduced) |
53433 (2148) |
54952 (3667) |
55657 (4372) |
56973 (5688) |
58751 (7466) |
60338 (9053) |
60832 (9547) |
62220 (678) |
63078 (1536) |
63489 (1947) |
64658 (3116) | |