10459edo
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Prime factorization
10459 (prime)
Step size
0.114734 ¢
Fifth
6118\10459 (701.941 ¢)
Semitones (A1:m2)
990:787 (113.6 ¢ : 90.3 ¢)
Consistency limit
25
Distinct consistency limit
25
| ← 10458edo | 10459edo | 10460edo → |
10459 equal divisions of the octave (abbreviated 10459edo or 10459ed2), also called 10459-tone equal temperament (10459tet) or 10459 equal temperament (10459et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 10459 equal parts of about 0.115 ¢ each. Each step represents a frequency ratio of 21/10459, or the 10459th root of 2.
10459edo is a fairly strong 23-limit system, consistent to the 25-odd-limit. Some of the simpler commas it tempers out include 123201/123200 and 1990656/1990625 in the 13-limit; 37180/37179 in the 17-limit; 28900/28899, 43681/43680, 89376/89375 in the 19-limit; and 16929/16928, 19551/19550, and 25025/25024 in the 23-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0141 | -0.0053 | -0.0144 | -0.0224 | +0.0116 | +0.0259 | -0.0085 | +0.0075 |
| Relative (%) | +0.0 | -12.3 | -4.6 | -12.5 | -19.5 | +10.1 | +22.6 | -7.4 | +6.6 | |
| Steps (reduced) |
10459 (0) |
16577 (6118) |
24285 (3367) |
29362 (8444) |
36182 (4805) |
38703 (7326) |
42751 (915) |
44429 (2593) |
47312 (5476) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0432 | +0.0070 | +0.0375 | +0.0417 | -0.0348 | -0.0510 | -0.0367 | +0.0501 | +0.0480 |
| Relative (%) | +37.7 | +6.1 | +32.7 | +36.4 | -30.3 | -44.5 | -32.0 | +43.6 | +41.8 | |
| Steps (reduced) |
50810 (8974) |
51816 (9980) |
54486 (2191) |
56035 (3740) |
56753 (4458) |
58095 (5800) |
59908 (7613) |
61527 (9232) |
62030 (9735) | |
Subsets and supersets
10459edo is the 1280th prime edo.