5407372813edo
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Prime factorization
5407372813 (prime)
Step size
2.21919e-07¢
Fifth
3163110323\5407372813 (701.955¢)
Semitones (A1:m2)
512281009:406566824 (113.7¢ : 90.22¢)
Consistency limit
155
Distinct consistency limit
155
| ← 5407372812edo | 5407372813edo | 5407372814edo → |
5407372813 equal divisions of the octave (abbreviated 5407372813edo or 5407372813ed2), also called 5407372813-tone equal temperament (5407372813tet) or 5407372813 equal temperament (5407372813et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5407372813 equal parts of about 2.22e-07 ¢ each. Each step represents a frequency ratio of 21/5407372813, or the 5407372813th root of 2.
5407372813edo is consistent in the 155-odd-limit and thus has been used in Scale Workshop to quickly decide the constant structure property for JI scales.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0000000000 | -0.0000000053 | -0.0000000077 | +0.0000000053 | -0.0000000115 | -0.0000000048 | +0.0000000167 | +0.0000000467 | -0.0000000230 | -0.0000000274 | -0.0000000113 |
| relative (%) | +0 | -2 | -3 | +2 | -5 | -2 | +8 | +21 | -10 | -12 | -5 | |
| Steps (reduced) |
5407372813 (0) |
8570483136 (3163110323) |
12555530854 (1740785228) |
15180414682 (4365669056) |
18706436483 (2484318044) |
20009657128 (3787538689) |
22102435442 (472944190) |
22970127748 (1340636496) |
24460585939 (2831094687) |
26268914359 (4639423107) |
26789186439 (5159695187) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0000000237 | -0.0000000012 | +0.0000000630 | +0.0000000101 | -0.0000000070 | +0.0000000660 | -0.0000000403 | +0.0000000634 | +0.0000000367 | +0.0000000161 | +0.0000000431 | +0.0000000292 | +0.0000000349 | -0.0000000027 |
| relative (%) | +11 | -1 | +28 | +5 | -3 | +30 | -18 | +29 | +17 | +7 | +19 | +13 | +16 | -1 | |
| Steps (reduced) |
28169456500 (1132592435) |
28970281054 (1933416989) |
29341836511 (2304972446) |
30035732744 (2998868679) |
30973001341 (3936137276) |
31809644094 (4772780029) |
32069707840 (5032843775) |
32801605770 (357368892) |
33253975381 (809738503) |
33470689037 (1026452159) |
34086892637 (1642655759) |
34472214903 (2027978025) |
35016704899 (2572468021) |
35688189271 (3243952393) | |