5407372813edo
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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.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000000000 | -0.0000000053 | -0.0000000077 | +0.0000000053 | -0.0000000115 | -0.0000000048 | +0.0000000167 | +0.0000000467 | -0.0000000230 |
| Relative (%) | +0.0 | -2.4 | -3.5 | +2.4 | -5.2 | -2.2 | +7.5 | +21.0 | -10.4 | |
| Steps (reduced) |
5407372813 (0) |
8570483136 (3163110323) |
12555530854 (1740785228) |
15180414682 (4365669056) |
18706436483 (2484318044) |
20009657128 (3787538689) |
22102435442 (472944190) |
22970127748 (1340636496) |
24460585939 (2831094687) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0000000274 | -0.0000000113 | +0.0000000237 | -0.0000000012 | +0.0000000630 | +0.0000000101 | -0.0000000070 | +0.0000000660 | -0.0000000403 |
| Relative (%) | -12.4 | -5.1 | +10.7 | -0.5 | +28.4 | +4.5 | -3.2 | +29.7 | -18.2 | |
| Steps (reduced) |
26268914359 (4639423107) |
26789186439 (5159695187) |
28169456500 (1132592435) |
28970281054 (1933416989) |
29341836511 (2304972446) |
30035732744 (2998868679) |
30973001341 (3936137276) |
31809644094 (4772780029) |
32069707840 (5032843775) | |
| Harmonic | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000000634 | +0.0000000367 | +0.0000000161 | +0.0000000431 | +0.0000000292 | +0.0000000349 | -0.0000000027 | -0.0000000081 | +0.0000000442 |
| Relative (%) | +28.5 | +16.5 | +7.2 | +19.4 | +13.2 | +15.7 | -1.2 | -3.6 | +19.9 | |
| Steps (reduced) |
32801605770 (357368892) |
33253975381 (809738503) |
33470689037 (1026452159) |
34086892637 (1642655759) |
34472214903 (2027978025) |
35016704899 (2572468021) |
35688189271 (3243952393) |
36003431755 (3559194877) |
36156401165 (3712164287) | |
| Harmonic | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0000000006 | -0.0000000381 | -0.0000000352 | +0.0000000264 | +0.0000000350 | -0.0000000449 | +0.0000000013 | -0.0000000028 | +0.0000000185 |
| Relative (%) | -0.3 | -17.2 | -15.8 | +11.9 | +15.8 | -20.3 | +0.6 | -1.3 | +8.3 | |
| Steps (reduced) |
36453625302 (4009388424) |
36598095911 (4153859033) |
36879250301 (4435013423) |
37790423574 (5346186696) |
38032340321 (180730630) |
38381705711 (530096020) |
38494768414 (643158723) |
39036735590 (1185125899) |
39140752997 (1289143306) | |