5809edo
← 5808edo | 5809edo | 5810edo → |
5809 equal divisions of the octave (abbreviated 5809edo or 5809ed2), also called 5809-tone equal temperament (5809tet) or 5809 equal temperament (5809et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5809 equal parts of about 0.207 ¢ each. Each step represents a frequency ratio of 21/5809, or the 5809th root of 2.
5809edo is a fairly strong 19-limit system, consistent to the 21-odd-limit, though its full 43-limit interpretation using the patent val is obvious.
We may note that it is an egads and euzenius system, supporting hemiegads. Some simpler commas it tempers out in the higher limits include 123201/123200 in the 13-limit; 14400/14399, 194481/194480, and 336141/336140 in the 17-limit; 10830/10829, 23409/23408, 28900/28899, 43681/43680, and 89376/89375 in the 19-limit; 7866/7865, 8625/8624, 21505/21054, and 25921/25920 in the 23-limit.
Prime harmonics
Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +0.0000 | -0.0097 | -0.0166 | +0.0155 | +0.0334 | +0.0301 | -0.0148 | -0.0436 | -0.0767 | -0.0024 | +0.0152 | +0.0590 | -0.0040 | -0.0355 | +0.0813 |
Relative (%) | +0.0 | -4.7 | -8.0 | +7.5 | +16.2 | +14.6 | -7.2 | -21.1 | -37.1 | -1.2 | +7.4 | +28.5 | -2.0 | -17.2 | +39.3 | |
Steps (reduced) |
5809 (0) |
9207 (3398) |
13488 (1870) |
16308 (4690) |
20096 (2669) |
21496 (4069) |
23744 (508) |
24676 (1440) |
26277 (3041) |
28220 (4984) |
28779 (5543) |
30262 (1217) |
31122 (2077) |
31521 (2476) |
32267 (3222) |
Subsets and supersets
Since 5809 factors into 37 × 157, 5809edo contains 37edo and 157edo as subsets.