5809edo

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Template:EDO intro

← 5808edo 5809edo 5810edo →
Prime factorization 37 × 157
Step size 0.206576 ¢ 
Fifth 3398\5809 (701.945 ¢)
Semitones (A1:m2) 550:437 (113.6 ¢ : 90.27 ¢)
Consistency limit 21
Distinct consistency limit 21

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

Approximation of prime harmonics in 5809edo
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.