5585edo

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← 5584edo5585edo5586edo →
Prime factorization 5 × 1117
Step size 0.214861¢ 
Fifth 3267\5585 (701.952¢)
Semitones (A1:m2) 529:420 (113.7¢ : 90.24¢)
Consistency limit 15
Distinct consistency limit 15
Special properties

5585 equal divisions of the octave (abbreviated 5585edo or 5585ed2), also called 5585-tone equal temperament (5585tet) or 5585 equal temperament (5585et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5585 equal parts of about 0.215 ¢ each. Each step represents a frequency ratio of 21/5585, or the 5585th root of 2. It is a zeta peak edo, which has to do with the fact that it is a strong 13-limit division, with a lower 13-limit relative error than any smaller edo, though 6079, only slightly larger, beats it. A basis for its 13-limit commas is {123201/123200, 151263/151250, 8858304/8857805, 8859375/8859136, 62752536/62748517}.

Prime harmonics

Approximation of prime harmonics in 5585edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0033 +0.0068 -0.0166 +0.0160 +0.0095 -0.1031 +0.0698 -0.0201 +0.0378 -0.0400
Relative (%) +0.0 -1.6 +3.2 -7.7 +7.4 +4.4 -48.0 +32.5 -9.4 +17.6 -18.6
Steps
(reduced)
5585
(0)
8852
(3267)
12968
(1798)
15679
(4509)
19321
(2566)
20667
(3912)
22828
(488)
23725
(1385)
25264
(2924)
27132
(4792)
27669
(5329)