539edo

← 538edo

539edo

540edo →

Prime factorization	72 × 11
Step size	2.22635¢
Fifth	315\539 (701.299¢) (→45\77)
Semitones (A1:m2)	49:42 (109.1¢ : 93.51¢)
Consistency limit	3
Distinct consistency limit	3

539 equal divisions of the octave (abbreviated 539edo or 539ed2), also called 539-tone equal temperament (539tet) or 539 equal temperament (539et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 539 equal parts of about 2.23 ¢ each. Each step represents a frequency ratio of 2^1/539, or the 539th root of 2.

539edo is inconsistent to the 5-odd-limit. If harmonic 5 is used at all, the 539c val has better overall accuracy than the patent val. Meanwhile, the patent val tempers out the sensipent comma, 78732/78125, and provides the optimal patent val for the 5-limit sensipent temperament, tuning it more accurate than 65et by a tiny margin.

Odd harmonics

Approximation of odd harmonics in 539edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.656	+1.070	-0.366	+0.914	+0.816	+1.031	+0.414	-0.317	+0.817	-1.022	-0.445
	Relative (%)	-29.5	+48.1	-16.4	+41.0	+36.6	+46.3	+18.6	-14.2	+36.7	-45.9	-20.0
Steps (reduced)		854 (315)	1252 (174)	1513 (435)	1709 (92)	1865 (248)	1995 (378)	2106 (489)	2203 (47)	2290 (134)	2367 (211)	2438 (282)

Subsets and supersets

Since 539 factors into 7² × 11, 539edo has subset edos 7, 11, 49, and 77.