559edo

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559edo

560edo →

Prime factorization	13 × 43
Step size	2.14669 ¢
Fifth	327\559 (701.968 ¢)
Semitones (A1:m2)	53:42 (113.8 ¢ : 90.16 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

559edo is a very strong 5-limit system. The equal temperament tempers out the luna comma, [38 -2 -15⟩ and the minortone comma, [-16 35 -17⟩ in the 5-limit, as well as the monzisma, [54 -37 2⟩; 4375/4374, 2100875/2097152, and 282475249/281250000 in the 7-limit; 12005/11979, 41503/41472, 160083/160000, and 172032/171875 in the 11-limit. Rank-2 temperaments it supports include mitonic, lunatic, acrokleismic, monzism, and meridic.

Prime harmonics

Approximation of prime harmonics in 559edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.013	+0.091	-0.668	+0.382	+0.975	+0.232	+0.877	+0.706	+0.834	-0.850
	Relative (%)	+0.0	+0.6	+4.2	-31.1	+17.8	+45.4	+10.8	+40.9	+32.9	+38.9	-39.6
Steps (reduced)		559 (0)	886 (327)	1298 (180)	1569 (451)	1934 (257)	2069 (392)	2285 (49)	2375 (139)	2529 (293)	2716 (480)	2769 (533)

Subsets and supersets

Since 559 factors into 13 × 43, 559edo contains 13edo and 43edo as subsets.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [886 -559⟩ | [⟨559 886]] | −0.0040 | 0.0040 | 0.19 |- | 2.3.5 | [38 -2 -15⟩, [-16 35 -17⟩ | [⟨559 886 1298]] | −0.0157 | 0.0168 | 0.78 |- | 2.3.5.7 | 4375/4374, 2100875/2097152, [-4 -2 -9 10⟩ | [⟨559 886 1298 1569]] | +0.0478 | 0.1109 | 5.16 |- | 2.3.5.7.11 | 4375/4374, 12005/11979, 41503/41472, 172032/171875 | [⟨559 886 1298 1569 1934]] | 0.0161 | 0.1175 | 5.48 Template:Comma basis end

• 559et has a lower relative error than any previous equal temperaments in the 5-limit, past 441 and before 612.

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 90\559 | 182.47 | 10/9 | Mitonic |- | 1 | 90\559 | 193.20 | 352/315 | Lunatic |- | 1 | 116\559 | 249.02 | [-27 11 3 1⟩ | Monzismic |- | 1 | 147\559 | 315.56 | 6/5 | Acrokleismic |- | 13 | 232\559
(17\559) | 498.03
(36.494) | 4/3
(?) | Aluminium |- | 43 | 232\559
(2\559) | 498.03
(4.29) | 4/3
(385/384) | Meridic Template:Rank-2 end Template:Orf