584edo

← 583edo

584edo

585edo →

Prime factorization	23 × 73
Step size	2.05479¢
Fifth	342\584 (702.74¢) (→171\292)
Semitones (A1:m2)	58:42 (119.2¢ : 86.3¢)
Dual sharp fifth	342\584 (702.74¢) (→171\292)
Dual flat fifth	341\584 (700.685¢)
Dual major 2nd	99\584 (203.425¢)
Consistency limit	5
Distinct consistency limit	5

584 equal divisions of the octave (584edo), or 584-tone equal temperament (584tet), 584 equal temperament (584et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 584 equal parts of about 2.05 ¢ each.

Theory

584et tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (hemiluna temperament), and 12005/11979, 131072/130977, 5632/5625, 537109375/536870912, 9453125/9437184, 160083/160000 and 391314/390625 in the 11-limit.

Approximation of odd harmonics in 584edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	+0.785	-0.012	-1.018	-0.485	-0.633	-0.117	+0.772	-0.161	+0.432	-0.233	+0.493
	relative (%)	+38	-1	-50	-24	-31	-6	+38	-8	+21	-11	+24
Steps (reduced)		926 (342)	1356 (188)	1639 (471)	1851 (99)	2020 (268)	2161 (409)	2282 (530)	2387 (51)	2481 (145)	2565 (229)	2642 (306)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[463 -292⟩	⟨584 926]	-0.2476	0.2475	12.05
2.3.5	[3 -18 11⟩, [21 -20 4⟩	⟨584 926 1356]	-0.1633	0.2346	11.42
2.3.5.7	1500625/1492992, 1605632/1594323, 235298/234375	⟨584​ 926 ​1356 ​1639]	-0.0319	0.3052	14.85
2.3.5.7.11	5632/5625, 160083/160000, 26411/26244, 968000/964467	⟨584​ 926 ​1356 ​1639​ 2020​]	+0.0111	0.2862	13.93
2.3.5.7.11.13	2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776	⟨584​ 926 ​1356​ 1639 ​2020 ​2161]	+0.0145	0.2613	12.72

​

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	47\584	96.58	200/189	Hemiluna

Scales

• Hemiluna14

Music

• Are You From The Moon? by Francium