569edo

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569edo

570edo →

Prime factorization	569 (prime)
Step size	2.10896 ¢
Fifth	333\569 (702.285 ¢)
Semitones (A1:m2)	55:42 (116 ¢ : 88.58 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

569edo is only consistent to the 5-odd-limit. The equal temperament tempers out 1600000/1594323 (amity comma) in the 5-limit. Using the patent val, it tempers out 65625/65536, 823543/820125, and 33554432/33480783 in the 7-limit; 42592/42525, 42875/42768, 43923/43904, and 151263/151250 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 569edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.330	-0.373	-0.812	-0.879	+0.949	+0.493	-0.149	+0.197	-0.403	+0.131
	Relative (%)	+0.0	+15.6	-17.7	-38.5	-41.7	+45.0	+23.4	-7.1	+9.3	-19.1	+6.2
Steps (reduced)		569 (0)	902 (333)	1321 (183)	1597 (459)	1968 (261)	2106 (399)	2326 (50)	2417 (141)	2574 (298)	2764 (488)	2819 (543)

Subsets and supersets

569edo is the 104th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[902 -569⟩	[⟨569 902]]	-0.1040	0.1040	4.93
2.3.5	1600000/1594323, [-94 -11 48⟩	[⟨569 902 1321]]	-0.0157	0.1510	7.16
2.3.5.7	65625/65536, 823543/820125, 1600000/1594323	[⟨569 902 1321 1597]]	+0.0605	0.1858	8.81
2.3.5.7.11	42592/42525, 42875/42768, 43923/43904, 151263/151250	[⟨569 902 1321 1597 1968]]	+0.0992	0.1834	8.70

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	161\569	339.54	243/200	Paramity

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Francium

• "Cuckoo Pickpocket" from Cursed Cuckoo Creations (2024) – Spotify | Bandcamp | YouTube
• "ME" from CAPSLOCK (2024) – Spotify | Bandcamp | YouTube