4327edo

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4327edo

4328edo →

Prime factorization	4327 (prime)
Step size	0.277328¢
Fifth	2531\4327 (701.918¢)
Semitones (A1:m2)	409:326 (113.4¢ : 90.41¢)
Consistency limit	11
Distinct consistency limit	11

4327 equal divisions of the octave (abbreviated 4327edo or 4327ed2), also called 4327-tone equal temperament (4327tet) or 4327 equal temperament (4327et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4327 equal parts of about 0.277 ¢ each. Each step represents a frequency ratio of 2^1/4327, or the 4327th root of 2.

Theory

4327edo is consistent to the 11-odd-limit, tempering out 117649/117612, 50014503/50000000, 234365481/234256000 and 369140625/369098752. It supports mikkolic.

Odd harmonics

Approximation of odd harmonics in 4327edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.037	+0.005	-0.118	-0.074	+0.011	+0.055	-0.032	-0.125	+0.060	+0.123	-0.126
	Relative (%)	-13.3	+1.7	-42.5	-26.5	+3.9	+19.7	-11.6	-45.2	+21.8	+44.3	-45.3
Steps (reduced)		6858 (2531)	10047 (1393)	12147 (3493)	13716 (735)	14969 (1988)	16012 (3031)	16905 (3924)	17686 (378)	18381 (1073)	19006 (1698)	19573 (2265)

Subsets and supersets

4327edo is the 591st prime EDO.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-6858 4327⟩	[⟨4327 6858]]	0.0116	0.0116	4.18
2.3.5	[-69 45 -1⟩, [96 83 -98⟩	[⟨4327 6858 10047]]	0.0071	0.0115	4.15
2.3.5.7	[-9 5 -8 7⟩, [3 -24 3 10⟩, [-57 16 10 3⟩	[⟨4327 6858 10047 12147]]	0.0158	0.0181	6.53
2.3.5.7.11	117649/117612, 50014503/50000000, 234365481/234256000, 369140625/369098752	[⟨4327 6858 10047 12147 14969]]	0.0120	0.0179	6.45
2.3.5.7.11.13	123201/123200, 4100625/4100096, 1990656/1990625, 4917248/4915625, 3195731/3194880	[⟨4327 6858 10047 12147 14969 16012]]	0.0075	0.0191	6.89

Music

Francium

• "Modern Milk" from Naughty Girl Era (2024) – Spotify | Bandcamp | YouTube – mikkolic in 4327edo