624edo

← 623edo

624edo

625edo →

Prime factorization	24 × 3 × 13
Step size	1.92308 ¢
Fifth	365\624 (701.923 ¢)
Semitones (A1:m2)	59:47 (113.5 ¢ : 90.38 ¢)
Consistency limit	27
Distinct consistency limit	27

Theory

624edo is consistent to the 27-odd-limit. The equal temperament tempers out [23 6 -14⟩ (vishnuzma) and [-69 45 -1⟩ (counterschisma) in the 5-limit; 250047/250000, 2460375/2458624, and 134217728/133984375 in the 7-limit; 9801/9800, 46656/46585, 131072/130977, and 151263/151250 in the 11-limit; 1716/1715, 2080/2079, 4096/4095, 34398/34375, and 39366/39325 in the 13-limit; 936/935, 1701/1700, 2025/2023, and 2058/2057 in the 17-limit; 1521/1520, 2376/2375, 2432/2431, and 3328/3325 in the 19-limit; 2024/2023, 2025/2024, and 3888/3887 in the 23-limit.

It provides an excellent optimal patent val for the rank-6 temperament tempering out 936/935, as well as the rank-5 2.3.5.11.13 subgroup restriction thereof.

Prime harmonics

Approximation of prime harmonics in 624edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.032	+0.225	+0.405	+0.605	-0.143	+0.814	+0.564	+0.572	-0.731	-0.805
	Relative (%)	+0.0	-1.7	+11.7	+21.1	+31.5	-7.4	+42.3	+29.3	+29.7	-38.0	-41.8
Steps (reduced)		624 (0)	989 (365)	1449 (201)	1752 (504)	2159 (287)	2309 (437)	2551 (55)	2651 (155)	2823 (327)	3031 (535)	3091 (595)

Subsets and supersets

Since 624 factors into 2⁴ × 3 × 13, 624edo has subset edos 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 156, and 312.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-989 624⟩ | [⟨624 989]] | +0.0101 | 0.0101 | 0.52 |- | 2.3.5 | [23 6 -14⟩, [-69 45 -1⟩ | [⟨624 989 1449]] | −0.0256 | 0.0510 | 2.65 |- | 2.3.5.7 | 250047/250000, 2460375/2458624, [27 0 -8 -3⟩ | [⟨624 989 1449 1752]] | −0.0552 | 0.0678 | 3.52 |- | 2.3.5.7.11 | 9801/9800, 46656/46585, 131072/130977, 151263/151250 | [⟨624 989 1449 1752 2159]] | −0.0792 | 0.0772 | 4.02 |- | 2.3.5.7.11.13 | 1716/1715, 2080/2079, 4096/4095, 34398/34375, 39366/39325 | [⟨624 989 1449 1752 2159 2309]] | −0.0595 | 0.0831 | 4.32 |- | 2.3.5.7.11.13.17 | 936/935, 1701/1700, 1716/1715, 2025/2023, 4096/4095, 11016/11011 | [⟨624 989 1449 1752 2159 2309 2551]] | −0.0795 | 0.0911 | 4.74 |- | 2.3.5.7.11.13.17.19 | 936/935, 1521/1520, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 11016/11011 | [⟨624 989 1449 1752 2159 2309 2551 2651]] | −0.0861 | 0.0870 | 4.53 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 259\624 | 498.08 | 4/3 | Counterschismic |- | 1 | 311\624 | 598.08 | 847/600 | Vydubychi |- | 2 | 37\624 | 71.15 | 25/24 | Vishnu (5-limit) |- | 3 | 73\624 | 140.38 | 243/224 | Septichrome |- | 6 | 177\624
(31\624) | 340.38
(59.62) | 162/133
(88/85) | Semiseptichrome |- | 12 | 259\624
(1\624) | 498.08
(1.92) | 4/3
(32805/32768) | Atomic |- | 13 | 259\624
(19\624) | 498.08
(36.54) | 4/3
(?) | Aluminium |- | 16 | 259\624
(14\624) | 498.08
(48.077) | 4/3
(?) | Sulfur |- | 24 | 303\624
(17\624) | 582.692
(32.692) | 7/5
(?) | Chromium |- | 26 | 259\624
(19\624) | 498.08
(36.54) | 4/3
(?) | Iron Template:Rank-2 end Template:Orf

Music

Eliora

• Etude in Iron (2024)