624edo

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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, tempering out 6115295232/6103515625 (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.

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)

Miscellaneous properties

Since 624 = 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

Subgroup	Comma List	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
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

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	73\624	140.38	243/224	Septichrome
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)
12	259\624 (1\624)	498.08 (1.92)	4/3 (32805/32768)	Atomic
24	303\624 (17\624)	582.692 (32.692)	7/5 (?)	Chromium