24ed7/4

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24ed7/4

25ed7/4 →

Prime factorization	23 × 3
Step size	40.3677¢
Octave	30\24ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth	47\24ed7/4 (1897.28¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

24 equal divisions of 7/4 (abbreviated 24ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 24 equal parts of about 40.4 ¢ each. Each step represents a frequency ratio of (7/4)^1/24, or the 24th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	40.368
2	80.735	19/18, 26/25
3	121.103	14/13, 15/14
4	161.471	11/10, 12/11, 21/19, 23/21
5	201.839
6	242.206	15/13
7	282.574	13/11, 20/17
8	322.942	6/5, 23/19
9	363.31
10	403.677	19/15
11	444.045	9/7, 13/10, 22/17
12	484.413	25/19
13	524.781	15/11, 19/14
14	565.148	18/13, 25/18
15	605.516	17/12, 24/17
16	645.884	13/9, 19/13
17	686.252
18	726.619	26/17
19	766.987	14/9
20	807.355
21	847.723	18/11, 23/14
22	888.09	5/3
23	928.458	17/10
24	968.826

Harmonics

Approximation of harmonics in 24ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.0	-4.7	-18.3	-0.9	+6.4	-18.3	-7.3	-9.3	+10.1	+6.6	+17.4
	Relative (%)	+27.3	-11.6	-45.3	-2.3	+15.8	-45.3	-18.0	-23.1	+25.0	+16.3	+43.1
Steps (reduced)		30 (6)	47 (23)	59 (11)	69 (21)	77 (5)	83 (11)	89 (17)	94 (22)	99 (3)	103 (7)	107 (11)

Approximation of harmonics in 24ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-0.1	-7.3	-5.6	+3.8	+19.9	+1.7	-11.2	-19.2	+17.4	+17.6	-19.0
	Relative (%)	-0.2	-18.0	-13.9	+9.3	+49.3	+4.2	-27.7	-47.7	+43.1	+43.6	-47.1
Steps (reduced)		110 (14)	113 (17)	116 (20)	119 (23)	122 (2)	124 (4)	126 (6)	128 (8)	131 (11)	133 (13)	134 (14)