24ed7/3

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24ed7/3

25ed7/3 →

Prime factorization	23 × 3
Step size	61.1196¢
Octave	20\24ed7/3 (1222.39¢) (→5\6ed7/3)
Twelfth	31\24ed7/3 (1894.71¢)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

24 equal divisions of 7/3 (abbreviated 24ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 24 equal parts of about 61.1⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/24, or the 24th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	61.1	25/24, 26/25
2	122.2	14/13, 15/14
3	183.4	19/17, 21/19
4	244.5	15/13
5	305.6	6/5
6	366.7	21/17
7	427.8	9/7, 14/11, 23/18
8	489
9	550.1
10	611.2
11	672.3	22/15
12	733.4	23/15
13	794.6	11/7
14	855.7	18/11, 23/14
15	916.8	22/13
16	977.9	23/13
17	1039	11/6
18	1100.2	17/9
19	1161.3
20	1222.4
21	1283.5	19/9, 23/11, 25/12
22	1344.6	13/6
23	1405.8
24	1466.9	7/3

Harmonics

Approximation of harmonics in 24ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+22.4	-7.2	-16.3	+25.2	+15.1	-7.2	+6.1	-14.5	-13.5	+4.8	-23.6
	Relative (%)	+36.6	-11.9	-26.7	+41.2	+24.8	-11.9	+9.9	-23.7	-22.2	+7.9	-38.6
Steps (reduced)		20 (20)	31 (7)	39 (15)	46 (22)	51 (3)	55 (7)	59 (11)	62 (14)	65 (17)	68 (20)	70 (22)

Approximation of harmonics in 24ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+21.2	+15.1	+17.9	+28.5	-15.4	+7.9	-24.6	+8.9	-14.5	+27.2	+11.4
	Relative (%)	+34.7	+24.8	+29.4	+46.5	-25.2	+12.9	-40.2	+14.5	-23.7	+44.5	+18.6
Steps (reduced)		73 (1)	75 (3)	77 (5)	79 (7)	80 (8)	82 (10)	83 (11)	85 (13)	86 (14)	88 (16)	89 (17)