24ed11/5

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24ed11/5

25ed11/5 →

Prime factorization	23 × 3
Step size	56.8752¢
Octave	21\24ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth	33\24ed11/5 (1876.88¢) (→11\8ed11/5)
Consistency limit	5
Distinct consistency limit	2
Special properties	Highly composite

24 equal divisions of 11/5 (abbreviated 24ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 24 equal parts of about 56.9⁠ ⁠¢ each. Each step represents a frequency ratio of (11/5)^1/24, or the 24th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	56.9	26/25
2	113.8	15/14, 16/15, 17/16
3	170.6	11/10
4	227.5	8/7, 17/15, 25/22
5	284.4	13/11, 20/17
6	341.3	17/14
7	398.1	5/4
8	455	13/10, 17/13, 22/17
9	511.9	23/17
10	568.8
11	625.6	10/7, 23/16
12	682.5
13	739.4	20/13, 23/15, 26/17
14	796.3
15	853.1	13/8, 23/14
16	910	17/10, 22/13
17	966.9	7/4
18	1023.8	20/11
19	1080.6	13/7, 15/8
20	1137.5	23/12, 25/13
21	1194.4	2/1
22	1251.3
23	1308.1	15/7, 17/8
24	1365	11/5

Harmonics

Approximation of harmonics in 24ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.6	-25.1	-11.2	+0.6	+26.2	-13.2	-16.9	+6.7	-5.1	+0.6	+20.6
	Relative (%)	-9.9	-44.1	-19.8	+1.0	+46.0	-23.2	-29.7	+11.8	-8.9	+1.0	+36.1
Steps (reduced)		21 (21)	33 (9)	42 (18)	49 (1)	55 (7)	59 (11)	63 (15)	67 (19)	70 (22)	73 (1)	76 (4)

Approximation of harmonics in 24ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	-18.8	-24.5	-22.5	-13.7	+1.1	+21.3	-10.7	+18.6	-5.1	-25.1
	Relative (%)	-7.5	-33.1	-43.1	-39.5	-24.1	+1.9	+37.4	-18.8	+32.7	-8.9	-44.2
Steps (reduced)		78 (6)	80 (8)	82 (10)	84 (12)	86 (14)	88 (16)	90 (18)	91 (19)	93 (21)	94 (22)	95 (23)