24ed5/4

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24ed5/4

25ed5/4 →

Prime factorization	23 × 3
Step size	16.0964¢
Octave	75\24ed5/4 (1207.23¢) (→25\8ed5/4)
Twelfth	118\24ed5/4 (1899.38¢) (→59\12ed5/4)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

24 equal divisions of 5/4 (abbreviated 24ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 24 equal parts of about 16.1 ¢ each. Each step represents a frequency ratio of (5/4)^1/24, or the 24th root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.1
2	32.2
3	48.3
4	64.4	23/22
5	80.5	26/25
6	96.6	18/17, 19/18, 20/19
7	112.7	15/14
8	128.8	13/12, 14/13
9	144.9	25/23
10	161	11/10, 12/11, 21/19, 23/21
11	177.1
12	193.2	10/9, 19/17
13	209.3	25/22
14	225.3	17/15
15	241.4	15/13
16	257.5	7/6, 22/19
17	273.6
18	289.7	13/11, 20/17
19	305.8	25/21
20	321.9	6/5, 23/19
21	338	17/14
22	354.1	11/9, 21/17
23	370.2
24	386.3

Harmonics

Approximation of harmonics in 24ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.23	-2.58	-1.64	-1.64	+4.65	-4.68	+5.59	-5.16	+5.59	+1.55	-4.21
	Relative (%)	+44.9	-16.0	-10.2	-10.2	+28.9	-29.1	+34.8	-32.0	+34.8	+9.7	-26.2
Steps (reduced)		75 (3)	118 (22)	149 (5)	173 (5)	193 (1)	209 (17)	224 (8)	236 (20)	248 (8)	258 (18)	267 (3)

Approximation of harmonics in 24ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	+2.55	-4.21	-3.27	+4.45	+2.07	+5.05	-3.27	-7.26	-7.31	-3.79
	Relative (%)	+12.9	+15.9	-26.2	-20.3	+27.6	+12.9	+31.4	-20.3	-45.1	-45.4	-23.5
Steps (reduced)		276 (12)	284 (20)	291 (3)	298 (10)	305 (17)	311 (23)	317 (5)	322 (10)	327 (15)	332 (20)	337 (1)