24ed5/2

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24ed5/2

25ed5/2 →

Prime factorization	23 × 3
Step size	66.0964¢
Octave	18\24ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth	29\24ed5/2 (1916.8¢)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

24 equal divisions of 5/2 (abbreviated 24ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 24 equal parts of about 66.1 ¢ each. Each step represents a frequency ratio of (5/2)^1/24, or the 24th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	66.096	23/22, 24/23, 25/24, 26/25
2	132.193	13/12, 14/13, 15/14, 25/23
3	198.289	19/17
4	264.386	7/6, 22/19
5	330.482	17/14, 23/19
6	396.578	5/4, 19/15, 24/19
7	462.675	13/10, 17/13, 25/19
8	528.771	15/11, 19/14, 23/17
9	594.868	7/5, 17/12, 24/17
10	660.964	19/13, 22/15, 25/17
11	727.06	23/15, 26/17
12	793.157	11/7, 19/12
13	859.253	18/11, 23/14
14	925.35	12/7, 17/10
15	991.446	23/13, 25/14
16	1057.542	11/6, 24/13
17	1123.639	19/10, 21/11, 23/12, 25/13
18	1189.735	2/1
19	1255.832
20	1321.928	15/7
21	1388.024
22	1454.121	7/3, 23/10
23	1520.217	12/5
24	1586.314	5/2

Harmonics

Approximation of harmonics in 24ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.3	+14.8	-20.5	-10.3	+4.6	+2.1	-30.8	+29.7	-20.5	+12.8	-5.7
	Relative (%)	-15.5	+22.5	-31.1	-15.5	+6.9	+3.2	-46.6	+44.9	-31.1	+19.3	-8.6
Steps (reduced)		18 (18)	29 (5)	36 (12)	42 (18)	47 (23)	51 (3)	54 (6)	58 (10)	60 (12)	63 (15)	65 (17)

Approximation of harmonics in 24ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-12.1	-8.2	+4.6	+25.0	-13.8	+19.4	-8.1	-30.8	+16.9	+2.5	-8.4
	Relative (%)	-18.3	-12.4	+6.9	+37.9	-20.9	+29.4	-12.2	-46.6	+25.6	+3.8	-12.7
Steps (reduced)		67 (19)	69 (21)	71 (23)	73 (1)	74 (2)	76 (4)	77 (5)	78 (6)	80 (8)	81 (9)	82 (10)