20ed5/2

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20ed5/2

21ed5/2 →

Prime factorization	22 × 5
Step size	79.3157¢
Octave	15\20ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth	24\20ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit	8
Distinct consistency limit	3

20 equal divisions of 5/2 (abbreviated 20ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 20 equal parts of about 79.3 ¢ each. Each step represents a frequency ratio of (5/2)^1/20, or the 20th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	79.316	19/18, 20/19, 21/20, 22/21, 23/22, 24/23, 25/24
2	158.631	11/10, 12/11, 21/19, 23/21, 25/23
3	237.947	8/7, 15/13, 22/19, 23/20
4	317.263	6/5, 23/19, 25/21
5	396.578	5/4, 19/15, 24/19
6	475.894	17/13, 21/16, 25/19
7	555.21	11/8, 18/13, 25/18
8	634.525	13/9, 16/11, 23/16
9	713.841	3/2
10	793.157	11/7, 19/12
11	872.473	5/3, 23/14
12	951.788	19/11
13	1031.104	9/5, 20/11
14	1110.42	17/9, 19/10, 21/11, 23/12
15	1189.735	2/1
16	1269.051	21/10, 23/11, 25/12
17	1348.367	13/6, 24/11
18	1427.682	16/7, 23/10, 25/11
19	1506.998	12/5, 19/8
20	1586.314	5/2

Harmonics

Approximation of harmonics in 20ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.3	+1.6	-20.5	-10.3	-8.6	-37.6	-30.8	+3.2	-20.5	-26.9	-18.9
	Relative (%)	-12.9	+2.0	-25.9	-12.9	-10.9	-47.4	-38.8	+4.1	-25.9	-33.9	-23.8
Steps (reduced)		15 (15)	24 (4)	30 (10)	35 (15)	39 (19)	42 (2)	45 (5)	48 (8)	50 (10)	52 (12)	54 (14)

Approximation of harmonics in 20ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.2	+31.5	-8.6	+38.3	+12.6	-7.0	-21.3	-30.8	-35.9	-37.2	-34.8
	Relative (%)	+1.5	+39.7	-10.9	+48.2	+15.9	-8.9	-26.9	-38.8	-45.3	-46.9	-43.9
Steps (reduced)		56 (16)	58 (18)	59 (19)	61 (1)	62 (2)	63 (3)	64 (4)	65 (5)	66 (6)	67 (7)	68 (8)