40ed5/2

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40ed5/2

41ed5/2 →

Prime factorization	23 × 5
Step size	39.6578¢
Octave	30\40ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth	48\40ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit	3
Distinct consistency limit	3

40 equal divisions of 5/2 (abbreviated 40ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 40 equal parts of about 39.7⁠ ⁠¢ each. Each step represents a frequency ratio of (5/2)^1/40, or the 40th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	39.7
2	79.3	22/21, 23/22
3	119	15/14, 29/27
4	158.6	23/21
5	198.3	19/17, 28/25
6	237.9
7	277.6	27/23
8	317.3	6/5
9	356.9	27/22
10	396.6	29/23
11	436.2	9/7
12	475.9	29/22
13	515.6
14	555.2	29/21
15	594.9
16	634.5	13/9
17	674.2
18	713.8
19	753.5	17/11
20	793.2
21	832.8	21/13, 29/18
22	872.5
23	912.1	22/13
24	951.8	19/11, 26/15
25	991.4	23/13
26	1031.1
27	1070.8	13/7
28	1110.4
29	1150.1
30	1189.7
31	1229.4
32	1269.1	25/12, 27/13
33	1308.7
34	1348.4
35	1388	29/13
36	1427.7
37	1467.3	7/3
38	1507
39	1546.7	22/9
40	1586.3	5/2

Harmonics

Approximation of harmonics in 40ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.3	+1.6	+19.1	-10.3	-8.6	+2.1	+8.9	+3.2	+19.1	+12.8	-18.9
	Relative (%)	-25.9	+4.1	+48.2	-25.9	-21.8	+5.3	+22.4	+8.2	+48.2	+32.2	-47.7
Steps (reduced)		30 (30)	48 (8)	61 (21)	70 (30)	78 (38)	85 (5)	91 (11)	96 (16)	101 (21)	105 (25)	108 (28)

Approximation of harmonics in 40ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.2	-8.2	-8.6	-1.4	+12.6	-7.0	+18.3	+8.9	+3.7	+2.5	+4.9
	Relative (%)	+2.9	-20.6	-21.8	-3.5	+31.8	-17.7	+46.3	+22.4	+9.4	+6.3	+12.2
Steps (reduced)		112 (32)	115 (35)	118 (38)	121 (1)	124 (4)	126 (6)	129 (9)	131 (11)	133 (13)	135 (15)	137 (17)