39ed5/2

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39ed5/2

40ed5/2 →

Prime factorization	3 × 13
Step size	40.6747¢
Octave	30\39ed5/2 (1220.24¢) (→10\13ed5/2)
Twelfth	47\39ed5/2 (1911.71¢)
Consistency limit	3
Distinct consistency limit	3

39 equal divisions of 5/2 (abbreviated 39ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 39 equal parts of about 40.7⁠ ⁠¢ each. Each step represents a frequency ratio of (5/2)^1/39, or the 39th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	40.7
2	81.3	22/21
3	122	15/14
4	162.7
5	203.4	28/25
6	244
7	284.7	13/11
8	325.4	23/19
9	366.1	21/17, 26/21
10	406.7	29/23
11	447.4	22/17
12	488.1
13	528.8
14	569.4	25/18
15	610.1
16	650.8	19/13
17	691.5
18	732.1	26/17, 29/19
19	772.8
20	813.5
21	854.2
22	894.8
23	935.5
24	976.2
25	1016.9	9/5
26	1057.5
27	1098.2	17/9
28	1138.9	27/14
29	1179.6
30	1220.2
31	1260.9
32	1301.6
33	1342.3
34	1382.9	29/13
35	1423.6
36	1464.3	7/3
37	1505
38	1545.6	22/9
39	1586.3	5/2

Harmonics

Approximation of harmonics in 39ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+20.2	+9.8	-0.2	+20.2	-10.7	+7.2	+20.0	+19.5	-0.2	-2.5	+9.6
	Relative (%)	+49.8	+24.0	-0.5	+49.8	-26.2	+17.6	+49.3	+48.0	-0.5	-6.1	+23.5
Steps (reduced)		30 (30)	47 (8)	59 (20)	69 (30)	76 (37)	83 (5)	89 (11)	94 (16)	98 (20)	102 (24)	106 (28)

Approximation of harmonics in 39ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.0	-13.3	-10.7	-0.4	+16.7	-0.9	-13.2	+20.0	+16.9	+17.7	-18.5
	Relative (%)	-17.2	-32.6	-26.2	-0.9	+41.0	-2.3	-32.4	+49.3	+41.6	+43.6	-45.6
Steps (reduced)		109 (31)	112 (34)	115 (37)	118 (1)	121 (4)	123 (6)	125 (8)	128 (11)	130 (13)	132 (15)	133 (16)