39ed7/3

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39ed7/3

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Prime factorization	3 × 13
Step size	37.6121¢
Octave	32\39ed7/3 (1203.59¢)
Twelfth	51\39ed7/3 (1918.22¢) (→17\13ed7/3)
Consistency limit	4
Distinct consistency limit	4

39 equal divisions of 7/3 (abbreviated 39ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 39 equal parts of about 37.6⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/39, or the 39th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	37.6
2	75.2	23/22, 26/25
3	112.8	15/14, 16/15
4	150.4	25/23
5	188.1	29/26
6	225.7	8/7, 25/22
7	263.3	7/6, 29/25
8	300.9	19/16
9	338.5
10	376.1
11	413.7	19/15
12	451.3	13/10, 22/17
13	489
14	526.6	19/14, 23/17
15	564.2
16	601.8
17	639.4	29/20
18	677	28/19
19	714.6
20	752.2	17/11, 20/13
21	789.9	19/12
22	827.5
23	865.1
24	902.7
25	940.3	12/7
26	977.9
27	1015.5
28	1053.1
29	1090.8	15/8
30	1128.4	25/13
31	1166
32	1203.6	2/1
33	1241.2
34	1278.8	23/11
35	1316.4	15/7
36	1354
37	1391.6	29/13
38	1429.3	16/7
39	1466.9	7/3

Harmonics

Approximation of harmonics in 39ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.6	+16.3	+7.2	-3.0	-17.8	+16.3	+10.8	-5.1	+0.6	-14.0	-14.2
	Relative (%)	+9.5	+43.2	+19.1	-8.0	-47.2	+43.2	+28.6	-13.5	+1.5	-37.2	-37.7
Steps (reduced)		32 (32)	51 (12)	64 (25)	74 (35)	82 (4)	90 (12)	96 (18)	101 (23)	106 (28)	110 (32)	114 (36)

Approximation of harmonics in 39ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.3	-17.8	+13.2	+14.3	-15.4	-1.5	+17.7	+4.2	-5.1	-10.4	-12.1
	Relative (%)	-6.1	-47.2	+35.2	+38.1	-40.9	-4.0	+47.1	+11.0	-13.5	-27.7	-32.3
Steps (reduced)		118 (1)	121 (4)	125 (8)	128 (11)	130 (13)	133 (16)	136 (19)	138 (21)	140 (23)	142 (25)	144 (27)