39ed7/4

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39ed7/4

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Prime factorization	3 × 13
Step size	24.8417¢
Octave	48\39ed7/4 (1192.4¢) (→16\13ed7/4)
Twelfth	77\39ed7/4 (1912.81¢)
Consistency limit	2
Distinct consistency limit	2

39 equal divisions of 7/4 (abbreviated 39ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 39 equal parts of about 24.8 ¢ each. Each step represents a frequency ratio of (7/4)^1/39, or the 39th root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	24.8
2	49.7
3	74.5	25/24, 26/25
4	99.4
5	124.2	14/13, 15/14
6	149.1	12/11
7	173.9
8	198.7	19/17, 28/25
9	223.6	25/22
10	248.4	15/13, 22/19
11	273.3	7/6
12	298.1
13	322.9	6/5
14	347.8
15	372.6
16	397.5	24/19, 29/23
17	422.3	14/11, 23/18
18	447.2	22/17
19	472	25/19
20	496.8
21	521.7	19/14
22	546.5	26/19
23	571.4
24	596.2	17/12, 24/17
25	621
26	645.9
27	670.7	25/17, 28/19
28	695.6
29	720.4
30	745.3	23/15
31	770.1
32	794.9	19/12
33	819.8	29/18
34	844.6
35	869.5	28/17
36	894.3
37	919.1	17/10
38	944	19/11
39	968.8

Harmonics

Approximation of harmonics in 39ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-7.6	+10.9	+9.6	-4.0	+3.3	+9.6	+2.0	-3.1	-11.6	-2.8	-4.3
	Relative (%)	-30.6	+43.7	+38.8	-16.3	+13.1	+38.8	+8.2	-12.6	-46.9	-11.1	-17.5
Steps (reduced)		48 (9)	77 (38)	97 (19)	112 (34)	125 (8)	136 (19)	145 (28)	153 (36)	160 (4)	167 (11)	173 (17)

Approximation of harmonics in 39ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.1	+2.0	+6.8	-5.6	-11.1	-10.7	-5.0	+5.6	-4.3	-10.4	+12.1
	Relative (%)	+24.7	+8.2	+27.4	-22.4	-44.9	-43.2	-20.0	+22.5	-17.5	-41.7	+48.5
Steps (reduced)		179 (23)	184 (28)	189 (33)	193 (37)	197 (2)	201 (6)	205 (10)	209 (14)	212 (17)	215 (20)	219 (24)