39ed11/5

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39ed11/5

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Prime factorization	3 × 13
Step size	35.0001¢
Octave	34\39ed11/5 (1190¢)
Twelfth	54\39ed11/5 (1890.01¢) (→18\13ed11/5)
Consistency limit	3
Distinct consistency limit	3

39 equal divisions of 11/5 (abbreviated 39ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 39 equal parts of about 35 ¢ each. Each step represents a frequency ratio of (11/5)^1/39, or the 39th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	35
2	70	23/22, 28/27
3	105
4	140
5	175
6	210	9/8, 17/15, 26/23
7	245	15/13, 23/20
8	280	20/17
9	315
10	350
11	385
12	420
13	455	13/10
14	490
15	525	23/17
16	560
17	595
18	630
19	665	22/15
20	700	3/2
21	735	23/15, 26/17, 29/19
22	770	14/9
23	805
24	840
25	875
26	910	22/13, 27/16
27	945	19/11, 26/15
28	980
29	1015
30	1050
31	1085
32	1120
33	1155
34	1190
35	1225
36	1260
37	1295
38	1330
39	1365	11/5

Harmonics

Approximation of harmonics in 39ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.0	-11.9	+15.0	+13.7	+13.1	-8.8	+5.0	+11.1	+3.7	+13.7	+3.1
	Relative (%)	-28.6	-34.1	+42.9	+39.1	+37.3	-25.2	+14.3	+31.7	+10.6	+39.1	+8.7
Steps (reduced)		34 (34)	54 (15)	69 (30)	80 (2)	89 (11)	96 (18)	103 (25)	109 (31)	114 (36)	119 (2)	123 (6)

Approximation of harmonics in 39ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.5	+16.2	+1.7	-5.0	-4.9	+1.1	+12.5	-6.3	+14.2	+3.7	-3.3
	Relative (%)	+12.8	+46.3	+5.0	-14.2	-14.1	+3.2	+35.7	-18.0	+40.7	+10.6	-9.3
Steps (reduced)		127 (10)	131 (14)	134 (17)	137 (20)	140 (23)	143 (26)	146 (29)	148 (31)	151 (34)	153 (36)	155 (38)