39ed15/8

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39ed15/8

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Prime factorization	3 × 13
Step size	27.9043¢
Octave	43\39ed15/8 (1199.89¢) (convergent)
Twelfth	68\39ed15/8 (1897.49¢) (semiconvergent)
Consistency limit	8
Distinct consistency limit	6

Division of the just major seventh into 39 equal parts (39ED15/8) is almost identical to 43 EDO, but with the 15/8 rather than the 2/1 being just. The octave is about 0.11 cents compressed and the step size is about 44.35 cents.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	27.904
2	55.809	29/28
3	83.713	20/19, 21/20, 22/21, 23/22
4	111.617	16/15, 17/16
5	139.522	13/12, 25/23
6	167.426	11/10, 21/19
7	195.33	19/17, 28/25, 29/26
8	223.235	17/15, 25/22
9	251.139	15/13, 22/19, 29/25
10	279.043	20/17
11	306.948	25/21
12	334.852	17/14, 23/19, 28/23, 29/24
13	362.756	16/13, 21/17, 26/21
14	390.661	5/4
15	418.565	14/11
16	446.469	22/17
17	474.374	21/16, 25/19, 29/22
18	502.278	4/3
19	530.182	15/11, 19/14, 23/17
20	558.087	11/8, 18/13, 29/21
21	585.991	7/5
22	613.895	10/7
23	641.799	13/9, 16/11, 29/20
24	669.704	22/15, 25/17, 28/19
25	697.608	3/2
26	725.512	29/19
27	753.417	17/11
28	781.321	11/7
29	809.225	8/5
30	837.13	13/8, 21/13
31	865.034	23/14, 28/17
32	892.938
33	920.843	17/10, 29/17
34	948.747	19/11, 26/15
35	976.651
36	1004.556	25/14
37	1032.46	20/11, 29/16
38	1060.364	24/13
39	1088.269	15/8

Harmonics

Approximation of harmonics in 39ed15/8

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	-0.11	-4.46	-0.23	+4.12	-4.57	+7.60	-0.34	-8.92	+4.00	+6.43	-4.69	-3.74	+7.48	-0.34	-0.46
	Relative (%)	-0.4	-16.0	-0.8	+14.8	-16.4	+27.2	-1.2	-32.0	+14.4	+23.0	-16.8	-13.4	+26.8	-1.2	-1.6
Steps (reduced)		43 (4)	68 (29)	86 (8)	100 (22)	111 (33)	121 (4)	129 (12)	136 (19)	143 (26)	149 (32)	154 (37)	159 (3)	164 (8)	168 (12)	172 (16)