39ed15/8

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39ed15/8

40ed15/8 →

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	8

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	27.9
2	55.8	29/28
3	83.7	20/19, 21/20, 22/21, 23/22
4	111.6	16/15, 17/16
5	139.5	13/12, 25/23
6	167.4	11/10, 21/19
7	195.3	19/17, 28/25, 29/26
8	223.2	17/15, 25/22
9	251.1	15/13, 22/19, 29/25
10	279	20/17
11	306.9	25/21
12	334.9	17/14, 23/19, 28/23, 29/24
13	362.8	16/13, 21/17, 26/21
14	390.7	5/4
15	418.6	14/11
16	446.5	22/17
17	474.4	21/16, 25/19, 29/22
18	502.3	4/3
19	530.2	15/11, 19/14, 23/17
20	558.1	11/8, 18/13, 29/21
21	586	7/5
22	613.9	10/7
23	641.8	13/9, 16/11, 29/20
24	669.7	22/15, 25/17, 28/19
25	697.6	3/2
26	725.5	29/19
27	753.4	17/11
28	781.3	11/7
29	809.2	8/5
30	837.1	13/8, 21/13
31	865	23/14, 28/17
32	892.9
33	920.8	17/10, 29/17
34	948.7	19/11, 26/15
35	976.7
36	1004.6	25/14
37	1032.5	20/11, 29/16
38	1060.4	24/13
39	1088.3	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)