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	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	27.9
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
Error	Absolute (¢)	-0.11	-4.46	-0.23	+4.12	-4.57	+7.60	-0.34	-8.92
	Relative (%)	-0.4	-16.0	-0.8	+14.8	-16.4	+27.2	-1.2	-32.0
Steps (reduced)		43 (4)	68 (29)	86 (8)	100 (22)	111 (33)	121 (4)	129 (12)	136 (19)

Approximation of harmonics in 39ed15/8

Harmonic		10	11	12	13	14	15	16	17
Error	Absolute (¢)	+4.00	+6.43	-4.69	-3.74	+7.48	-0.34	-0.46	+6.21
	Relative (%)	+14.4	+23.0	-16.8	-13.4	+26.8	-1.2	-1.6	+22.2
Steps (reduced)		143 (26)	149 (32)	154 (37)	159 (3)	164 (8)	168 (12)	172 (16)	176 (20)

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