87ed7

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87ed7

88ed7 →

Prime factorization	3 × 29
Step size	38.7221¢
Octave	31\87ed7 (1200.39¢) (semiconvergent)
Twelfth	49\87ed7 (1897.38¢)
Consistency limit	12
Distinct consistency limit	9

Division of the 7th harmonic into 87 equal parts (87ed7) is related to 31 edo, but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	38.7221
2	77.4443
3	116.1664	77/72, 15/14
4	154.8885
5	193.6107	19/17, 85/76
6	232.3328	8/7
7	271.0550
8	309.7771
9	348.4992	11/9, 49/40
10	387.2214	5/4
11	425.9435
12	464.6656	98/75
13	503.3878	91/68, 75/56
14	542.1099
15	580.8321	7/5
16	619.5542	10/7
17	658.2763
18	696.9985	112/75, 121/81, 136/91, 187/125
19	735.7206
20	774.4427
21	813.1649	8/5
22	851.8870
23	890.6091
24	929.3313	65/38
25	968.0534
26	1006.7756
27	1045.4977	64/35
28	1084.2198
29	1122.9420
30	1161.6641	88/45, 96/49, 49/25
31	1200.3862	2/1
32	1239.1084
33	1277.8305	44/21
34	1316.5527
35	1355.2748
36	1393.9969	38/17, 85/38
37	1432.7191
38	1471.4412
39	1510.1633
40	1548.8855
41	1587.6076
42	1626.3297	64/25
43	1665.0519
44	1703.7740
45	1742.4962	52/19
46	1781.2183
47	1819.9404
48	1858.6626	38/13
49	1897.3847
50	1936.1068
51	1974.8290	25/8
52	2013.5511
53	2052.2733
54	2090.9954
55	2129.7175
56	2168.4397
57	2207.1618	68/19
58	2245.8839
59	2284.6061
60	2323.3282	65/17
61	2362.0503
62	2400.7725
63	2439.4946	45/11
64	2478.2168
65	2516.9389
66	2555.6610	35/8
67	2594.3832
68	2633.1053
69	2671.8274
70	2710.5496
71	2749.2717
72	2787.9939	5/1
73	2826.7160
74	2865.4381
75	2904.1603	75/14
76	2942.8824
77	2981.6045
78	3020.3267	40/7, 63/11
79	3059.0488
80	3097.7709
81	3136.4931	49/8
82	3175.2152
83	3213.9374
84	3252.6595	98/15, 72/11
85	3291.3816
86	3330.1038
87	3368.8259	exact 7/1	harmonic seventh plus two octaves