87ed7/3

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87ed7/3

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Prime factorization	3 × 29
Step size	16.8606¢
Octave	71\87ed7/3 (1197.1¢)
Twelfth	113\87ed7/3 (1905.25¢)
Consistency limit	3
Distinct consistency limit	3

87 equal divisions of 7/3 (abbreviated 87ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 87 equal parts of about 16.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/87, or the 87th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.861
2	33.721
3	50.582	34/33, 35/34, 36/35
4	67.442	26/25
5	84.303	41/39
6	101.164	18/17, 35/33
7	118.024	15/14, 31/29
8	134.885
9	151.745	12/11
10	168.606
11	185.466	39/35
12	202.327
13	219.188	17/15, 25/22
14	236.048	39/34
15	252.909	22/19
16	269.769	7/6
17	286.63	13/11, 33/28
18	303.491	37/31
19	320.351
20	337.212	17/14
21	354.072
22	370.933
23	387.793	5/4
24	404.654	24/19
25	421.515	23/18, 37/29
26	438.375
27	455.236	13/10
28	472.096
29	488.957
30	505.818
31	522.678	23/17
32	539.539	15/11, 41/30
33	556.399	29/21
34	573.26	39/28
35	590.12
36	606.981
37	623.842	33/23
38	640.702
39	657.563	19/13, 41/28
40	674.423	31/21, 34/23
41	691.284
42	708.145
43	725.005	35/23, 38/25
44	741.866	23/15
45	758.726
46	775.587	36/23
47	792.448	30/19
48	809.308
49	826.169	29/18
50	843.029	13/8
51	859.89	23/14
52	876.75
53	893.611
54	910.472	22/13
55	927.332	29/17, 41/24
56	944.193	19/11
57	961.053
58	977.914	37/21
59	994.775
60	1011.635
61	1028.496
62	1045.356
63	1062.217	24/13
64	1079.077	28/15, 41/22
65	1095.938
66	1112.799	19/10
67	1129.659	25/13
68	1146.52	33/17
69	1163.38
70	1180.241
71	1197.102	2/1
72	1213.962
73	1230.823
74	1247.683	35/17, 37/18, 39/19
75	1264.544
76	1281.404
77	1298.265	36/17
78	1315.126
79	1331.986	41/19
80	1348.847	24/11, 37/17
81	1365.707	11/5
82	1382.568
83	1399.429
84	1416.289	34/15
85	1433.15
86	1450.01	30/13
87	1466.871	7/3

Harmonics

Approximation of harmonics in 87ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.90	+3.29	-5.80	-4.32	+0.39	+3.29	+8.17	+6.58	-7.22	-3.61	-2.51
	Relative (%)	-17.2	+19.5	-34.4	-25.6	+2.3	+19.5	+48.4	+39.0	-42.8	-21.4	-14.9
Steps (reduced)		71 (71)	113 (26)	142 (55)	165 (78)	184 (10)	200 (26)	214 (40)	226 (52)	236 (62)	246 (72)	255 (81)

Approximation of harmonics in 87ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.19	+0.39	-1.03	+5.27	+1.47	+3.68	-5.62	+6.75	+6.58	-6.51	+0.83
	Relative (%)	-36.7	+2.3	-6.1	+31.2	+8.7	+21.8	-33.3	+40.0	+39.0	-38.6	+4.9
Steps (reduced)		263 (2)	271 (10)	278 (17)	285 (24)	291 (30)	297 (36)	302 (41)	308 (47)	313 (52)	317 (56)	322 (61)