86ed7/3

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86ed7/3

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Prime factorization	2 × 43
Step size	17.0566¢
Octave	70\86ed7/3 (1193.96¢) (→35\43ed7/3)
Twelfth	112\86ed7/3 (1910.34¢) (→56\43ed7/3)
Consistency limit	2
Distinct consistency limit	2

86 equal divisions of 7/3 (abbreviated 86ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 86 equal parts of about 17.1⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/86, or the 86th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.1
2	34.1
3	51.2	34/33, 35/34, 36/35
4	68.2	25/24, 26/25
5	85.3	41/39
6	102.3	35/33
7	119.4	15/14
8	136.5	13/12
9	153.5	12/11
10	170.6
11	187.6	39/35
12	204.7
13	221.7	25/22, 33/29
14	238.8	39/34
15	255.8
16	272.9	34/29, 41/35
17	290	13/11
18	307	37/31
19	324.1	35/29, 41/34
20	341.1	28/23
21	358.2
22	375.2	36/29, 41/33
23	392.3
24	409.4	19/15
25	426.4
26	443.5
27	460.5	30/23
28	477.6
29	494.6
30	511.7	39/29
31	528.8	19/14
32	545.8
33	562.9
34	579.9
35	597	41/29
36	614
37	631.1
38	648.2
39	665.2
40	682.3
41	699.3
42	716.4
43	733.4	29/19
44	750.5
45	767.5
46	784.6
47	801.7
48	818.7
49	835.8
50	852.8
51	869.9	38/23
52	886.9
53	904
54	921.1
55	938.1
56	955.2	33/19
57	972.2
58	989.3	23/13
59	1006.3	34/19
60	1023.4
61	1040.5	31/17
62	1057.5	35/19
63	1074.6
64	1091.6
65	1108.7	36/19
66	1125.7	23/12
67	1142.8	29/15
68	1159.9
69	1176.9
70	1194
71	1211
72	1228.1
73	1245.1	37/18, 39/19
74	1262.2	29/14
75	1279.2	23/11
76	1296.3	36/17
77	1313.4
78	1330.4	28/13, 41/19
79	1347.5	37/17
80	1364.5	11/5
81	1381.6
82	1398.6
83	1415.7	34/15
84	1432.8
85	1449.8	30/13
86	1466.9	7/3

Harmonics

Approximation of harmonics in 86ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.04	+8.39	+4.99	-6.08	+2.35	+8.39	-1.05	-0.28	+4.94	-6.55	-3.68
	Relative (%)	-35.4	+49.2	+29.2	-35.7	+13.8	+49.2	-6.2	-1.6	+29.0	-38.4	-21.6
Steps (reduced)		70 (70)	112 (26)	141 (55)	163 (77)	182 (10)	198 (26)	211 (39)	223 (51)	234 (62)	243 (71)	252 (80)

Approximation of harmonics in 86ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.80	+2.35	+2.31	-7.08	+7.36	-6.31	+2.42	-1.10	-0.28	+4.47	-4.26
	Relative (%)	-34.0	+13.8	+13.5	-41.5	+43.1	-37.0	+14.2	-6.4	-1.6	+26.2	-25.0
Steps (reduced)		260 (2)	268 (10)	275 (17)	281 (23)	288 (30)	293 (35)	299 (41)	304 (46)	309 (51)	314 (56)	318 (60)