86edt

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86edt

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Prime factorization	2 × 43
Step size	22.1158¢
Octave	54\86edt (1194.25¢) (→27\43edt)
Consistency limit	2
Distinct consistency limit	2

86 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 86edt or 86ed3), is a nonoctave tuning system that divides the interval of 3/1 into 86 equal parts of about 22.1 ¢ each. Each step represents a frequency ratio of 3^1/86, or the 86th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	22.116
2	44.232
3	66.347	26/25, 27/26
4	88.463	20/19, 39/37, 41/39
5	110.579	33/31
6	132.695	27/25
7	154.81	23/21
8	176.926	41/37
9	199.042	37/33
10	221.158	25/22, 33/29
11	243.273	23/20
12	265.389	7/6
13	287.505	13/11
14	309.621
15	331.736	23/19
16	353.852	27/22
17	375.968	41/33
18	398.084	34/27, 39/31
19	420.199	37/29
20	442.315
21	464.431	17/13
22	486.547	41/31
23	508.662
24	530.778	19/14, 34/25
25	552.894
26	575.01
27	597.125	41/29
28	619.241	10/7
29	641.357
30	663.473	22/15
31	685.588
32	707.704
33	729.82	35/23
34	751.936	17/11
35	774.051	36/23
36	796.167	19/12
37	818.283
38	840.399
39	862.514
40	884.63	5/3
41	906.746
42	928.862
43	950.978	26/15
44	973.093
45	995.209
46	1017.325	9/5
47	1039.441	31/17
48	1061.556
49	1083.672
50	1105.788	36/19
51	1127.904	23/12
52	1150.019	33/17, 35/18
53	1172.135
54	1194.251
55	1216.367
56	1238.482
57	1260.598
58	1282.714	21/10
59	1304.83
60	1326.945
61	1349.061	37/17
62	1371.177
63	1393.293
64	1415.408	34/15
65	1437.524	39/17
66	1459.64
67	1481.756
68	1503.871	31/13
69	1525.987	41/17
70	1548.103	22/9
71	1570.219
72	1592.334
73	1614.45	33/13
74	1636.566	18/7
75	1658.682
76	1680.797	29/11
77	1702.913
78	1725.029
79	1747.145
80	1769.26	25/9
81	1791.376	31/11
82	1813.492	37/13
83	1835.608	26/9
84	1857.723
85	1879.839
86	1901.955	3/1

Harmonics

Approximation of harmonics in 86edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.75	+0.00	+10.62	+0.27	-5.75	-7.23	+4.87	+0.00	-5.48	+6.44	+10.62
	Relative (%)	-26.0	+0.0	+48.0	+1.2	-26.0	-32.7	+22.0	+0.0	-24.8	+29.1	+48.0
Steps (reduced)		54 (54)	86 (0)	109 (23)	126 (40)	140 (54)	152 (66)	163 (77)	172 (0)	180 (8)	188 (16)	195 (23)

Approximation of harmonics in 86edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.74	+9.14	+0.27	-0.88	+4.74	-5.75	-10.89	+10.89	-7.23	+0.69	-9.91
	Relative (%)	+21.4	+41.3	+1.2	-4.0	+21.4	-26.0	-49.2	+49.2	-32.7	+3.1	-44.8
Steps (reduced)		201 (29)	207 (35)	212 (40)	217 (45)	222 (50)	226 (54)	230 (58)	235 (63)	238 (66)	242 (70)	245 (73)