86edt

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86edt

87edt →

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	22.1
2	44.2
3	66.3	26/25, 27/26
4	88.5	20/19, 39/37, 41/39
5	110.6	33/31
6	132.7	27/25
7	154.8	23/21
8	176.9	41/37
9	199	37/33
10	221.2	25/22, 33/29
11	243.3	23/20
12	265.4	7/6
13	287.5	13/11
14	309.6
15	331.7	23/19
16	353.9	27/22
17	376	41/33
18	398.1	34/27, 39/31
19	420.2	37/29
20	442.3
21	464.4	17/13
22	486.5	41/31
23	508.7
24	530.8	19/14, 34/25
25	552.9
26	575
27	597.1	41/29
28	619.2	10/7
29	641.4
30	663.5	22/15
31	685.6
32	707.7
33	729.8	35/23
34	751.9	17/11
35	774.1	36/23
36	796.2	19/12
37	818.3
38	840.4
39	862.5
40	884.6	5/3
41	906.7
42	928.9
43	951	26/15
44	973.1
45	995.2
46	1017.3	9/5
47	1039.4	31/17
48	1061.6
49	1083.7
50	1105.8	36/19
51	1127.9	23/12
52	1150	33/17, 35/18
53	1172.1
54	1194.3
55	1216.4
56	1238.5
57	1260.6
58	1282.7	21/10
59	1304.8
60	1326.9
61	1349.1	37/17
62	1371.2
63	1393.3
64	1415.4	34/15
65	1437.5	39/17
66	1459.6
67	1481.8
68	1503.9	31/13
69	1526	41/17
70	1548.1	22/9
71	1570.2
72	1592.3
73	1614.5	33/13
74	1636.6	18/7
75	1658.7
76	1680.8	29/11
77	1702.9
78	1725
79	1747.1
80	1769.3	25/9
81	1791.4	31/11
82	1813.5	37/13
83	1835.6	26/9
84	1857.7
85	1879.8
86	1902	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)