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	Hekts	Approximate ratios
0	0	0	1/1
1	22.1	15.1
2	44.2	30.2
3	66.3	45.3	26/25, 27/26
4	88.5	60.5	20/19, 39/37, 41/39
5	110.6	75.6	33/31
6	132.7	90.7	27/25
7	154.8	105.8	23/21
8	176.9	120.9	41/37
9	199	136	37/33
10	221.2	151.2	25/22, 33/29
11	243.3	166.3	23/20
12	265.4	181.4	7/6
13	287.5	196.5	13/11
14	309.6	211.6
15	331.7	226.7	23/19
16	353.9	241.9	27/22
17	376	257	41/33
18	398.1	272.1	34/27, 39/31
19	420.2	287.2	37/29
20	442.3	302.3
21	464.4	317.4	17/13
22	486.5	332.6	41/31
23	508.7	347.7
24	530.8	362.8	19/14, 34/25
25	552.9	377.9
26	575	393
27	597.1	408.1	41/29
28	619.2	423.3	10/7
29	641.4	438.4
30	663.5	453.5	22/15
31	685.6	468.6
32	707.7	483.7
33	729.8	498.8	35/23
34	751.9	514	17/11
35	774.1	529.1	36/23
36	796.2	544.2	19/12
37	818.3	559.3
38	840.4	574.4
39	862.5	589.5
40	884.6	604.7	5/3
41	906.7	619.8
42	928.9	634.9
43	951	650	26/15
44	973.1	665.1
45	995.2	680.2
46	1017.3	695.3	9/5
47	1039.4	710.5	31/17
48	1061.6	725.6
49	1083.7	740.7
50	1105.8	755.8	36/19
51	1127.9	770.9	23/12
52	1150	786	33/17, 35/18
53	1172.1	801.2
54	1194.3	816.3
55	1216.4	831.4
56	1238.5	846.5
57	1260.6	861.6
58	1282.7	876.7	21/10
59	1304.8	891.9
60	1326.9	907
61	1349.1	922.1	37/17
62	1371.2	937.2
63	1393.3	952.3
64	1415.4	967.4	34/15
65	1437.5	982.6	39/17
66	1459.6	997.7
67	1481.8	1012.8
68	1503.9	1027.9	31/13
69	1526	1043	41/17
70	1548.1	1058.1	22/9
71	1570.2	1073.3
72	1592.3	1088.4
73	1614.5	1103.5	33/13
74	1636.6	1118.6	18/7
75	1658.7	1133.7
76	1680.8	1148.8	29/11
77	1702.9	1164
78	1725	1179.1
79	1747.1	1194.2
80	1769.3	1209.3	25/9
81	1791.4	1224.4	31/11
82	1813.5	1239.5	37/13
83	1835.6	1254.7	26/9
84	1857.7	1269.8
85	1879.8	1284.9
86	1902	1300	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)