85ed4

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85ed4

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Prime factorization	5 × 17
Step size	28.2353 ¢
Octave	43\85ed4 (1214.12 ¢)
Twelfth	67\85ed4 (1891.76 ¢)
Consistency limit	1
Distinct consistency limit	1

85 equal divisions of the 4th harmonic (abbreviated 85ed4) is a nonoctave tuning system that divides the interval of 4/1 into 85 equal parts of about 28.2 ¢ each. Each step represents a frequency ratio of 4^1/85, or the 85th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	28.2
2	56.5	31/30
3	84.7
4	112.9
5	141.2
6	169.4
7	197.6	28/25, 37/33
8	225.9	33/29, 41/36
9	254.1	22/19
10	282.4
11	310.6
12	338.8	17/14
13	367.1
14	395.3
15	423.5	23/18, 37/29
16	451.8
17	480
18	508.2
19	536.5	15/11
20	564.7	18/13
21	592.9	31/22
22	621.2
23	649.4
24	677.6
25	705.9
26	734.1	26/17
27	762.4
28	790.6	30/19, 41/26
29	818.8
30	847.1	31/19
31	875.3
32	903.5
33	931.8
34	960
35	988.2	23/13
36	1016.5
37	1044.7
38	1072.9	13/7
39	1101.2
40	1129.4
41	1157.6
42	1185.9
43	1214.1
44	1242.4
45	1270.6	25/12
46	1298.8	36/17
47	1327.1
48	1355.3
49	1383.5
50	1411.8
51	1440
52	1468.2	7/3
53	1496.5
54	1524.7	41/17
55	1552.9
56	1581.2
57	1609.4
58	1637.6	18/7
59	1665.9
60	1694.1
61	1722.4
62	1750.6
63	1778.8
64	1807.1
65	1835.3
66	1863.5
67	1891.8
68	1920
69	1948.2
70	1976.5
71	2004.7	35/11
72	2032.9
73	2061.2	23/7
74	2089.4
75	2117.6	17/5
76	2145.9
77	2174.1
78	2202.4
79	2230.6
80	2258.8
81	2287.1
82	2315.3
83	2343.5
84	2371.8
85	2400

Harmonics

Approximation of harmonics in 85ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+14.1	-10.2	+0.0	+9.0	+3.9	-8.8	+14.1	+7.9	-5.1	-0.7	-10.2
	Relative (%)	+50.0	-36.1	+0.0	+31.8	+13.9	-31.3	+50.0	+27.8	-18.2	-2.6	-36.1
Steps (reduced)		43 (43)	67 (67)	85 (0)	99 (14)	110 (25)	119 (34)	128 (43)	135 (50)	141 (56)	147 (62)	152 (67)

Approximation of harmonics in 85ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.6	+5.3	-1.2	+0.0	+8.0	-6.3	+13.1	+9.0	+9.2	+13.4	-7.1
	Relative (%)	-26.9	+18.7	-4.3	+0.0	+28.3	-22.2	+46.3	+31.8	+32.7	+47.4	-25.1
Steps (reduced)		157 (72)	162 (77)	166 (81)	170 (0)	174 (4)	177 (7)	181 (11)	184 (14)	187 (17)	190 (20)	192 (22)