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	28.235
2	56.471	31/30
3	84.706
4	112.941
5	141.176
6	169.412
7	197.647	28/25, 37/33
8	225.882	33/29, 41/36
9	254.118	22/19
10	282.353
11	310.588
12	338.824	17/14
13	367.059
14	395.294
15	423.529	23/18, 37/29
16	451.765
17	480
18	508.235
19	536.471	15/11
20	564.706	18/13
21	592.941	31/22
22	621.176
23	649.412
24	677.647
25	705.882
26	734.118	26/17
27	762.353
28	790.588	30/19, 41/26
29	818.824
30	847.059	31/19
31	875.294
32	903.529
33	931.765
34	960
35	988.235	23/13
36	1016.471
37	1044.706
38	1072.941	13/7
39	1101.176
40	1129.412
41	1157.647
42	1185.882
43	1214.118
44	1242.353
45	1270.588	25/12
46	1298.824	36/17
47	1327.059
48	1355.294
49	1383.529
50	1411.765
51	1440
52	1468.235	7/3
53	1496.471
54	1524.706	41/17
55	1552.941
56	1581.176
57	1609.412
58	1637.647	18/7
59	1665.882
60	1694.118
61	1722.353
62	1750.588
63	1778.824
64	1807.059
65	1835.294
66	1863.529
67	1891.765
68	1920
69	1948.235
70	1976.471
71	2004.706	35/11
72	2032.941
73	2061.176	23/7
74	2089.412
75	2117.647	17/5
76	2145.882
77	2174.118
78	2202.353
79	2230.588
80	2258.824
81	2287.059
82	2315.294
83	2343.529
84	2371.765
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)