85edt

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85edt

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Prime factorization	5 × 17
Step size	22.3759¢
Octave	54\85edt (1208.3¢)
Consistency limit	2
Distinct consistency limit	2

85 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 85edt or 85ed3), is a nonoctave tuning system that divides the interval of 3/1 into 85 equal parts of about 22.4 ¢ each. Each step represents a frequency ratio of 3^1/85, or the 85th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	22.376
2	44.752
3	67.128	27/26
4	89.504	39/37, 41/39
5	111.88
6	134.256
7	156.632	23/21
8	179.008	41/37
9	201.383
10	223.759	25/22, 33/29
11	246.135	38/33
12	268.511	7/6
13	290.887
14	313.263	6/5
15	335.639
16	358.015
17	380.391
18	402.767	29/23
19	425.143	23/18
20	447.519
21	469.895	38/29
22	492.271
23	514.647	31/23
24	537.023	15/11
25	559.399	29/21
26	581.774	7/5
27	604.15
28	626.526	33/23
29	648.902
30	671.278	31/21
31	693.654
32	716.03
33	738.406	23/15, 26/17
34	760.782
35	783.158	11/7
36	805.534	35/22
37	827.91	29/18
38	850.286	18/11, 31/19
39	872.662
40	895.038
41	917.414
42	939.79	31/18
43	962.165
44	984.541
45	1006.917	34/19
46	1029.293	38/21
47	1051.669	11/6
48	1074.045
49	1096.421
50	1118.797	21/11
51	1141.173	29/15
52	1163.549
53	1185.925
54	1208.301
55	1230.677
56	1253.053
57	1275.429	23/11
58	1297.805
59	1320.181	15/7
60	1342.556
61	1364.932	11/5
62	1387.308
63	1409.684
64	1432.06
65	1454.436
66	1476.812
67	1499.188
68	1521.564	41/17
69	1543.94
70	1566.316
71	1588.692	5/2
72	1611.068	38/15
73	1633.444	18/7
74	1655.82
75	1678.196	29/11
76	1700.572
77	1722.947
78	1745.323
79	1767.699
80	1790.075
81	1812.451	37/13
82	1834.827	26/9
83	1857.203
84	1879.579
85	1901.955	3/1

Harmonics

Approximation of harmonics in 85edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.30	+0.00	-5.77	+10.68	+8.30	+9.94	+2.53	+0.00	-3.40	+10.61	-5.77
	Relative (%)	+37.1	+0.0	-25.8	+47.7	+37.1	+44.4	+11.3	+0.0	-15.2	+47.4	-25.8
Steps (reduced)		54 (54)	85 (0)	107 (22)	125 (40)	139 (54)	151 (66)	161 (76)	170 (0)	178 (8)	186 (16)	192 (22)

Approximation of harmonics in 85edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-10.09	-4.13	+10.68	+10.83	-4.62	+8.30	+4.20	+4.90	+9.94	-3.47	+9.08
	Relative (%)	-45.1	-18.5	+47.7	+48.4	-20.7	+37.1	+18.8	+21.9	+44.4	-15.5	+40.6
Steps (reduced)		198 (28)	204 (34)	210 (40)	215 (45)	219 (49)	224 (54)	228 (58)	232 (62)	236 (66)	239 (69)	243 (73)