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	3
Distinct consistency limit	3

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	Hekts	Approximate ratios
0	0	0	1/1
1	22.4	15.3
2	44.8	30.6
3	67.1	45.9	27/26
4	89.5	61.2	39/37, 41/39
5	111.9	76.5
6	134.3	91.8
7	156.6	107.1	23/21
8	179	122.4	41/37
9	201.4	137.6
10	223.8	152.9	25/22, 33/29
11	246.1	168.2	38/33
12	268.5	183.5	7/6
13	290.9	198.8
14	313.3	214.1	6/5
15	335.6	229.4
16	358	244.7
17	380.4	260
18	402.8	275.3	29/23
19	425.1	290.6	23/18
20	447.5	305.9
21	469.9	321.2	38/29
22	492.3	336.5
23	514.6	351.8	31/23
24	537	367.1	15/11
25	559.4	382.4	29/21
26	581.8	397.6	7/5
27	604.2	412.9
28	626.5	428.2	33/23
29	648.9	443.5
30	671.3	458.8	31/21
31	693.7	474.1
32	716	489.4
33	738.4	504.7	23/15, 26/17
34	760.8	520
35	783.2	535.3	11/7
36	805.5	550.6	35/22
37	827.9	565.9	29/18
38	850.3	581.2	18/11, 31/19
39	872.7	596.5
40	895	611.8
41	917.4	627.1
42	939.8	642.4	31/18
43	962.2	657.6
44	984.5	672.9
45	1006.9	688.2	34/19
46	1029.3	703.5	38/21
47	1051.7	718.8	11/6
48	1074	734.1
49	1096.4	749.4
50	1118.8	764.7	21/11
51	1141.2	780	29/15
52	1163.5	795.3
53	1185.9	810.6
54	1208.3	825.9
55	1230.7	841.2
56	1253.1	856.5
57	1275.4	871.8	23/11
58	1297.8	887.1
59	1320.2	902.4	15/7
60	1342.6	917.6
61	1364.9	932.9	11/5
62	1387.3	948.2
63	1409.7	963.5
64	1432.1	978.8
65	1454.4	994.1
66	1476.8	1009.4
67	1499.2	1024.7
68	1521.6	1040	41/17
69	1543.9	1055.3
70	1566.3	1070.6
71	1588.7	1085.9	5/2
72	1611.1	1101.2	38/15
73	1633.4	1116.5	18/7
74	1655.8	1131.8
75	1678.2	1147.1	29/11
76	1700.6	1162.4
77	1722.9	1177.6
78	1745.3	1192.9
79	1767.7	1208.2
80	1790.1	1223.5
81	1812.5	1238.8	37/13
82	1834.8	1254.1	26/9
83	1857.2	1269.4
84	1879.6	1284.7
85	1902	1300	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)