82edt

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82edt

83edt →

Prime factorization	2 × 41
Step size	23.1946¢
Octave	52\82edt (1206.12¢) (→26\41edt)
Consistency limit	2
Distinct consistency limit	2

82 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 82edt or 82ed3), is a nonoctave tuning system that divides the interval of 3/1 into 82 equal parts of about 23.2 ¢ each. Each step represents a frequency ratio of 3^1/82, or the 82nd root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	23.2
2	46.4	37/36, 38/37
3	69.6	26/25
4	92.8	19/18
5	116	31/29
6	139.2
7	162.4	11/10, 34/31
8	185.6	39/35
9	208.8	35/31
10	231.9
11	255.1	22/19, 29/25
12	278.3	27/23, 34/29
13	301.5	25/21, 31/26
14	324.7	35/29
15	347.9	11/9
16	371.1	26/21, 31/25
17	394.3
18	417.5	14/11
19	440.7
20	463.9	17/13
21	487.1
22	510.3	39/29
23	533.5	34/25
24	556.7	29/21
25	579.9	7/5
26	603.1
27	626.3	33/23
28	649.4
29	672.6	28/19, 31/21
30	695.8
31	719
32	742.2	23/15
33	765.4	14/9
34	788.6	30/19
35	811.8
36	835	34/21
37	858.2	23/14
38	881.4	5/3
39	904.6
40	927.8
41	951	26/15
42	974.2
43	997.4
44	1020.6	9/5
45	1043.8
46	1067	37/20
47	1090.1
48	1113.3	19/10
49	1136.5	27/14
50	1159.7
51	1182.9
52	1206.1
53	1229.3
54	1252.5	35/17
55	1275.7	23/11
56	1298.9
57	1322.1	15/7
58	1345.3
59	1368.5
60	1391.7	29/13
61	1414.9	34/15
62	1438.1	39/17
63	1461.3
64	1484.5	33/14
65	1507.6
66	1530.8
67	1554	27/11
68	1577.2
69	1600.4
70	1623.6	23/9
71	1646.8
72	1670
73	1693.2
74	1716.4	35/13
75	1739.6	30/11
76	1762.8
77	1786
78	1809.2
79	1832.4
80	1855.6
81	1878.8
82	1902	3/1

Harmonics

Approximation of harmonics in 82edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.1	+0.0	-11.0	-3.0	+6.1	-5.6	-4.8	+0.0	+3.2	+0.5	-11.0
	Relative (%)	+26.4	+0.0	-47.2	-12.8	+26.4	-24.2	-20.9	+0.0	+13.6	+2.2	-47.2
Steps (reduced)		52 (52)	82 (0)	103 (21)	120 (38)	134 (52)	145 (63)	155 (73)	164 (0)	172 (8)	179 (15)	185 (21)

Approximation of harmonics in 82edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-10.4	+0.5	-3.0	+1.3	-10.9	+6.1	+5.3	+9.3	-5.6	+6.6	-0.7
	Relative (%)	-44.7	+2.2	-12.8	+5.5	-47.0	+26.4	+22.8	+40.0	-24.2	+28.6	-3.2
Steps (reduced)		191 (27)	197 (33)	202 (38)	207 (43)	211 (47)	216 (52)	220 (56)	224 (60)	227 (63)	231 (67)	234 (70)