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	23.195
2	46.389	37/36, 38/37
3	69.584	26/25
4	92.778	19/18
5	115.973	31/29
6	139.167
7	162.362	11/10, 34/31
8	185.557	39/35
9	208.751	35/31
10	231.946
11	255.14	22/19, 29/25
12	278.335	27/23, 34/29
13	301.529	25/21, 31/26
14	324.724	35/29
15	347.919	11/9
16	371.113	26/21, 31/25
17	394.308
18	417.502	14/11
19	440.697
20	463.891	17/13
21	487.086
22	510.281	39/29
23	533.475	34/25
24	556.67	29/21
25	579.864	7/5
26	603.059
27	626.253	33/23
28	649.448
29	672.643	28/19, 31/21
30	695.837
31	719.032
32	742.226	23/15
33	765.421	14/9
34	788.615	30/19
35	811.81
36	835.005	34/21
37	858.199	23/14
38	881.394	5/3
39	904.588
40	927.783
41	950.978	26/15
42	974.172
43	997.367
44	1020.561	9/5
45	1043.756
46	1066.95	37/20
47	1090.145
48	1113.34	19/10
49	1136.534	27/14
50	1159.729
51	1182.923
52	1206.118
53	1229.312
54	1252.507	35/17
55	1275.702	23/11
56	1298.896
57	1322.091	15/7
58	1345.285
59	1368.48
60	1391.674	29/13
61	1414.869	34/15
62	1438.064	39/17
63	1461.258
64	1484.453	33/14
65	1507.647
66	1530.842
67	1554.036	27/11
68	1577.231
69	1600.426
70	1623.62	23/9
71	1646.815
72	1670.009
73	1693.204
74	1716.398	35/13
75	1739.593	30/11
76	1762.788
77	1785.982
78	1809.177
79	1832.371
80	1855.566
81	1878.76
82	1901.955	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)