82edt

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82edt

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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	Hekts	Approximate ratios
0	0	0	1/1
1	23.2	15.9
2	46.4	31.7	37/36, 38/37
3	69.6	47.6	26/25
4	92.8	63.4	19/18
5	116	79.3	31/29
6	139.2	95.1
7	162.4	111	11/10, 34/31
8	185.6	126.8	39/35
9	208.8	142.7	35/31
10	231.9	158.5
11	255.1	174.4	22/19, 29/25
12	278.3	190.2	27/23, 34/29
13	301.5	206.1	25/21, 31/26
14	324.7	222	35/29
15	347.9	237.8	11/9
16	371.1	253.7	26/21, 31/25
17	394.3	269.5
18	417.5	285.4	14/11
19	440.7	301.2
20	463.9	317.1	17/13
21	487.1	332.9
22	510.3	348.8	39/29
23	533.5	364.6	34/25
24	556.7	380.5	29/21
25	579.9	396.3	7/5
26	603.1	412.2
27	626.3	428	33/23
28	649.4	443.9
29	672.6	459.8	28/19, 31/21
30	695.8	475.6
31	719	491.5
32	742.2	507.3	23/15
33	765.4	523.2	14/9
34	788.6	539	30/19
35	811.8	554.9
36	835	570.7	34/21
37	858.2	586.6	23/14
38	881.4	602.4	5/3
39	904.6	618.3
40	927.8	634.1
41	951	650	26/15
42	974.2	665.9
43	997.4	681.7
44	1020.6	697.6	9/5
45	1043.8	713.4
46	1067	729.3	37/20
47	1090.1	745.1
48	1113.3	761	19/10
49	1136.5	776.8	27/14
50	1159.7	792.7
51	1182.9	808.5
52	1206.1	824.4
53	1229.3	840.2
54	1252.5	856.1	35/17
55	1275.7	872	23/11
56	1298.9	887.8
57	1322.1	903.7	15/7
58	1345.3	919.5
59	1368.5	935.4
60	1391.7	951.2	29/13
61	1414.9	967.1	34/15
62	1438.1	982.9	39/17
63	1461.3	998.8
64	1484.5	1014.6	33/14
65	1507.6	1030.5
66	1530.8	1046.3
67	1554	1062.2	27/11
68	1577.2	1078
69	1600.4	1093.9
70	1623.6	1109.8	23/9
71	1646.8	1125.6
72	1670	1141.5
73	1693.2	1157.3
74	1716.4	1173.2	35/13
75	1739.6	1189	30/11
76	1762.8	1204.9
77	1786	1220.7
78	1809.2	1236.6
79	1832.4	1252.4
80	1855.6	1268.3
81	1878.8	1284.1
82	1902	1300	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)