82ed7/3

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82ed7/3

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Prime factorization	2 × 41
Step size	17.8887¢
Octave	67\82ed7/3 (1198.54¢) (semiconvergent)
Twelfth	106\82ed7/3 (1896.2¢) (→53\41ed7/3)
Consistency limit	4
Distinct consistency limit	4

82 equal divisions of 7/3 (abbreviated 82ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 82 equal parts of about 17.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/82, or the 82nd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.889
2	35.777
3	53.666	31/30, 32/31, 33/32, 34/33
4	71.555	24/23
5	89.443	20/19, 39/37
6	107.332	17/16, 33/31
7	125.221	14/13
8	143.109	38/35
9	160.998	34/31
10	178.887	31/28
11	196.775	37/33
12	214.664	17/15, 26/23
13	232.553	8/7
14	250.441	15/13, 37/32
15	268.33	7/6
16	286.219	13/11, 33/28
17	304.107	31/26, 37/31
18	321.996
19	339.885	28/23, 39/32
20	357.773	16/13
21	375.662
22	393.551
23	411.439	19/15, 33/26
24	429.328
25	447.217	22/17
26	465.105	17/13, 38/29
27	482.994	37/28
28	500.883	4/3
29	518.771	31/23
30	536.66	15/11
31	554.549	40/29
32	572.437	32/23, 39/28
33	590.326
34	608.215	37/26
35	626.103	23/16, 33/23
36	643.992	29/20
37	661.881	22/15
38	679.769	34/23
39	697.658
40	715.547
41	733.435	26/17, 29/19
42	751.324	17/11, 37/24
43	769.213
44	787.101
45	804.99	35/22
46	822.879	37/23
47	840.767	13/8
48	858.656	23/14
49	876.545
50	894.433
51	912.322	22/13, 39/23
52	930.211	12/7
53	948.099	19/11
54	965.988	7/4
55	983.877	30/17
56	1001.765
57	1019.654
58	1037.543	20/11, 31/17
59	1055.432	35/19
60	1073.32	13/7
61	1091.209	15/8
62	1109.098	19/10
63	1126.986	23/12
64	1144.875	31/16
65	1162.764
66	1180.652
67	1198.541	2/1
68	1216.43
69	1234.318
70	1252.207	33/16, 35/17
71	1270.096
72	1287.984	40/19
73	1305.873	17/8
74	1323.762
75	1341.65	13/6
76	1359.539
77	1377.428	31/14
78	1395.316	38/17
79	1413.205
80	1431.094	16/7
81	1448.982	30/13, 37/16
82	1466.871	7/3

Harmonics

Approximation of harmonics in 82ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.46	-5.76	-2.92	+4.32	-7.22	-5.76	-4.38	+6.38	+2.86	-1.15	-8.67
	Relative (%)	-8.2	-32.2	-16.3	+24.1	-40.3	-32.2	-24.5	+35.6	+16.0	-6.4	-48.5
Steps (reduced)		67 (67)	106 (24)	134 (52)	156 (74)	173 (9)	188 (24)	201 (37)	213 (49)	223 (59)	232 (68)	240 (76)

Approximation of harmonics in 82ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.14	-7.22	-1.44	-5.84	-3.46	+4.92	+0.76	+1.40	+6.38	-2.61	-8.01
	Relative (%)	-23.1	-40.3	-8.0	-32.6	-19.3	+27.5	+4.2	+7.8	+35.6	-14.6	-44.8
Steps (reduced)		248 (2)	255 (9)	262 (16)	268 (22)	274 (28)	280 (34)	285 (39)	290 (44)	295 (49)	299 (53)	303 (57)