83ed7/3

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Prime factorization	83 (prime)
Step size	17.6731¢
Octave	68\83ed7/3 (1201.77¢)
Twelfth	108\83ed7/3 (1908.7¢)
Consistency limit	8
Distinct consistency limit	8

83 equal divisions of 7/3 (abbreviated 83ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 83 equal parts of about 17.7⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/83, or the 83rd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.7
2	35.3
3	53	33/32, 34/33, 35/34
4	70.7	25/24
5	88.4	39/37
6	106	17/16
7	123.7
8	141.4
9	159.1
10	176.7
11	194.4	28/25
12	212.1	26/23
13	229.8	8/7
14	247.4
15	265.1	7/6
16	282.8	20/17, 33/28
17	300.4	25/21
18	318.1	6/5
19	335.8	17/14, 40/33
20	353.5	38/31
21	371.1
22	388.8	5/4
23	406.5
24	424.2	37/29
25	441.8
26	459.5
27	477.2	29/22
28	494.8
29	512.5	39/29
30	530.2	34/25
31	547.9
32	565.5
33	583.2	7/5
34	600.9	17/12
35	618.6	10/7
36	636.2
37	653.9	19/13, 35/24
38	671.6
39	689.3
40	706.9
41	724.6
42	742.3
43	759.9
44	777.6
45	795.3
46	813	8/5
47	830.6
48	848.3	31/19
49	866	28/17, 33/20
50	883.7	5/3
51	901.3	37/22
52	919	17/10
53	936.7
54	954.3
55	972
56	989.7	23/13, 39/22
57	1007.4
58	1025
59	1042.7
60	1060.4
61	1078.1	28/15
62	1095.7	32/17
63	1113.4	40/21
64	1131.1
65	1148.8	33/17, 35/18
66	1166.4
67	1184.1
68	1201.8	2/1
69	1219.4
70	1237.1
71	1254.8	33/16
72	1272.5	25/12
73	1290.1
74	1307.8	17/8
75	1325.5
76	1343.2
77	1360.8
78	1378.5
79	1396.2
80	1413.9	34/15
81	1431.5	16/7
82	1449.2	37/16
83	1466.9	7/3

Harmonics

Approximation of harmonics in 83ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.77	+6.74	+3.55	+6.04	+8.52	+6.74	+5.32	-4.18	+7.82	+1.87	-7.38
	Relative (%)	+10.0	+38.2	+20.1	+34.2	+48.2	+38.2	+30.1	-23.7	+44.2	+10.6	-41.8
Steps (reduced)		68 (68)	108 (25)	136 (53)	158 (75)	176 (10)	191 (25)	204 (38)	215 (49)	226 (60)	235 (69)	243 (77)

Approximation of harmonics in 83ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.57	+8.52	-4.89	+7.10	+8.18	-2.41	-7.65	-8.08	-4.18	+3.64	-2.62
	Relative (%)	-25.9	+48.2	-27.6	+40.1	+46.3	-13.6	-43.3	-45.7	-23.7	+20.6	-14.8
Steps (reduced)		251 (2)	259 (10)	265 (16)	272 (23)	278 (29)	283 (34)	288 (39)	293 (44)	298 (49)	303 (54)	307 (58)