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	17.673
2	35.346
3	53.019	33/32, 34/33, 35/34
4	70.693	25/24
5	88.366	39/37
6	106.039	17/16
7	123.712
8	141.385
9	159.058
10	176.731
11	194.405	28/25
12	212.078	26/23
13	229.751	8/7
14	247.424
15	265.097	7/6
16	282.77	20/17, 33/28
17	300.443	25/21
18	318.117	6/5
19	335.79	17/14, 40/33
20	353.463	38/31
21	371.136
22	388.809	5/4
23	406.482
24	424.155	37/29
25	441.829
26	459.502
27	477.175	29/22
28	494.848
29	512.521	39/29
30	530.194	34/25
31	547.867
32	565.541
33	583.214	7/5
34	600.887	17/12
35	618.56	10/7
36	636.233
37	653.906	19/13, 35/24
38	671.579
39	689.253
40	706.926
41	724.599
42	742.272
43	759.945
44	777.618
45	795.291
46	812.965	8/5
47	830.638
48	848.311	31/19
49	865.984	28/17, 33/20
50	883.657	5/3
51	901.33	37/22
52	919.003	17/10
53	936.677
54	954.35
55	972.023
56	989.696	23/13, 39/22
57	1007.369
58	1025.042
59	1042.715
60	1060.389
61	1078.062	28/15
62	1095.735	32/17
63	1113.408	40/21
64	1131.081
65	1148.754	33/17, 35/18
66	1166.427
67	1184.101
68	1201.774	2/1
69	1219.447
70	1237.12
71	1254.793	33/16
72	1272.466	25/12
73	1290.139
74	1307.813	17/8
75	1325.486
76	1343.159
77	1360.832
78	1378.505
79	1396.178
80	1413.851	34/15
81	1431.525	16/7
82	1449.198	37/16
83	1466.871	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)