83edt

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83edt

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Prime factorization	83 (prime)
Step size	22.9151¢
Octave	52\83edt (1191.59¢)
Consistency limit	2
Distinct consistency limit	2

83 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 83edt or 83ed3), is a nonoctave tuning system that divides the interval of 3/1 into 83 equal parts of about 22.9 ¢ each. Each step represents a frequency ratio of 3^1/83, or the 83rd root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	22.9
2	45.8
3	68.7
4	91.7	19/18, 20/19, 39/37
5	114.6	31/29
6	137.5
7	160.4	23/21, 34/31
8	183.3	10/9
9	206.2
10	229.2
11	252.1	22/19
12	275	27/23, 34/29
13	297.9
14	320.8
15	343.7
16	366.6	21/17
17	389.6
18	412.5	33/26
19	435.4	9/7
20	458.3	30/23
21	481.2	29/22
22	504.1
23	527	19/14
24	550
25	572.9
26	595.8	31/22
27	618.7	10/7
28	641.6	29/20
29	664.5
30	687.5
31	710.4
32	733.3	26/17, 29/19
33	756.2	17/11, 31/20
34	779.1
35	802	27/17
36	824.9	29/18, 37/23
37	847.9	31/19
38	870.8
39	893.7
40	916.6	17/10, 39/23
41	939.5	31/18
42	962.4
43	985.4	23/13, 30/17
44	1008.3	34/19
45	1031.2
46	1054.1
47	1077
48	1099.9	17/9
49	1122.8
50	1145.8	33/17
51	1168.7
52	1191.6
53	1214.5
54	1237.4
55	1260.3	29/14
56	1283.2	21/10
57	1306.2
58	1329.1
59	1352
60	1374.9	31/14
61	1397.8
62	1420.7
63	1443.7	23/10
64	1466.6	7/3
65	1489.5	26/11
66	1512.4
67	1535.3	17/7
68	1558.2
69	1581.1
70	1604.1
71	1627	23/9
72	1649.9
73	1672.8
74	1695.7
75	1718.6	27/10
76	1741.5
77	1764.5
78	1787.4
79	1810.3	37/13
80	1833.2
81	1856.1
82	1879
83	1902	3/1

Harmonics

Approximation of harmonics in 83edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.4	+0.0	+6.1	+9.3	-8.4	-0.3	-2.3	+0.0	+0.9	-3.7	+6.1
	Relative (%)	-36.7	+0.0	+26.6	+40.7	-36.7	-1.3	-10.2	+0.0	+4.0	-16.1	+26.6
Steps (reduced)		52 (52)	83 (0)	105 (22)	122 (39)	135 (52)	147 (64)	157 (74)	166 (0)	174 (8)	181 (15)	188 (22)

Approximation of harmonics in 83edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.0	-8.7	+9.3	-10.7	-1.1	-8.4	-10.4	-7.5	-0.3	+10.8	+2.6
	Relative (%)	+21.8	-38.0	+40.7	-46.9	-4.9	-36.7	-45.2	-32.7	-1.3	+47.2	+11.4
Steps (reduced)		194 (28)	199 (33)	205 (39)	209 (43)	214 (48)	218 (52)	222 (56)	226 (60)	230 (64)	234 (68)	237 (71)