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	Hekts	Approximate ratios
0	0	0	1/1
1	22.9	15.7
2	45.8	31.3
3	68.7	47
4	91.7	62.7	19/18, 20/19, 39/37
5	114.6	78.3	31/29
6	137.5	94
7	160.4	109.6	23/21, 34/31
8	183.3	125.3	10/9
9	206.2	141
10	229.2	156.6
11	252.1	172.3	22/19
12	275	188	27/23, 34/29
13	297.9	203.6
14	320.8	219.3
15	343.7	234.9
16	366.6	250.6	21/17
17	389.6	266.3
18	412.5	281.9	33/26
19	435.4	297.6	9/7
20	458.3	313.3	30/23
21	481.2	328.9	29/22
22	504.1	344.6
23	527	360.2	19/14
24	550	375.9
25	572.9	391.6
26	595.8	407.2	31/22
27	618.7	422.9	10/7
28	641.6	438.6	29/20
29	664.5	454.2
30	687.5	469.9
31	710.4	485.5
32	733.3	501.2	26/17, 29/19
33	756.2	516.9	17/11, 31/20
34	779.1	532.5
35	802	548.2	27/17
36	824.9	563.9	29/18, 37/23
37	847.9	579.5	31/19
38	870.8	595.2
39	893.7	610.8
40	916.6	626.5	17/10, 39/23
41	939.5	642.2	31/18
42	962.4	657.8
43	985.4	673.5	23/13, 30/17
44	1008.3	689.2	34/19
45	1031.2	704.8
46	1054.1	720.5
47	1077	736.1
48	1099.9	751.8	17/9
49	1122.8	767.5
50	1145.8	783.1	33/17
51	1168.7	798.8
52	1191.6	814.5
53	1214.5	830.1
54	1237.4	845.8
55	1260.3	861.4	29/14
56	1283.2	877.1	21/10
57	1306.2	892.8
58	1329.1	908.4
59	1352	924.1
60	1374.9	939.8	31/14
61	1397.8	955.4
62	1420.7	971.1
63	1443.7	986.7	23/10
64	1466.6	1002.4	7/3
65	1489.5	1018.1	26/11
66	1512.4	1033.7
67	1535.3	1049.4	17/7
68	1558.2	1065.1
69	1581.1	1080.7
70	1604.1	1096.4
71	1627	1112	23/9
72	1649.9	1127.7
73	1672.8	1143.4
74	1695.7	1159
75	1718.6	1174.7	27/10
76	1741.5	1190.4
77	1764.5	1206
78	1787.4	1221.7
79	1810.3	1237.3	37/13
80	1833.2	1253
81	1856.1	1268.7
82	1879	1284.3
83	1902	1300	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)