103edt

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103edt

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Prime factorization	103 (prime)
Step size	18.4656¢
Octave	65\103edt (1200.26¢)
Consistency limit	5
Distinct consistency limit	5

103 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 103edt or 103ed3), is a nonoctave tuning system that divides the interval of 3/1 into 103 equal parts of about 18.5⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/103, or the 103rd root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.5
2	36.9	45/44
3	55.4	31/30, 32/31, 33/32
4	73.9	24/23
5	92.3	19/18
6	110.8	16/15
7	129.3	14/13, 41/38
8	147.7	37/34
9	166.2	11/10
10	184.7	10/9
11	203.1	9/8
12	221.6	25/22, 33/29
13	240.1	23/20, 31/27
14	258.5	29/25, 36/31, 43/37
15	277	27/23, 34/29
16	295.4	19/16, 32/27
17	313.9	6/5
18	332.4	23/19, 40/33
19	350.8	38/31
20	369.3	26/21
21	387.8	5/4
22	406.2	24/19, 43/34
23	424.7	23/18
24	443.2	31/24, 40/31
25	461.6	30/23
26	480.1	29/22, 33/25
27	498.6	4/3
28	517	31/23
29	535.5	15/11
30	554
31	572.4	32/23, 39/28
32	590.9	38/27, 45/32
33	609.4	27/19
34	627.8	23/16
35	646.3	16/11, 45/31
36	664.8	22/15
37	683.2	43/29
38	701.7	3/2
39	720.2	44/29
40	738.6	23/15
41	757.1	31/20
42	775.6	36/23
43	794	19/12
44	812.5	8/5
45	831	21/13
46	849.4	31/19
47	867.9	33/20, 38/23
48	886.3	5/3
49	904.8	27/16, 32/19
50	923.3	29/17
51	941.7	31/18
52	960.2	40/23
53	978.7	44/25
54	997.1	16/9
55	1015.6	9/5
56	1034.1	20/11
57	1052.5
58	1071	13/7
59	1089.5	15/8
60	1107.9	36/19
61	1126.4	23/12
62	1144.9	31/16
63	1163.3	45/23
64	1181.8
65	1200.3	2/1
66	1218.7
67	1237.2	45/22
68	1255.7	31/15, 33/16
69	1274.1
70	1292.6	19/9
71	1311.1	32/15
72	1329.5	28/13, 41/19
73	1348	37/17
74	1366.5	11/5
75	1384.9
76	1403.4	9/4
77	1421.8	25/11
78	1440.3	23/10
79	1458.8
80	1477.2
81	1495.7	19/8
82	1514.2	12/5
83	1532.6
84	1551.1
85	1569.6
86	1588	5/2
87	1606.5	43/17
88	1625	23/9
89	1643.4	31/12
90	1661.9
91	1680.4	29/11
92	1698.8	8/3
93	1717.3	27/10
94	1735.8	30/11
95	1754.2
96	1772.7	39/14
97	1791.2	45/16
98	1809.6
99	1828.1	23/8
100	1846.6	32/11
101	1865	44/15
102	1883.5
103	1902	3/1

Harmonics

Approximation of harmonics in 103edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.26	+0.00	+0.53	+1.99	+0.26	-8.09	+0.79	+0.00	+2.25	+3.44	+0.53
	Relative (%)	+1.4	+0.0	+2.8	+10.8	+1.4	-43.8	+4.3	+0.0	+12.2	+18.6	+2.8
Steps (reduced)		65 (65)	103 (0)	130 (27)	151 (48)	168 (65)	182 (79)	195 (92)	206 (0)	216 (10)	225 (19)	233 (27)

Approximation of harmonics in 103edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.79	-7.83	+1.99	+1.05	+6.89	+0.26	-1.01	+2.51	-8.09	+3.70	+0.61
	Relative (%)	-47.6	-42.4	+10.8	+5.7	+37.3	+1.4	-5.5	+13.6	-43.8	+20.0	+3.3
Steps (reduced)		240 (34)	247 (41)	254 (48)	260 (54)	266 (60)	271 (65)	276 (70)	281 (75)	285 (79)	290 (84)	294 (88)