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	18.466
2	36.931	45/44
3	55.397	31/30, 32/31, 33/32
4	73.862	24/23
5	92.328	19/18
6	110.793	16/15
7	129.259	14/13, 41/38
8	147.725	37/34
9	166.19	11/10
10	184.656	10/9
11	203.121	9/8
12	221.587	25/22, 33/29
13	240.053	23/20, 31/27
14	258.518	29/25, 36/31, 43/37
15	276.984	27/23, 34/29
16	295.449	19/16, 32/27
17	313.915	6/5
18	332.38	23/19, 40/33
19	350.846	38/31
20	369.312	26/21
21	387.777	5/4
22	406.243	24/19, 43/34
23	424.708	23/18
24	443.174	31/24, 40/31
25	461.64	30/23
26	480.105	29/22, 33/25
27	498.571	4/3
28	517.036	31/23
29	535.502	15/11
30	553.967
31	572.433	32/23, 39/28
32	590.899	38/27, 45/32
33	609.364	27/19
34	627.83	23/16
35	646.295	16/11, 45/31
36	664.761	22/15
37	683.227	43/29
38	701.692	3/2
39	720.158	44/29
40	738.623	23/15
41	757.089	31/20
42	775.554	36/23
43	794.02	19/12
44	812.486	8/5
45	830.951	21/13
46	849.417	31/19
47	867.882	33/20, 38/23
48	886.348	5/3
49	904.814	27/16, 32/19
50	923.279	29/17
51	941.745	31/18
52	960.21	40/23
53	978.676	44/25
54	997.141	16/9
55	1015.607	9/5
56	1034.073	20/11
57	1052.538
58	1071.004	13/7
59	1089.469	15/8
60	1107.935	36/19
61	1126.401	23/12
62	1144.866	31/16
63	1163.332	45/23
64	1181.797
65	1200.263	2/1
66	1218.728
67	1237.194	45/22
68	1255.66	31/15, 33/16
69	1274.125
70	1292.591	19/9
71	1311.056	32/15
72	1329.522	28/13, 41/19
73	1347.988	37/17
74	1366.453	11/5
75	1384.919
76	1403.384	9/4
77	1421.85	25/11
78	1440.315	23/10
79	1458.781
80	1477.247
81	1495.712	19/8
82	1514.178	12/5
83	1532.643
84	1551.109
85	1569.575
86	1588.04	5/2
87	1606.506	43/17
88	1624.971	23/9
89	1643.437	31/12
90	1661.902
91	1680.368	29/11
92	1698.834	8/3
93	1717.299	27/10
94	1735.765	30/11
95	1754.23
96	1772.696	39/14
97	1791.162	45/16
98	1809.627
99	1828.093	23/8
100	1846.558	32/11
101	1865.024	44/15
102	1883.489
103	1901.955	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)