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	Hekts	Approximate ratios
0	0	0	1/1
1	18.5	12.6
2	36.9	25.2	45/44
3	55.4	37.9	31/30, 32/31, 33/32
4	73.9	50.5	24/23
5	92.3	63.1	19/18
6	110.8	75.7	16/15
7	129.3	88.3	14/13, 41/38
8	147.7	101	37/34
9	166.2	113.6	11/10
10	184.7	126.2	10/9
11	203.1	138.8	9/8
12	221.6	151.5	25/22, 33/29
13	240.1	164.1	23/20, 31/27
14	258.5	176.7	29/25, 36/31, 43/37
15	277	189.3	27/23, 34/29
16	295.4	201.9	19/16, 32/27
17	313.9	214.6	6/5
18	332.4	227.2	23/19, 40/33
19	350.8	239.8	38/31
20	369.3	252.4	26/21
21	387.8	265	5/4
22	406.2	277.7	24/19, 43/34
23	424.7	290.3	23/18
24	443.2	302.9	31/24, 40/31
25	461.6	315.5	30/23
26	480.1	328.2	29/22, 33/25
27	498.6	340.8	4/3
28	517	353.4	31/23
29	535.5	366	15/11
30	554	378.6
31	572.4	391.3	32/23, 39/28
32	590.9	403.9	38/27, 45/32
33	609.4	416.5	27/19
34	627.8	429.1	23/16
35	646.3	441.7	16/11, 45/31
36	664.8	454.4	22/15
37	683.2	467	43/29
38	701.7	479.6	3/2
39	720.2	492.2	44/29
40	738.6	504.9	23/15
41	757.1	517.5	31/20
42	775.6	530.1	36/23
43	794	542.7	19/12
44	812.5	555.3	8/5
45	831	568	21/13
46	849.4	580.6	31/19
47	867.9	593.2	33/20, 38/23
48	886.3	605.8	5/3
49	904.8	618.4	27/16, 32/19
50	923.3	631.1	29/17
51	941.7	643.7	31/18
52	960.2	656.3	40/23
53	978.7	668.9	44/25
54	997.1	681.6	16/9
55	1015.6	694.2	9/5
56	1034.1	706.8	20/11
57	1052.5	719.4
58	1071	732	13/7
59	1089.5	744.7	15/8
60	1107.9	757.3	36/19
61	1126.4	769.9	23/12
62	1144.9	782.5	31/16
63	1163.3	795.1	45/23
64	1181.8	807.8
65	1200.3	820.4	2/1
66	1218.7	833
67	1237.2	845.6	45/22
68	1255.7	858.3	31/15, 33/16
69	1274.1	870.9
70	1292.6	883.5	19/9
71	1311.1	896.1	32/15
72	1329.5	908.7	28/13, 41/19
73	1348	921.4	37/17
74	1366.5	934	11/5
75	1384.9	946.6
76	1403.4	959.2	9/4
77	1421.8	971.8	25/11
78	1440.3	984.5	23/10
79	1458.8	997.1
80	1477.2	1009.7
81	1495.7	1022.3	19/8
82	1514.2	1035	12/5
83	1532.6	1047.6
84	1551.1	1060.2
85	1569.6	1072.8
86	1588	1085.4	5/2
87	1606.5	1098.1	43/17
88	1625	1110.7	23/9
89	1643.4	1123.3	31/12
90	1661.9	1135.9
91	1680.4	1148.5	29/11
92	1698.8	1161.2	8/3
93	1717.3	1173.8	27/10
94	1735.8	1186.4	30/11
95	1754.2	1199
96	1772.7	1211.7	39/14
97	1791.2	1224.3	45/16
98	1809.6	1236.9
99	1828.1	1249.5	23/8
100	1846.6	1262.1	32/11
101	1865	1274.8	44/15
102	1883.5	1287.4
103	1902	1300	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)