103ed4

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103ed4

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Prime factorization	103 (prime)
Step size	23.301¢
Octave	52\103ed4 (1211.65¢)
Twelfth	82\103ed4 (1910.68¢)
Consistency limit	1
Distinct consistency limit	1

103 equal divisions of the 4th harmonic (abbreviated 103ed4) is a nonoctave tuning system that divides the interval of 4/1 into 103 equal parts of about 23.3⁠ ⁠¢ each. Each step represents a frequency ratio of 4^1/103, or the 103rd root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	23.3
2	46.6	39/38
3	69.9	26/25
4	93.2
5	116.5	31/29
6	139.8
7	163.1
8	186.4	39/35
9	209.7	44/39
10	233
11	256.3
12	279.6
13	302.9	25/21
14	326.2
15	349.5
16	372.8
17	396.1	44/35
18	419.4	37/29
19	442.7
20	466	17/13
21	489.3
22	512.6	35/26
23	535.9
24	559.2
25	582.5	7/5
26	605.8
27	629.1
28	652.4
29	675.7
30	699
31	722.3
32	745.6
33	768.9	39/25
34	792.2
35	815.5
36	838.8
37	862.1
38	885.4	5/3
39	908.7	22/13
40	932
41	955.3	33/19
42	978.6	44/25
43	1001.9	25/14, 41/23
44	1025.2	38/21
45	1048.5
46	1071.8	13/7
47	1095.1
48	1118.4
49	1141.7
50	1165
51	1188.3
52	1211.7
53	1235
54	1258.3
55	1281.6	44/21
56	1304.9
57	1328.2
58	1351.5
59	1374.8
60	1398.1
61	1421.4
62	1444.7
63	1468	7/3
64	1491.3
65	1514.6
66	1537.9	17/7
67	1561.2
68	1584.5	5/2
69	1607.8	38/15
70	1631.1
71	1654.4	13/5
72	1677.7	29/11
73	1701
74	1724.3
75	1747.6
76	1770.9	25/9
77	1794.2	31/11
78	1817.5
79	1840.8
80	1864.1	44/15
81	1887.4
82	1910.7
83	1934
84	1957.3
85	1980.6	22/7
86	2003.9
87	2027.2
88	2050.5
89	2073.8
90	2097.1
91	2120.4	17/5
92	2143.7
93	2167	7/2
94	2190.3
95	2213.6
96	2236.9
97	2260.2
98	2283.5
99	2306.8
100	2330.1
101	2353.4	35/9
102	2376.7
103	2400

Harmonics

Approximation of harmonics in 103ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.7	+8.7	+0.0	+9.8	-2.9	+9.8	+11.7	-5.9	-1.8	-3.7	+8.7
	Relative (%)	+50.0	+37.4	+0.0	+42.1	-12.6	+42.1	+50.0	-25.1	-7.9	-16.1	+37.4
Steps (reduced)		52 (52)	82 (82)	103 (0)	120 (17)	133 (30)	145 (42)	155 (52)	163 (60)	171 (68)	178 (75)	185 (82)

Approximation of harmonics in 103ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.0	-1.8	-4.8	+0.0	+11.5	+5.8	+5.4	+9.8	-4.8	+7.9	+0.9
	Relative (%)	+42.7	-7.9	-20.5	+0.0	+49.6	+24.9	+23.2	+42.1	-20.4	+33.9	+3.7
Steps (reduced)		191 (88)	196 (93)	201 (98)	206 (0)	211 (5)	215 (9)	219 (13)	223 (17)	226 (20)	230 (24)	233 (27)