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	23.301
2	46.602	39/38
3	69.903	26/25
4	93.204
5	116.505	31/29
6	139.806
7	163.107
8	186.408	39/35
9	209.709	44/39
10	233.01
11	256.311
12	279.612
13	302.913	25/21
14	326.214
15	349.515
16	372.816
17	396.117	44/35
18	419.417	37/29
19	442.718
20	466.019	17/13
21	489.32
22	512.621	35/26
23	535.922
24	559.223
25	582.524	7/5
26	605.825
27	629.126
28	652.427
29	675.728
30	699.029
31	722.33
32	745.631
33	768.932	39/25
34	792.233
35	815.534
36	838.835
37	862.136
38	885.437	5/3
39	908.738	22/13
40	932.039
41	955.34	33/19
42	978.641	44/25
43	1001.942	25/14, 41/23
44	1025.243	38/21
45	1048.544
46	1071.845	13/7
47	1095.146
48	1118.447
49	1141.748
50	1165.049
51	1188.35
52	1211.65
53	1234.951
54	1258.252
55	1281.553	44/21
56	1304.854
57	1328.155
58	1351.456
59	1374.757
60	1398.058
61	1421.359
62	1444.66
63	1467.961	7/3
64	1491.262
65	1514.563
66	1537.864	17/7
67	1561.165
68	1584.466	5/2
69	1607.767	38/15
70	1631.068
71	1654.369	13/5
72	1677.67	29/11
73	1700.971
74	1724.272
75	1747.573
76	1770.874	25/9
77	1794.175	31/11
78	1817.476
79	1840.777
80	1864.078	44/15
81	1887.379
82	1910.68
83	1933.981
84	1957.282
85	1980.583	22/7
86	2003.883
87	2027.184
88	2050.485
89	2073.786
90	2097.087
91	2120.388	17/5
92	2143.689
93	2166.99	7/2
94	2190.291
95	2213.592
96	2236.893
97	2260.194
98	2283.495
99	2306.796
100	2330.097
101	2353.398	35/9
102	2376.699
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)