105ed4

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105ed4

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Prime factorization	3 × 5 × 7
Step size	22.8571¢
Octave	53\105ed4 (1211.43¢)
Twelfth	83\105ed4 (1897.14¢)
Consistency limit	1
Distinct consistency limit	1

105 equal divisions of the 4th harmonic (abbreviated 105ed4) is a nonoctave tuning system that divides the interval of 4/1 into 105 equal parts of about 22.9 ¢ each. Each step represents a frequency ratio of 4^1/105, or the 105th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	22.857
2	45.714
3	68.571	26/25
4	91.429	19/18, 39/37
5	114.286	31/29
6	137.143
7	160	45/41
8	182.857
9	205.714
10	228.571
11	251.429
12	274.286	41/35
13	297.143
14	320
15	342.857
16	365.714
17	388.571
18	411.429	19/15, 33/26
19	434.286	9/7
20	457.143	43/33
21	480	33/25
22	502.857
23	525.714	42/31
24	548.571
25	571.429
26	594.286
27	617.143
28	640	42/29
29	662.857
30	685.714
31	708.571
32	731.429	29/19
33	754.286	17/11
34	777.143
35	800	46/29
36	822.857	37/23
37	845.714	31/19
38	868.571
39	891.429
40	914.286	39/23
41	937.143	43/25
42	960
43	982.857	30/17, 37/21
44	1005.714	25/14
45	1028.571
46	1051.429	11/6
47	1074.286
48	1097.143
49	1120
50	1142.857	29/15
51	1165.714
52	1188.571
53	1211.429
54	1234.286
55	1257.143	31/15
56	1280
57	1302.857
58	1325.714
59	1348.571
60	1371.429	42/19
61	1394.286	38/17
62	1417.143
63	1440
64	1462.857
65	1485.714	33/14
66	1508.571	43/18
67	1531.429	46/19
68	1554.286
69	1577.143
70	1600
71	1622.857	23/9
72	1645.714
73	1668.571
74	1691.429
75	1714.286	35/13
76	1737.143	30/11
77	1760
78	1782.857	14/5
79	1805.714
80	1828.571
81	1851.429
82	1874.286
83	1897.143
84	1920
85	1942.857	43/14
86	1965.714
87	1988.571	41/13
88	2011.429
89	2034.286
90	2057.143	23/7
91	2080
92	2102.857
93	2125.714
94	2148.571	45/13
95	2171.429
96	2194.286
97	2217.143	18/5
98	2240
99	2262.857
100	2285.714
101	2308.571
102	2331.429
103	2354.286
104	2377.143
105	2400

Harmonics

Approximation of harmonics in 105ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.4	-4.8	+0.0	+2.3	+6.6	-8.8	+11.4	-9.6	-9.2	+8.7	-4.8
	Relative (%)	+50.0	-21.1	+0.0	+9.9	+28.9	-38.6	+50.0	-42.1	-40.1	+38.0	-21.1
Steps (reduced)		53 (53)	83 (83)	105 (0)	122 (17)	136 (31)	147 (42)	158 (53)	166 (61)	174 (69)	182 (77)	188 (83)

Approximation of harmonics in 105ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.2	+2.6	-2.6	+0.0	+9.3	+1.8	-0.4	+2.3	+9.2	-2.7	-11.1
	Relative (%)	-27.3	+11.4	-11.2	+0.0	+40.8	+7.9	-1.6	+9.9	+40.3	-12.0	-48.7
Steps (reduced)		194 (89)	200 (95)	205 (100)	210 (0)	215 (5)	219 (9)	223 (13)	227 (17)	231 (21)	234 (24)	237 (27)