105ed4

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← 103ed4 105ed4 107ed4 →
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 41/105, or the 105th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 22.9
2 45.7
3 68.6 26/25
4 91.4 19/18, 39/37
5 114.3 31/29
6 137.1
7 160 45/41
8 182.9
9 205.7
10 228.6
11 251.4
12 274.3 41/35
13 297.1
14 320
15 342.9
16 365.7
17 388.6
18 411.4 19/15, 33/26
19 434.3 9/7
20 457.1 43/33
21 480 33/25
22 502.9
23 525.7 42/31
24 548.6
25 571.4
26 594.3
27 617.1
28 640 42/29
29 662.9
30 685.7
31 708.6
32 731.4 29/19
33 754.3 17/11
34 777.1
35 800 46/29
36 822.9 37/23
37 845.7 31/19
38 868.6
39 891.4
40 914.3 39/23
41 937.1 43/25
42 960
43 982.9 30/17, 37/21
44 1005.7 25/14
45 1028.6
46 1051.4 11/6
47 1074.3
48 1097.1
49 1120
50 1142.9 29/15
51 1165.7
52 1188.6
53 1211.4
54 1234.3
55 1257.1 31/15
56 1280
57 1302.9
58 1325.7
59 1348.6
60 1371.4 42/19
61 1394.3 38/17
62 1417.1
63 1440
64 1462.9
65 1485.7 33/14
66 1508.6 43/18
67 1531.4 46/19
68 1554.3
69 1577.1
70 1600
71 1622.9 23/9
72 1645.7
73 1668.6
74 1691.4
75 1714.3 35/13
76 1737.1 30/11
77 1760
78 1782.9 14/5
79 1805.7
80 1828.6
81 1851.4
82 1874.3
83 1897.1
84 1920
85 1942.9 43/14
86 1965.7
87 1988.6 41/13
88 2011.4
89 2034.3
90 2057.1 23/7
91 2080
92 2102.9
93 2125.7
94 2148.6 45/13
95 2171.4
96 2194.3
97 2217.1 18/5
98 2240
99 2262.9
100 2285.7
101 2308.6
102 2331.4
103 2354.3
104 2377.1
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)