115ed4

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← 113ed4 115ed4 117ed4 →
Prime factorization 5 × 23
Step size 20.8696¢ 
Octave 58\115ed4 (1210.43¢)
Twelfth 91\115ed4 (1899.13¢)
Consistency limit 1
Distinct consistency limit 1

115 equal divisions of the 4th harmonic (abbreviated 115ed4) is a nonoctave tuning system that divides the interval of 4/1 into 115 equal parts of about 20.9 ¢ each. Each step represents a frequency ratio of 41/115, or the 115th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 20.9
2 41.7 42/41, 43/42
3 62.6
4 83.5 43/41
5 104.3
6 125.2 29/27
7 146.1 37/34
8 167 43/39
9 187.8 39/35
10 208.7 35/31
11 229.6
12 250.4
13 271.3
14 292.2 45/38
15 313
16 333.9
17 354.8 43/35
18 375.7 41/33, 46/37
19 396.5 39/31
20 417.4 14/11
21 438.3
22 459.1 43/33
23 480
24 500.9
25 521.7 23/17
26 542.6
27 563.5 18/13
28 584.3
29 605.2
30 626.1 33/23
31 647 45/31
32 667.8
33 688.7
34 709.6
35 730.4 29/19
36 751.3
37 772.2
38 793
39 813.9
40 834.8 47/29
41 855.7
42 876.5
43 897.4
44 918.3
45 939.1 31/18
46 960 47/27
47 980.9
48 1001.7 41/23
49 1022.6
50 1043.5 42/23
51 1064.3
52 1085.2 43/23
53 1106.1
54 1127
55 1147.8 33/17
56 1168.7
57 1189.6
58 1210.4
59 1231.3
60 1252.2 35/17
61 1273
62 1293.9 19/9
63 1314.8
64 1335.7
65 1356.5
66 1377.4 31/14
67 1398.3
68 1419.1
69 1440
70 1460.9
71 1481.7
72 1502.6 31/13
73 1523.5 41/17
74 1544.3
75 1565.2 42/17
76 1586.1 5/2
77 1607 43/17
78 1627.8
79 1648.7
80 1669.6
81 1690.4
82 1711.3
83 1732.2
84 1753
85 1773.9 39/14
86 1794.8 31/11
87 1815.7
88 1836.5
89 1857.4 38/13
90 1878.3
91 1899.1
92 1920
93 1940.9 43/14, 46/15
94 1961.7
95 1982.6
96 2003.5 35/11
97 2024.3 29/9
98 2045.2
99 2066.1
100 2087
101 2107.8
102 2128.7
103 2149.6 45/13
104 2170.4
105 2191.3 39/11
106 2212.2
107 2233
108 2253.9
109 2274.8
110 2295.7
111 2316.5
112 2337.4 27/7
113 2358.3 43/11
114 2379.1
115 2400

Harmonics

Approximation of harmonics in 115ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +10.43 -2.82 +0.00 +10.21 +7.61 -8.83 +10.43 -5.65 -0.23 +1.73 -2.82
Relative (%) +50.0 -13.5 +0.0 +48.9 +36.5 -42.3 +50.0 -27.1 -1.1 +8.3 -13.5
Steps
(reduced)
58
(58)
91
(91)
115
(0)
134
(19)
149
(34)
161
(46)
173
(58)
182
(67)
191
(76)
199
(84)
206
(91)
Approximation of harmonics in 115ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +4.69 +1.61 +7.38 +0.00 -0.61 +4.79 -5.34 +10.21 +9.22 -8.71 -2.19
Relative (%) +22.5 +7.7 +35.4 +0.0 -2.9 +22.9 -25.6 +48.9 +44.2 -41.7 -10.5
Steps
(reduced)
213
(98)
219
(104)
225
(110)
230
(0)
235
(5)
240
(10)
244
(14)
249
(19)
253
(23)
256
(26)
260
(30)