113ed4

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 111ed4 113ed4 115ed4 →
Prime factorization 113 (prime)
Step size 21.2389¢ 
Octave 57\113ed4 (1210.62¢)
Twelfth 90\113ed4 (1911.5¢)
Consistency limit 1
Distinct consistency limit 1

113 equal divisions of the 4th harmonic (abbreviated 113ed4) is a nonoctave tuning system that divides the interval of 4/1 into 113 equal parts of about 21.2 ¢ each. Each step represents a frequency ratio of 41/113, or the 113th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 21.2
2 42.5
3 63.7 28/27
4 85 21/20, 41/39
5 106.2 33/31
6 127.4
7 148.7
8 169.9 43/39
9 191.2 19/17
10 212.4 26/23, 43/38
11 233.6
12 254.9 22/19, 29/25
13 276.1
14 297.3
15 318.6
16 339.8
17 361.1
18 382.3
19 403.5
20 424.8
21 446 22/17
22 467.3
23 488.5
24 509.7 47/35
25 531
26 552.2
27 573.5
28 594.7 31/22
29 615.9 10/7
30 637.2
31 658.4 19/13
32 679.6 37/25, 40/27
33 700.9 3/2
34 722.1 47/31
35 743.4
36 764.6 14/9
37 785.8
38 807.1
39 828.3
40 849.6 31/19
41 870.8 38/23, 43/26
42 892
43 913.3 39/23
44 934.5
45 955.8 33/19
46 977
47 998.2
48 1019.5
49 1040.7 31/17
50 1061.9
51 1083.2 43/23
52 1104.4
53 1125.7
54 1146.9 33/17
55 1168.1
56 1189.4
57 1210.6
58 1231.9
59 1253.1
60 1274.3
61 1295.6
62 1316.8
63 1338.1
64 1359.3 46/21
65 1380.5 20/9
66 1401.8 9/4
67 1423 25/11
68 1444.2
69 1465.5 7/3
70 1486.7
71 1508
72 1529.2
73 1550.4
74 1571.7
75 1592.9
76 1614.2 33/13
77 1635.4
78 1656.6
79 1677.9 29/11
80 1699.1
81 1720.4
82 1741.6 41/15
83 1762.8
84 1784.1
85 1805.3
86 1826.5
87 1847.8
88 1869
89 1890.3
90 1911.5
91 1932.7
92 1954
93 1975.2 47/15
94 1996.5
95 2017.7
96 2038.9
97 2060.2 23/7
98 2081.4
99 2102.7
100 2123.9
101 2145.1
102 2166.4
103 2187.6
104 2208.8
105 2230.1
106 2251.3
107 2272.6 26/7
108 2293.8
109 2315
110 2336.3
111 2357.5 39/10
112 2378.8
113 2400

Harmonics

Approximation of harmonics in 113ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +10.62 +9.55 +0.00 -4.01 -1.07 +8.17 +10.62 -2.14 +6.61 -9.73 +9.55
Relative (%) +50.0 +45.0 +0.0 -18.9 -5.0 +38.4 +50.0 -10.1 +31.1 -45.8 +45.0
Steps
(reduced)
57
(57)
90
(90)
113
(0)
131
(18)
146
(33)
159
(46)
170
(57)
179
(66)
188
(75)
195
(82)
203
(90)
Approximation of harmonics in 113ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -1.59 -2.45 +5.54 +0.00 +1.24 +8.48 -0.17 -4.01 -3.52 +0.89 +8.89
Relative (%) -7.5 -11.6 +26.1 +0.0 +5.8 +39.9 -0.8 -18.9 -16.6 +4.2 +41.9
Steps
(reduced)
209
(96)
215
(102)
221
(108)
226
(0)
231
(5)
236
(10)
240
(14)
244
(18)
248
(22)
252
(26)
256
(30)