112edt

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.
← 111edt112edt113edt →
Prime factorization 24 × 7
Step size 16.9817¢ 
Octave 71\112edt (1205.7¢)
Consistency limit 2
Distinct consistency limit 2

112 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 112edt or 112ed3), is a nonoctave tuning system that divides the interval of 3/1 into 112 equal parts of about 17 ¢ each. Each step represents a frequency ratio of 31/112, or the 112th root of 3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 16.982
2 33.963
3 50.945
4 67.927 26/25
5 84.909
6 101.89 35/33
7 118.872 15/14
8 135.854
9 152.836
10 169.817 43/39
11 186.799 39/35
12 203.781
13 220.763 25/22, 42/37
14 237.744 31/27, 47/41
15 254.726 22/19
16 271.708
17 288.69 13/11
18 305.671 31/26, 37/31
19 322.653 41/34
20 339.635 28/23, 45/37
21 356.617 27/22, 43/35
22 373.598 31/25
23 390.58
24 407.562 19/15
25 424.544 23/18
26 441.525
27 458.507 30/23, 43/33
28 475.489 25/19
29 492.47
30 509.452
31 526.434 42/31
32 543.416 26/19, 37/27
33 560.397 29/21, 47/34
34 577.379
35 594.361 31/22
36 611.343 37/26
37 628.324
38 645.306 45/31
39 662.288 22/15, 41/28
40 679.27 37/25
41 696.251
42 713.233
43 730.215 29/19
44 747.197
45 764.178 14/9
46 781.16 11/7
47 798.142
48 815.124
49 832.105 21/13
50 849.087 31/19
51 866.069
52 883.051 5/3
53 900.032 37/22, 42/25
54 917.014 17/10
55 933.996
56 950.978 26/15, 45/26
57 967.959
58 984.941 30/17
59 1001.923 25/14, 41/23
60 1018.904 9/5
61 1035.886
62 1052.868
63 1069.85 13/7
64 1086.831
65 1103.813
66 1120.795 21/11
67 1137.777 27/14
68 1154.758 37/19
69 1171.74
70 1188.722
71 1205.704
72 1222.685
73 1239.667 43/21, 45/22
74 1256.649 31/15
75 1273.631
76 1290.612
77 1307.594
78 1324.576
79 1341.558
80 1358.539
81 1375.521 31/14
82 1392.503 38/17
83 1409.485
84 1426.466 41/18
85 1443.448 23/10
86 1460.43
87 1477.411 47/20
88 1494.393 45/19
89 1511.375
90 1528.357
91 1545.338 22/9
92 1562.32 37/15
93 1579.302
94 1596.284
95 1613.265 33/13
96 1630.247
97 1647.229 44/17
98 1664.211
99 1681.192 37/14
100 1698.174
101 1715.156 35/13
102 1732.138
103 1749.119
104 1766.101
105 1783.083 14/5
106 1800.065
107 1817.046
108 1834.028
109 1851.01
110 1867.992
111 1884.973
112 1901.955 3/1

Harmonics

Approximation of harmonics in 112edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.70 +0.00 -5.57 -1.31 +5.70 -6.44 +0.13 +0.00 +4.40 -7.77 -5.57
Relative (%) +33.6 +0.0 -32.8 -7.7 +33.6 -37.9 +0.8 +0.0 +25.9 -45.8 -32.8
Steps
(reduced)
71
(71)
112
(0)
141
(29)
164
(52)
183
(71)
198
(86)
212
(100)
224
(0)
235
(11)
244
(20)
253
(29)
Approximation of harmonics in 112edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -8.29 -0.74 -1.31 +5.83 +2.77 +5.70 -2.99 -6.88 -6.44 -2.07 +5.88
Relative (%) -48.8 -4.3 -7.7 +34.3 +16.3 +33.6 -17.6 -40.5 -37.9 -12.2 +34.6
Steps
(reduced)
261
(37)
269
(45)
276
(52)
283
(59)
289
(65)
295
(71)
300
(76)
305
(81)
310
(86)
315
(91)
320
(96)