112edt
Jump to navigation
Jump to search
Prime factorization
24 × 7
Step size
16.9817¢
Octave
71\112edt (1205.7¢)
Consistency limit
2
Distinct consistency limit
2
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
← 111edt | 112edt | 113edt → |
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
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) |
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) |