143ed4
Jump to navigation
Jump to search
Prime factorization
11 × 13
Step size
16.7832¢
Octave
72\143ed4 (1208.39¢)
Twelfth
113\143ed4 (1896.5¢)
Consistency limit
1
Distinct consistency limit
1
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
← 141ed4 | 143ed4 | 145ed4 → |
143 equal divisions of the 4th harmonic (abbreviated 143ed4) is a nonoctave tuning system that divides the interval of 4/1 into 143 equal parts of about 16.8 ¢ each. Each step represents a frequency ratio of 41/143, or the 143rd root of 4.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 16.8 | |
2 | 33.6 | 50/49 |
3 | 50.3 | 35/34, 36/35 |
4 | 67.1 | |
5 | 83.9 | 43/41 |
6 | 100.7 | |
7 | 117.5 | 46/43 |
8 | 134.3 | |
9 | 151 | |
10 | 167.8 | 43/39 |
11 | 184.6 | |
12 | 201.4 | |
13 | 218.2 | 17/15 |
14 | 235 | 47/41 |
15 | 251.7 | |
16 | 268.5 | |
17 | 285.3 | 46/39 |
18 | 302.1 | 25/21 |
19 | 318.9 | |
20 | 335.7 | |
21 | 352.4 | |
22 | 369.2 | |
23 | 386 | |
24 | 402.8 | 29/23 |
25 | 419.6 | |
26 | 436.4 | |
27 | 453.1 | 13/10 |
28 | 469.9 | |
29 | 486.7 | |
30 | 503.5 | |
31 | 520.3 | |
32 | 537.1 | 15/11 |
33 | 553.8 | |
34 | 570.6 | |
35 | 587.4 | |
36 | 604.2 | |
37 | 621 | |
38 | 637.8 | |
39 | 654.5 | 54/37 |
40 | 671.3 | |
41 | 688.1 | |
42 | 704.9 | |
43 | 721.7 | 47/31 |
44 | 738.5 | 23/15 |
45 | 755.2 | 17/11 |
46 | 772 | |
47 | 788.8 | |
48 | 805.6 | |
49 | 822.4 | 37/23 |
50 | 839.2 | |
51 | 855.9 | 41/25 |
52 | 872.7 | |
53 | 889.5 | |
54 | 906.3 | |
55 | 923.1 | 29/17 |
56 | 939.9 | 31/18, 43/25 |
57 | 956.6 | |
58 | 973.4 | |
59 | 990.2 | 39/22 |
60 | 1007 | 34/19 |
61 | 1023.8 | |
62 | 1040.6 | 31/17 |
63 | 1057.3 | 35/19 |
64 | 1074.1 | |
65 | 1090.9 | |
66 | 1107.7 | 36/19, 55/29 |
67 | 1124.5 | |
68 | 1141.3 | 29/15 |
69 | 1158 | 41/21 |
70 | 1174.8 | |
71 | 1191.6 | |
72 | 1208.4 | |
73 | 1225.2 | |
74 | 1242 | 43/21 |
75 | 1258.7 | |
76 | 1275.5 | 23/11 |
77 | 1292.3 | |
78 | 1309.1 | |
79 | 1325.9 | |
80 | 1342.7 | |
81 | 1359.4 | |
82 | 1376.2 | |
83 | 1393 | |
84 | 1409.8 | |
85 | 1426.6 | 41/18 |
86 | 1443.4 | |
87 | 1460.1 | |
88 | 1476.9 | 54/23 |
89 | 1493.7 | |
90 | 1510.5 | 55/23 |
91 | 1527.3 | |
92 | 1544.1 | |
93 | 1560.8 | |
94 | 1577.6 | |
95 | 1594.4 | |
96 | 1611.2 | |
97 | 1628 | |
98 | 1644.8 | |
99 | 1661.5 | 47/18 |
100 | 1678.3 | 29/11 |
101 | 1695.1 | |
102 | 1711.9 | |
103 | 1728.7 | 19/7 |
104 | 1745.5 | |
105 | 1762.2 | 36/13 |
106 | 1779 | |
107 | 1795.8 | |
108 | 1812.6 | |
109 | 1829.4 | |
110 | 1846.2 | |
111 | 1862.9 | |
112 | 1879.7 | |
113 | 1896.5 | |
114 | 1913.3 | |
115 | 1930.1 | |
116 | 1946.9 | |
117 | 1963.6 | |
118 | 1980.4 | |
119 | 1997.2 | |
120 | 2014 | |
121 | 2030.8 | 42/13 |
122 | 2047.6 | |
123 | 2064.3 | |
124 | 2081.1 | |
125 | 2097.9 | |
126 | 2114.7 | |
127 | 2131.5 | |
128 | 2148.3 | |
129 | 2165 | |
130 | 2181.8 | |
131 | 2198.6 | |
132 | 2215.4 | |
133 | 2232.2 | |
134 | 2249 | 11/3 |
135 | 2265.7 | |
136 | 2282.5 | |
137 | 2299.3 | |
138 | 2316.1 | |
139 | 2332.9 | 50/13 |
140 | 2349.7 | |
141 | 2366.4 | |
142 | 2383.2 | |
143 | 2400 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +8.39 | -5.45 | +0.00 | -0.30 | +2.94 | +4.60 | +8.39 | +5.88 | +8.09 | -5.86 | -5.45 |
Relative (%) | +50.0 | -32.5 | +0.0 | -1.8 | +17.5 | +27.4 | +50.0 | +35.0 | +48.2 | -34.9 | -32.5 | |
Steps (reduced) |
72 (72) |
113 (113) |
143 (0) |
166 (23) |
185 (42) |
201 (58) |
215 (72) |
227 (84) |
238 (95) |
247 (104) |
256 (113) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +7.02 | -3.79 | -5.75 | +0.00 | -4.26 | -2.51 | +4.58 | -0.30 | -0.85 | +2.53 | -7.30 |
Relative (%) | +41.9 | -22.6 | -34.3 | +0.0 | -25.4 | -15.0 | +27.3 | -1.8 | -5.1 | +15.1 | -43.5 | |
Steps (reduced) |
265 (122) |
272 (129) |
279 (136) |
286 (0) |
292 (6) |
298 (12) |
304 (18) |
309 (23) |
314 (28) |
319 (33) |
323 (37) |