131ed4
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Prime factorization
131 (prime)
Step size
18.3206¢
Octave
66\131ed4 (1209.16¢)
Twelfth
104\131ed4 (1905.34¢)
Consistency limit
1
Distinct consistency limit
1
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131 equal divisions of the 4th harmonic (abbreviated 131ed4) is a nonoctave tuning system that divides the interval of 4/1 into 131 equal parts of about 18.3 ¢ each. Each step represents a frequency ratio of 41/131, or the 131st root of 4.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 18.3 | |
2 | 36.6 | 46/45, 47/46, 50/49 |
3 | 55 | |
4 | 73.3 | 49/47 |
5 | 91.6 | 39/37 |
6 | 109.9 | 49/46 |
7 | 128.2 | |
8 | 146.6 | 49/45 |
9 | 164.9 | 11/10 |
10 | 183.2 | 10/9 |
11 | 201.5 | |
12 | 219.8 | |
13 | 238.2 | 47/41 |
14 | 256.5 | 29/25 |
15 | 274.8 | 41/35 |
16 | 293.1 | 45/38 |
17 | 311.5 | |
18 | 329.8 | 23/19 |
19 | 348.1 | 11/9 |
20 | 366.4 | 21/17, 47/38 |
21 | 384.7 | |
22 | 403.1 | 29/23 |
23 | 421.4 | 37/29 |
24 | 439.7 | 49/38 |
25 | 458 | |
26 | 476.3 | 25/19 |
27 | 494.7 | |
28 | 513 | 35/26, 39/29 |
29 | 531.3 | |
30 | 549.6 | |
31 | 567.9 | 43/31 |
32 | 586.3 | |
33 | 604.6 | |
34 | 622.9 | |
35 | 641.2 | |
36 | 659.5 | |
37 | 677.9 | 37/25 |
38 | 696.2 | |
39 | 714.5 | |
40 | 732.8 | 29/19 |
41 | 751.1 | |
42 | 769.5 | 39/25 |
43 | 787.8 | 41/26, 52/33 |
44 | 806.1 | |
45 | 824.4 | 37/23 |
46 | 842.7 | |
47 | 861.1 | |
48 | 879.4 | |
49 | 897.7 | |
50 | 916 | |
51 | 934.4 | |
52 | 952.7 | 26/15 |
53 | 971 | |
54 | 989.3 | 23/13 |
55 | 1007.6 | |
56 | 1026 | 38/21, 47/26 |
57 | 1044.3 | |
58 | 1062.6 | |
59 | 1080.9 | |
60 | 1099.2 | 17/9 |
61 | 1117.6 | |
62 | 1135.9 | 27/14, 52/27 |
63 | 1154.2 | 37/19 |
64 | 1172.5 | |
65 | 1190.8 | |
66 | 1209.2 | |
67 | 1227.5 | |
68 | 1245.8 | 39/19 |
69 | 1264.1 | |
70 | 1282.4 | |
71 | 1300.8 | |
72 | 1319.1 | 15/7 |
73 | 1337.4 | |
74 | 1355.7 | 46/21 |
75 | 1374 | |
76 | 1392.4 | 38/17 |
77 | 1410.7 | |
78 | 1429 | |
79 | 1447.3 | |
80 | 1465.6 | 7/3 |
81 | 1484 | 33/14 |
82 | 1502.3 | 50/21 |
83 | 1520.6 | |
84 | 1538.9 | |
85 | 1557.3 | |
86 | 1575.6 | |
87 | 1593.9 | |
88 | 1612.2 | |
89 | 1630.5 | |
90 | 1648.9 | |
91 | 1667.2 | |
92 | 1685.5 | 45/17 |
93 | 1703.8 | |
94 | 1722.1 | 46/17 |
95 | 1740.5 | 41/15 |
96 | 1758.8 | 47/17 |
97 | 1777.1 | |
98 | 1795.4 | |
99 | 1813.7 | |
100 | 1832.1 | 49/17 |
101 | 1850.4 | |
102 | 1868.7 | 50/17 |
103 | 1887 | |
104 | 1905.3 | |
105 | 1923.7 | |
106 | 1942 | |
107 | 1960.3 | |
108 | 1978.6 | 47/15 |
109 | 1996.9 | |
110 | 2015.3 | |
111 | 2033.6 | |
112 | 2051.9 | |
113 | 2070.2 | 43/13 |
114 | 2088.5 | |
115 | 2106.9 | |
116 | 2125.2 | |
117 | 2143.5 | |
118 | 2161.8 | |
119 | 2180.2 | |
120 | 2198.5 | |
121 | 2216.8 | |
122 | 2235.1 | |
123 | 2253.4 | |
124 | 2271.8 | 26/7 |
125 | 2290.1 | |
126 | 2308.4 | |
127 | 2326.7 | |
128 | 2345 | |
129 | 2363.4 | |
130 | 2381.7 | |
131 | 2400 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +9.16 | +3.39 | +0.00 | -1.58 | -5.77 | +2.17 | +9.16 | +6.78 | +7.58 | +7.46 | +3.39 |
Relative (%) | +50.0 | +18.5 | +0.0 | -8.6 | -31.5 | +11.8 | +50.0 | +37.0 | +41.4 | +40.7 | +18.5 | |
Steps (reduced) |
66 (66) |
104 (104) |
131 (0) |
152 (21) |
169 (38) |
184 (53) |
197 (66) |
208 (77) |
218 (87) |
227 (96) |
235 (104) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -6.94 | -6.99 | +1.81 | +0.00 | +4.97 | -2.38 | -4.38 | -1.58 | +5.55 | -1.70 | -5.37 |
Relative (%) | -37.9 | -38.2 | +9.9 | +0.0 | +27.1 | -13.0 | -23.9 | -8.6 | +30.3 | -9.3 | -29.3 | |
Steps (reduced) |
242 (111) |
249 (118) |
256 (125) |
262 (0) |
268 (6) |
273 (11) |
278 (16) |
283 (21) |
288 (26) |
292 (30) |
296 (34) |