133ed4

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.
← 131ed4 133ed4 135ed4 →
Prime factorization 7 × 19
Step size 18.0451¢ 
Octave 67\133ed4 (1209.02¢)
Twelfth 105\133ed4 (1894.74¢) (→15\19ed4)
Consistency limit 1
Distinct consistency limit 1

133 equal divisions of the 4th harmonic (abbreviated 133ed4) is a nonoctave tuning system that divides the interval of 4/1 into 133 equal parts of about 18 ¢ each. Each step represents a frequency ratio of 41/133, or the 133rd root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 18
2 36.1
3 54.1
4 72.2
5 90.2 39/37
6 108.3 33/31, 49/46, 50/47
7 126.3
8 144.4
9 162.4
10 180.5
11 198.5 37/33
12 216.5
13 234.6
14 252.6
15 270.7
16 288.7 13/11
17 306.8 37/31, 43/36
18 324.8 35/29
19 342.9 50/41
20 360.9
21 378.9 51/41
22 397 39/31
23 415 47/37
24 433.1
25 451.1
26 469.2 38/29
27 487.2
28 505.3
29 523.3 23/17
30 541.4 41/30
31 559.4 29/21
32 577.4
33 595.5
34 613.5 47/33
35 631.6 49/34
36 649.6
37 667.7
38 685.7
39 703.8
40 721.8 47/31
41 739.8
42 757.9
43 775.9 36/23, 47/30
44 794
45 812
46 830.1 21/13
47 848.1 31/19
48 866.2
49 884.2 5/3
50 902.3
51 920.3 17/10
52 938.3
53 956.4 33/19
54 974.4
55 992.5
56 1010.5
57 1028.6
58 1046.6
59 1064.7
60 1082.7 43/23
61 1100.8
62 1118.8 21/11
63 1136.8
64 1154.9 37/19
65 1172.9
66 1191
67 1209
68 1227.1
69 1245.1 39/19
70 1263.2
71 1281.2
72 1299.2 36/17
73 1317.3
74 1335.3
75 1353.4
76 1371.4
77 1389.5 29/13
78 1407.5
79 1425.6 41/18
80 1443.6 23/10
81 1461.7
82 1479.7
83 1497.7
84 1515.8
85 1533.8
86 1551.9 49/20
87 1569.9
88 1588
89 1606 43/17
90 1624.1
91 1642.1
92 1660.2 47/18
93 1678.2 29/11
94 1696.2
95 1714.3 35/13
96 1732.3
97 1750.4
98 1768.4 25/9
99 1786.5
100 1804.5 17/6
101 1822.6
102 1840.6
103 1858.6 38/13
104 1876.7
105 1894.7
106 1912.8
107 1930.8
108 1948.9
109 1966.9
110 1985
111 2003 35/11
112 2021.1
113 2039.1
114 2057.1
115 2075.2
116 2093.2
117 2111.3
118 2129.3
119 2147.4 38/11
120 2165.4
121 2183.5
122 2201.5
123 2219.5
124 2237.6
125 2255.6
126 2273.7
127 2291.7
128 2309.8 19/5
129 2327.8 23/6
130 2345.9
131 2363.9
132 2382
133 2400

Harmonics

Approximation of harmonics in 133ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +9.02 -7.22 +0.00 -7.37 +1.80 +5.61 +9.02 +3.61 +1.66 -0.94 -7.22
Relative (%) +50.0 -40.0 +0.0 -40.8 +10.0 +31.1 +50.0 +20.0 +9.2 -5.2 -40.0
Steps
(reduced)
67
(67)
105
(105)
133
(0)
154
(21)
172
(39)
187
(54)
200
(67)
211
(78)
221
(88)
230
(97)
238
(105)
Approximation of harmonics in 133ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -1.43 -3.41 +3.46 +0.00 +3.32 -5.41 -8.79 -7.37 -1.61 +8.08 +3.30
Relative (%) -7.9 -18.9 +19.2 +0.0 +18.4 -30.0 -48.7 -40.8 -8.9 +44.8 +18.3
Steps
(reduced)
246
(113)
253
(120)
260
(127)
266
(0)
272
(6)
277
(11)
282
(16)
287
(21)
292
(26)
297
(31)
301
(35)