126edt

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.
← 125edt 126edt 127edt →
Prime factorization 2 × 32 × 7
Step size 15.0949¢ 
Octave 79\126edt (1192.5¢)
Consistency limit 2
Distinct consistency limit 2

126 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 126edt or 126ed3), is a nonoctave tuning system that divides the interval of 3/1 into 126 equal parts of about 15.1 ¢ each. Each step represents a frequency ratio of 31/126, or the 126th root of 3.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 15.1
2 30.2
3 45.3 38/37, 39/38
4 60.4 30/29
5 75.5 47/45
6 90.6 39/37
7 105.7 50/47
8 120.8
9 135.9
10 150.9
11 166 11/10
12 181.1 10/9
13 196.2 37/33
14 211.3 35/31
15 226.4 49/43
16 241.5
17 256.6
18 271.7
19 286.8 46/39
20 301.9
21 317
22 332.1 23/19
23 347.2 11/9
24 362.3 37/30
25 377.4 41/33, 46/37, 51/41
26 392.5
27 407.6 19/15, 43/34
28 422.7 37/29
29 437.8
30 452.8 13/10
31 467.9 38/29
32 483 41/31
33 498.1
34 513.2 39/29
35 528.3
36 543.4
37 558.5 29/21
38 573.6 46/33
39 588.7
40 603.8
41 618.9 10/7
42 634 49/34
43 649.1
44 664.2
45 679.3
46 694.4
47 709.5
48 724.6 41/27
49 739.6 23/15
50 754.7 17/11
51 769.8
52 784.9
53 800 27/17, 46/29
54 815.1
55 830.2 21/13
56 845.3
57 860.4 51/31
58 875.5
59 890.6
60 905.7
61 920.8 46/27
62 935.9
63 951
64 966.1
65 981.2 37/21
66 996.3
67 1011.4
68 1026.5 38/21
69 1041.5 31/17
70 1056.6 35/19
71 1071.7 13/7
72 1086.8
73 1101.9 17/9
74 1117
75 1132.1
76 1147.2 33/17
77 1162.3 45/23
78 1177.4
79 1192.5
80 1207.6
81 1222.7
82 1237.8 47/23
83 1252.9
84 1268
85 1283.1 21/10
86 1298.2
87 1313.3
88 1328.3
89 1343.4 50/23
90 1358.5 46/21
91 1373.6
92 1388.7 29/13
93 1403.8
94 1418.9
95 1434
96 1449.1 30/13
97 1464.2
98 1479.3
99 1494.4 45/19
100 1509.5 43/18
101 1524.6 41/17
102 1539.7
103 1554.8 27/11
104 1569.9 47/19
105 1585
106 1600.1
107 1615.2
108 1630.2
109 1645.3
110 1660.4
111 1675.5 50/19
112 1690.6
113 1705.7
114 1720.8 27/10
115 1735.9 30/11
116 1751
117 1766.1
118 1781.2
119 1796.3
120 1811.4 37/13
121 1826.5
122 1841.6 29/10
123 1856.7 38/13
124 1871.8
125 1886.9
126 1902 3/1

Harmonics

Approximation of harmonics in 126edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -7.50 +0.00 +0.09 +6.24 -7.50 -2.67 -7.42 +0.00 -1.27 -0.23 +0.09
Relative (%) -49.7 +0.0 +0.6 +41.3 -49.7 -17.7 -49.1 +0.0 -8.4 -1.5 +0.6
Steps
(reduced)
79
(79)
126
(0)
159
(33)
185
(59)
205
(79)
223
(97)
238
(112)
252
(0)
264
(12)
275
(23)
285
(33)
Approximation of harmonics in 126edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 +4.92 +6.24 +0.17 +0.88 -7.50 +4.56 +6.33 -2.67 +7.36 +5.88
Relative (%) -17.4 +32.6 +41.3 +1.1 +5.8 -49.7 +30.2 +41.9 -17.7 +48.8 +39.0
Steps
(reduced)
294
(42)
303
(51)
311
(59)
318
(66)
325
(73)
331
(79)
338
(86)
344
(92)
349
(97)
355
(103)
360
(108)