124edt

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← 123edt 124edt 125edt →
Prime factorization 22 × 31
Step size 15.3383¢ 
Octave 78\124edt (1196.39¢) (→39\62edt)
Consistency limit 4
Distinct consistency limit 4

124 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 124edt or 124ed3), is a nonoctave tuning system that divides the interval of 3/1 into 124 equal parts of about 15.3 ¢ each. Each step represents a frequency ratio of 31/124, or the 124th root of 3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 15.338
2 30.677
3 46.015
4 61.353 28/27, 29/28
5 76.692 23/22, 47/45
6 92.03 19/18, 39/37
7 107.368 33/31, 50/47
8 122.707 29/27, 44/41
9 138.045
10 153.383 47/43
11 168.722 43/39
12 184.06 10/9
13 199.399 37/33, 46/41
14 214.737
15 230.075
16 245.414
17 260.752 43/37, 50/43
18 276.09 27/23, 34/29
19 291.429
20 306.767 37/31
21 322.105 47/39
22 337.444 17/14, 45/37
23 352.782 27/22
24 368.12 26/21
25 383.459
26 398.797 34/27, 39/31
27 414.135 33/26, 47/37
28 429.474 50/39
29 444.812 22/17
30 460.15 30/23, 43/33
31 475.489
32 490.827
33 506.165
34 521.504 23/17, 50/37
35 536.842 15/11
36 552.18
37 567.519 43/31
38 582.857 7/5
39 598.196 41/29
40 613.534 47/33
41 628.872
42 644.211 29/20, 45/31
43 659.549 41/28
44 674.887 31/21, 34/23
45 690.226
46 705.564
47 720.902 44/29, 47/31, 50/33
48 736.241 26/17
49 751.579
50 766.917
51 782.256 11/7
52 797.594 46/29
53 812.932
54 828.271 50/31
55 843.609 44/27
56 858.947 23/14
57 874.286
58 889.624
59 904.962
60 920.301 17/10
61 935.639
62 950.978 26/15, 45/26
63 966.316
64 981.654 30/17, 37/21
65 996.993
66 1012.331
67 1027.669
68 1043.008 42/23
69 1058.346
70 1073.684
71 1089.023
72 1104.361
73 1119.699 21/11
74 1135.038
75 1150.376
76 1165.714 49/25, 51/26
77 1181.053
78 1196.391
79 1211.729
80 1227.068
81 1242.406 41/20, 43/21
82 1257.744 31/15
83 1273.083
84 1288.421 40/19
85 1303.759
86 1319.098 15/7
87 1334.436
88 1349.775
89 1365.113 11/5
90 1380.451 51/23
91 1395.79 47/21
92 1411.128
93 1426.466 41/18
94 1441.805 23/10
95 1457.143 51/22
96 1472.481
97 1487.82 26/11
98 1503.158 31/13, 50/21
99 1518.496
100 1533.835
101 1549.173 22/9
102 1564.511 37/15, 42/17
103 1579.85
104 1595.188
105 1610.526
106 1625.865 23/9
107 1641.203
108 1656.541
109 1671.88
110 1687.218
111 1702.556
112 1717.895 27/10
113 1733.233
114 1748.572
115 1763.91
116 1779.248
117 1794.587 31/11
118 1809.925 37/13
119 1825.263
120 1840.602
121 1855.94
122 1871.278
123 1886.617
124 1901.955 3/1

Harmonics

Approximation of harmonics in 124edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.61 +0.00 -7.22 +5.27 -3.61 +5.61 +4.51 +0.00 +1.66 +5.37 -7.22
Relative (%) -23.5 +0.0 -47.1 +34.3 -23.5 +36.6 +29.4 +0.0 +10.8 +35.0 -47.1
Steps
(reduced)
78
(78)
124
(0)
156
(32)
182
(58)
202
(78)
220
(96)
235
(111)
248
(0)
260
(12)
271
(23)
280
(32)
Approximation of harmonics in 124edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +7.59 +2.00 +5.27 +0.90 +3.32 -3.61 -5.18 -1.95 +5.61 +1.77 +1.50
Relative (%) +49.5 +13.0 +34.3 +5.9 +21.6 -23.5 -33.8 -12.7 +36.6 +11.5 +9.8
Steps
(reduced)
290
(42)
298
(50)
306
(58)
313
(65)
320
(72)
326
(78)
332
(84)
338
(90)
344
(96)
349
(101)
354
(106)