124edt
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Prime factorization
22 × 31
Step size
15.3383¢
Octave
78\124edt (1196.39¢) (→39\62edt)
Consistency limit
4
Distinct consistency limit
4
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← 123edt | 124edt | 125edt → |
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 | 15.3 | |
2 | 30.7 | |
3 | 46 | |
4 | 61.4 | 28/27, 29/28 |
5 | 76.7 | 23/22, 47/45 |
6 | 92 | 19/18, 39/37 |
7 | 107.4 | 33/31, 50/47 |
8 | 122.7 | 29/27, 44/41 |
9 | 138 | |
10 | 153.4 | 47/43 |
11 | 168.7 | 43/39 |
12 | 184.1 | 10/9 |
13 | 199.4 | 37/33, 46/41 |
14 | 214.7 | |
15 | 230.1 | |
16 | 245.4 | |
17 | 260.8 | 43/37, 50/43 |
18 | 276.1 | 27/23, 34/29 |
19 | 291.4 | |
20 | 306.8 | 37/31 |
21 | 322.1 | 47/39 |
22 | 337.4 | 17/14, 45/37 |
23 | 352.8 | 27/22 |
24 | 368.1 | 26/21 |
25 | 383.5 | |
26 | 398.8 | 34/27, 39/31 |
27 | 414.1 | 33/26, 47/37 |
28 | 429.5 | 50/39 |
29 | 444.8 | 22/17 |
30 | 460.2 | 30/23, 43/33 |
31 | 475.5 | |
32 | 490.8 | |
33 | 506.2 | |
34 | 521.5 | 23/17, 50/37 |
35 | 536.8 | 15/11 |
36 | 552.2 | |
37 | 567.5 | 43/31 |
38 | 582.9 | 7/5 |
39 | 598.2 | 41/29 |
40 | 613.5 | 47/33 |
41 | 628.9 | |
42 | 644.2 | 29/20, 45/31 |
43 | 659.5 | 41/28 |
44 | 674.9 | 31/21, 34/23 |
45 | 690.2 | |
46 | 705.6 | |
47 | 720.9 | 44/29, 47/31, 50/33 |
48 | 736.2 | 26/17 |
49 | 751.6 | |
50 | 766.9 | |
51 | 782.3 | 11/7 |
52 | 797.6 | 46/29 |
53 | 812.9 | |
54 | 828.3 | 50/31 |
55 | 843.6 | 44/27 |
56 | 858.9 | 23/14 |
57 | 874.3 | |
58 | 889.6 | |
59 | 905 | |
60 | 920.3 | 17/10 |
61 | 935.6 | |
62 | 951 | 26/15, 45/26 |
63 | 966.3 | |
64 | 981.7 | 30/17, 37/21 |
65 | 997 | |
66 | 1012.3 | |
67 | 1027.7 | |
68 | 1043 | 42/23 |
69 | 1058.3 | |
70 | 1073.7 | |
71 | 1089 | |
72 | 1104.4 | |
73 | 1119.7 | 21/11 |
74 | 1135 | |
75 | 1150.4 | |
76 | 1165.7 | 49/25, 51/26 |
77 | 1181.1 | |
78 | 1196.4 | |
79 | 1211.7 | |
80 | 1227.1 | |
81 | 1242.4 | 41/20, 43/21 |
82 | 1257.7 | 31/15 |
83 | 1273.1 | |
84 | 1288.4 | 40/19 |
85 | 1303.8 | |
86 | 1319.1 | 15/7 |
87 | 1334.4 | |
88 | 1349.8 | |
89 | 1365.1 | 11/5 |
90 | 1380.5 | 51/23 |
91 | 1395.8 | 47/21 |
92 | 1411.1 | |
93 | 1426.5 | 41/18 |
94 | 1441.8 | 23/10 |
95 | 1457.1 | 51/22 |
96 | 1472.5 | |
97 | 1487.8 | 26/11 |
98 | 1503.2 | 31/13, 50/21 |
99 | 1518.5 | |
100 | 1533.8 | |
101 | 1549.2 | 22/9 |
102 | 1564.5 | 37/15, 42/17 |
103 | 1579.8 | |
104 | 1595.2 | |
105 | 1610.5 | |
106 | 1625.9 | 23/9 |
107 | 1641.2 | |
108 | 1656.5 | |
109 | 1671.9 | |
110 | 1687.2 | |
111 | 1702.6 | |
112 | 1717.9 | 27/10 |
113 | 1733.2 | |
114 | 1748.6 | |
115 | 1763.9 | |
116 | 1779.2 | |
117 | 1794.6 | 31/11 |
118 | 1809.9 | 37/13 |
119 | 1825.3 | |
120 | 1840.6 | |
121 | 1855.9 | |
122 | 1871.3 | |
123 | 1886.6 | |
124 | 1902 | 3/1 |
Harmonics
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) |
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) |