125ed4

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← 123ed4 125ed4 127ed4 →
Prime factorization 53
Step size 19.2¢ 
Octave 63\125ed4 (1209.6¢)
Twelfth 99\125ed4 (1900.8¢)
Consistency limit 1
Distinct consistency limit 1

125 equal divisions of the 4th harmonic (abbreviated 125ed4) is a nonoctave tuning system that divides the interval of 4/1 into 125 equal parts of exactly 19.2 ¢ each. Each step represents a frequency ratio of 41/125, or the 125th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 19.2
2 38.4
3 57.6 30/29, 31/30
4 76.8 23/22, 45/43, 47/45
5 96
6 115.2 31/29
7 134.4 27/25
8 153.6 47/43
9 172.8 21/19
10 192 19/17
11 211.2 26/23
12 230.4
13 249.6 15/13
14 268.8
15 288 13/11
16 307.2 37/31
17 326.4
18 345.6 11/9
19 364.8 21/17, 37/30
20 384
21 403.2 29/23
22 422.4 37/29
23 441.6
24 460.8 30/23
25 480 29/22, 33/25
26 499.2
27 518.4 31/23
28 537.6 15/11
29 556.8
30 576
31 595.2 31/22
32 614.4
33 633.6
34 652.8 51/35
35 672
36 691.2
37 710.4
38 729.6
39 748.8
40 768 39/25
41 787.2 41/26
42 806.4 43/27
43 825.6 29/18
44 844.8
45 864
46 883.2 5/3
47 902.4
48 921.6
49 940.8 31/18, 43/25
50 960 47/27
51 979.2
52 998.4
53 1017.6 9/5
54 1036.8
55 1056 35/19
56 1075.2
57 1094.4 47/25
58 1113.6
59 1132.8 25/13
60 1152
61 1171.2
62 1190.4
63 1209.6
64 1228.8
65 1248 37/18
66 1267.2 27/13
67 1286.4
68 1305.6
69 1324.8
70 1344 50/23
71 1363.2 11/5
72 1382.4
73 1401.6
74 1420.8 25/11
75 1440
76 1459.2
77 1478.4
78 1497.6
79 1516.8
80 1536 17/7
81 1555.2 27/11
82 1574.4
83 1593.6
84 1612.8 33/13
85 1632
86 1651.2
87 1670.4
88 1689.6
89 1708.8 51/19
90 1728 19/7
91 1747.2
92 1766.4
93 1785.6
94 1804.8
95 1824 43/15
96 1843.2 29/10
97 1862.4
98 1881.6
99 1900.8 3/1
100 1920
101 1939.2
102 1958.4 31/10
103 1977.6 47/15
104 1996.8
105 2016
106 2035.2
107 2054.4
108 2073.6
109 2092.8
110 2112
111 2131.2
112 2150.4 45/13
113 2169.6
114 2188.8
115 2208
116 2227.2
117 2246.4
118 2265.6 37/10
119 2284.8
120 2304
121 2323.2
122 2342.4
123 2361.6 43/11
124 2380.8
125 2400

Harmonics

Approximation of harmonics in 125ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +9.60 -1.16 +0.00 -2.31 +8.44 -8.83 +9.60 -2.31 +7.29 -4.12 -1.16
Relative (%) +50.0 -6.0 +0.0 -12.1 +44.0 -46.0 +50.0 -12.0 +37.9 -21.4 -6.0
Steps
(reduced)
63
(63)
99
(99)
125
(0)
145
(20)
162
(37)
175
(50)
188
(63)
198
(73)
208
(83)
216
(91)
224
(99)
Approximation of harmonics in 125ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -5.33 +0.77 -3.47 +0.00 -8.96 +7.29 -9.51 -2.31 +9.22 +5.48 +5.33
Relative (%) -27.7 +4.0 -18.1 +0.0 -46.6 +38.0 -49.5 -12.1 +48.0 +28.6 +27.7
Steps
(reduced)
231
(106)
238
(113)
244
(119)
250
(0)
255
(5)
261
(11)
265
(15)
270
(20)
275
(25)
279
(29)
283
(33)