127ed4

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← 125ed4127ed4129ed4 →
Prime factorization 127 (prime)
Step size 18.8976¢ 
Octave 64\127ed4 (1209.45¢)
Twelfth 101\127ed4 (1908.66¢)
Consistency limit 1
Distinct consistency limit 1

127 equal divisions of the 4th harmonic (abbreviated 127ed4) is a nonoctave tuning system that divides the interval of 4/1 into 127 equal parts of about 18.9 ¢ each. Each step represents a frequency ratio of 41/127, or the 127th root of 4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 18.898
2 37.795 46/45, 47/46
3 56.693 31/30
4 75.591 47/45
5 94.488
6 113.386
7 132.283
8 151.181
9 170.079 43/39
10 188.976
11 207.874
12 226.772
13 245.669 38/33
14 264.567
15 283.465 33/28
16 302.362
17 321.26 47/39
18 340.157 45/37
19 359.055
20 377.953 46/37
21 396.85 39/31
22 415.748 14/11, 47/37
23 434.646
24 453.543 13/10
25 472.441
26 491.339
27 510.236 51/38
28 529.134 19/14
29 548.031
30 566.929 43/31
31 585.827
32 604.724
33 623.622 43/30
34 642.52
35 661.417
36 680.315 40/27
37 699.213
38 718.11
39 737.008 26/17
40 755.906
41 774.803
42 793.701
43 812.598
44 831.496 21/13
45 850.394
46 869.291 43/26
47 888.189
48 907.087 49/29
49 925.984
50 944.882 19/11, 50/29
51 963.78
52 982.677 30/17
53 1001.575 41/23
54 1020.472
55 1039.37 31/17, 51/28
56 1058.268
57 1077.165
58 1096.063
59 1114.961
60 1133.858
61 1152.756 37/19
62 1171.654
63 1190.551
64 1209.449
65 1228.346
66 1247.244
67 1266.142
68 1285.039 21/10
69 1303.937
70 1322.835
71 1341.732
72 1360.63
73 1379.528
74 1398.425
75 1417.323
76 1436.22 39/17
77 1455.118 51/22
78 1474.016
79 1492.913 45/19
80 1511.811
81 1530.709 46/19
82 1549.606
83 1568.504 47/19
84 1587.402
85 1606.299 43/17
86 1625.197
87 1644.094
88 1662.992
89 1681.89 37/14
90 1700.787
91 1719.685
92 1738.583 30/11
93 1757.48
94 1776.378
95 1795.276 31/11
96 1814.173
97 1833.071
98 1851.969
99 1870.866
100 1889.764
101 1908.661
102 1927.559
103 1946.457
104 1965.354 28/9
105 1984.252
106 2003.15
107 2022.047 45/14
108 2040.945
109 2059.843 23/7
110 2078.74
111 2097.638 47/14
112 2116.535
113 2135.433
114 2154.331
115 2173.228
116 2192.126 39/11
117 2211.024
118 2229.921
119 2248.819 11/3
120 2267.717
121 2286.614
122 2305.512
123 2324.409
124 2343.307
125 2362.205
126 2381.102
127 2400

Harmonics

Approximation of harmonics in 127ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +9.45 +6.71 +0.00 -8.36 -2.74 -5.05 +9.45 -5.48 +1.09 +6.16 +6.71
Relative (%) +50.0 +35.5 +0.0 -44.2 -14.5 -26.7 +50.0 -29.0 +5.8 +32.6 +35.5
Steps
(reduced)
64
(64)
101
(101)
127
(0)
147
(20)
164
(37)
178
(51)
191
(64)
201
(74)
211
(84)
220
(93)
228
(101)
Approximation of harmonics in 127ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +0.42 +4.40 -1.65 +0.00 +8.43 +3.96 +4.85 -8.36 +1.66 -3.29 -4.65
Relative (%) +2.2 +23.3 -8.8 +0.0 +44.6 +21.0 +25.7 -44.2 +8.8 -17.4 -24.6
Steps
(reduced)
235
(108)
242
(115)
248
(121)
254
(0)
260
(6)
265
(11)
270
(16)
274
(20)
279
(25)
283
(29)
287
(33)