137ed4

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← 135ed4 137ed4 139ed4 →
Prime factorization 137 (prime)
Step size 17.5182¢ 
Octave 69\137ed4 (1208.76¢)
Twelfth 109\137ed4 (1909.49¢)
Consistency limit 1
Distinct consistency limit 1

137 equal divisions of the 4th harmonic (abbreviated 137ed4) is a nonoctave tuning system that divides the interval of 4/1 into 137 equal parts of about 17.5 ¢ each. Each step represents a frequency ratio of 41/137, or the 137th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 17.5
2 35 51/50, 52/51
3 52.6 34/33
4 70.1
5 87.6 41/39
6 105.1
7 122.6
8 140.1
9 157.7 23/21
10 175.2
11 192.7 19/17
12 210.2 35/31
13 227.7
14 245.3 38/33
15 262.8 50/43
16 280.3
17 297.8
18 315.3
19 332.8
20 350.4
21 367.9
22 385.4
23 402.9 29/23
24 420.4 37/29
25 438
26 455.5
27 473
28 490.5
29 508 51/38
30 525.5
31 543.1 26/19
32 560.6
33 578.1
34 595.6
35 613.1
36 630.7
37 648.2
38 665.7
39 683.2 43/29
40 700.7 3/2
41 718.2 50/33
42 735.8 26/17
43 753.3 17/11
44 770.8 39/25
45 788.3 41/26, 52/33
46 805.8
47 823.4 37/23
48 840.9
49 858.4 23/14
50 875.9
51 893.4
52 910.9
53 928.5
54 946 19/11
55 963.5
56 981 37/21
57 998.5
58 1016.1
59 1033.6
60 1051.1
61 1068.6
62 1086.1
63 1103.6
64 1121.2 21/11
65 1138.7
66 1156.2
67 1173.7
68 1191.2
69 1208.8
70 1226.3
71 1243.8 39/19
72 1261.3 29/14
73 1278.8
74 1296.4
75 1313.9
76 1331.4 41/19
77 1348.9
78 1366.4 11/5
79 1383.9 20/9
80 1401.5
81 1419
82 1436.5 39/17
83 1454 51/22
84 1471.5
85 1489.1 26/11
86 1506.6
87 1524.1 41/17
88 1541.6
89 1559.1
90 1576.6
91 1594.2
92 1611.7
93 1629.2
94 1646.7
95 1664.2
96 1681.8 37/14
97 1699.3
98 1716.8
99 1734.3
100 1751.8
101 1769.3
102 1786.9
103 1804.4
104 1821.9 43/15
105 1839.4
106 1856.9
107 1874.5
108 1892
109 1909.5
110 1927
111 1944.5
112 1962
113 1979.6
114 1997.1
115 2014.6
116 2032.1
117 2049.6
118 2067.2 33/10
119 2084.7 10/3
120 2102.2
121 2119.7 17/5
122 2137.2
123 2154.7
124 2172.3
125 2189.8 39/11
126 2207.3
127 2224.8 47/13
128 2242.3
129 2259.9
130 2277.4 41/11
131 2294.9
132 2312.4 19/5
133 2329.9
134 2347.4
135 2365
136 2382.5
137 2400

Harmonics

Approximation of harmonics in 137ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +8.76 +7.53 +0.00 -0.91 -1.23 -5.32 +8.76 -2.45 +7.85 +0.51 +7.53
Relative (%) +50.0 +43.0 +0.0 -5.2 -7.0 -30.4 +50.0 -14.0 +44.8 +2.9 +43.0
Steps
(reduced)
69
(69)
109
(109)
137
(0)
159
(22)
177
(40)
192
(55)
206
(69)
217
(80)
228
(91)
237
(100)
246
(109)
Approximation of harmonics in 137ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -8.41 +3.44 +6.62 +0.00 +0.15 +6.31 +0.30 -0.91 +2.21 -8.25 +2.38
Relative (%) -48.0 +19.6 +37.8 +0.0 +0.9 +36.0 +1.7 -5.2 +12.6 -47.1 +13.6
Steps
(reduced)
253
(116)
261
(124)
268
(131)
274
(0)
280
(6)
286
(12)
291
(17)
296
(22)
301
(27)
305
(31)
310
(36)