141ed4

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← 139ed4 141ed4 143ed4 →
Prime factorization 3 × 47
Step size 17.0213¢ 
Octave 71\141ed4 (1208.51¢)
Twelfth 112\141ed4 (1906.38¢)
Consistency limit 1
Distinct consistency limit 1

141 equal divisions of the 4th harmonic (abbreviated 141ed4) is a nonoctave tuning system that divides the interval of 4/1 into 141 equal parts of about 17 ¢ each. Each step represents a frequency ratio of 41/141, or the 141st root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 17
2 34
3 51.1 34/33, 35/34
4 68.1 26/25, 51/49
5 85.1 41/39
6 102.1 35/33
7 119.1 15/14
8 136.2
9 153.2 47/43
10 170.2 43/39
11 187.2 39/35
12 204.3
13 221.3 25/22
14 238.3 39/34
15 255.3
16 272.3 41/35, 55/47
17 289.4 13/11
18 306.4 37/31
19 323.4 41/34, 47/39
20 340.4
21 357.4 43/35
22 374.5 41/33
23 391.5
24 408.5
25 425.5 55/43
26 442.6
27 459.6 43/33
28 476.6
29 493.6
30 510.6 47/35, 51/38
31 527.7
32 544.7
33 561.7 47/34
34 578.7
35 595.7 55/39
36 612.8 47/33
37 629.8
38 646.8
39 663.8 22/15
40 680.9
41 697.9
42 714.9
43 731.9 29/19
44 748.9
45 766 14/9
46 783 11/7
47 800
48 817
49 834 34/21, 55/34
50 851.1
51 868.1 38/23
52 885.1 5/3
53 902.1
54 919.1
55 936.2
56 953.2 26/15
57 970.2
58 987.2 23/13
59 1004.3 25/14
60 1021.3
61 1038.3
62 1055.3 46/25
63 1072.3 13/7
64 1089.4
65 1106.4
66 1123.4
67 1140.4
68 1157.4 41/21
69 1174.5
70 1191.5
71 1208.5
72 1225.5
73 1242.6
74 1259.6
75 1276.6 23/11
76 1293.6
77 1310.6 49/23
78 1327.7
79 1344.7
80 1361.7
81 1378.7 51/23
82 1395.7 47/21
83 1412.8
84 1429.8
85 1446.8
86 1463.8
87 1480.9
88 1497.9
89 1514.9
90 1531.9
91 1548.9 22/9
92 1566
93 1583
94 1600
95 1617
96 1634
97 1651.1
98 1668.1 55/21
99 1685.1
100 1702.1
101 1719.1 27/10
102 1736.2
103 1753.2
104 1770.2 25/9
105 1787.2
106 1804.3
107 1821.3
108 1838.3
109 1855.3
110 1872.3
111 1889.4
112 1906.4
113 1923.4
114 1940.4 46/15
115 1957.4
116 1974.5
117 1991.5
118 2008.5
119 2025.5
120 2042.6
121 2059.6 23/7
122 2076.6
123 2093.6
124 2110.6
125 2127.7
126 2144.7 38/11
127 2161.7
128 2178.7
129 2195.7
130 2212.8
131 2229.8
132 2246.8
133 2263.8
134 2280.9
135 2297.9 49/13
136 2314.9
137 2331.9
138 2348.9
139 2366 51/13
140 2383
141 2400

Harmonics

Approximation of harmonics in 141ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +8.51 +4.43 +0.00 +5.18 -4.08 +1.39 +8.51 -8.17 -3.33 +1.87 +4.43
Relative (%) +50.0 +26.0 +0.0 +30.4 -24.0 +8.1 +50.0 -48.0 -19.6 +11.0 +26.0
Steps
(reduced)
71
(71)
112
(112)
141
(0)
164
(23)
182
(41)
198
(57)
212
(71)
223
(82)
234
(93)
244
(103)
253
(112)
Approximation of harmonics in 141ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +2.03 -7.12 -7.42 +0.00 -2.83 +0.35 -8.15 +5.18 +5.81 -6.64 +1.51
Relative (%) +11.9 -41.9 -43.6 +0.0 -16.6 +2.0 -47.9 +30.4 +34.2 -39.0 +8.9
Steps
(reduced)
261
(120)
268
(127)
275
(134)
282
(0)
288
(6)
294
(12)
299
(17)
305
(23)
310
(28)
314
(32)
319
(37)