101ed4

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← 99ed4 101ed4 103ed4 →
Prime factorization 101 (prime)
Step size 23.7624¢ 
Octave 51\101ed4 (1211.88¢)
Twelfth 80\101ed4 (1900.99¢)
Consistency limit 1
Distinct consistency limit 1

101 equal divisions of the 4th harmonic (abbreviated 101ed4) is a nonoctave tuning system that divides the interval of 4/1 into 101 equal parts of about 23.8 ¢ each. Each step represents a frequency ratio of 41/101, or the 101st root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 23.8
2 47.5
3 71.3
4 95 19/18, 37/35
5 118.8
6 142.6 25/23
7 166.3 11/10
8 190.1
9 213.9
10 237.6 31/27, 39/34
11 261.4 43/37
12 285.1
13 308.9
14 332.7
15 356.4 43/35
16 380.2
17 404
18 427.7
19 451.5 35/27
20 475.2
21 499
22 522.8 23/17
23 546.5 37/27
24 570.3
25 594.1
26 617.8 10/7
27 641.6
28 665.3 25/17
29 689.1
30 712.9
31 736.6
32 760.4 45/29
33 784.2 11/7
34 807.9 43/27
35 831.7 21/13
36 855.4
37 879.2
38 903
39 926.7 29/17
40 950.5
41 974.3
42 998
43 1021.8
44 1045.5
45 1069.3 13/7
46 1093.1
47 1116.8
48 1140.6 29/15
49 1164.4 45/23
50 1188.1
51 1211.9
52 1235.6
53 1259.4
54 1283.2 21/10
55 1306.9
56 1330.7 41/19
57 1354.5
58 1378.2
59 1402
60 1425.7 41/18
61 1449.5 30/13
62 1473.3
63 1497
64 1520.8
65 1544.6
66 1568.3
67 1592.1
68 1615.8
69 1639.6
70 1663.4 34/13
71 1687.1 45/17
72 1710.9
73 1734.7 30/11
74 1758.4
75 1782.2
76 1805.9
77 1829.7
78 1853.5
79 1877.2
80 1901 3/1
81 1924.8
82 1948.5
83 1972.3
84 1996 19/6
85 2019.8
86 2043.6
87 2067.3 33/10
88 2091.1
89 2114.9
90 2138.6
91 2162.4
92 2186.1
93 2209.9
94 2233.7
95 2257.4
96 2281.2
97 2305
98 2328.7
99 2352.5 35/9
100 2376.2
101 2400

Harmonics

Approximation of harmonics in 101ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +11.9 -1.0 +0.0 -6.1 +10.9 +5.4 +11.9 -1.9 +5.8 +7.1 -1.0
Relative (%) +50.0 -4.1 +0.0 -25.7 +45.9 +22.9 +50.0 -8.1 +24.3 +29.9 -4.1
Steps
(reduced)
51
(51)
80
(80)
101
(0)
117
(16)
131
(30)
142
(41)
152
(51)
160
(59)
168
(67)
175
(74)
181
(80)
Approximation of harmonics in 101ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +3.0 -6.4 -7.1 +0.0 -9.9 +10.0 +11.4 -6.1 +4.5 -4.8 -10.5
Relative (%) +12.8 -27.1 -29.8 +0.0 -41.7 +41.9 +48.0 -25.7 +18.8 -20.1 -44.0
Steps
(reduced)
187
(86)
192
(91)
197
(96)
202
(0)
206
(4)
211
(9)
215
(13)
218
(16)
222
(20)
225
(23)
228
(26)