109ed4

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← 107ed4 109ed4 111ed4 →
Prime factorization 109 (prime)
Step size 22.0183¢ 
Octave 55\109ed4 (1211.01¢)
Twelfth 86\109ed4 (1893.58¢)
Consistency limit 1
Distinct consistency limit 1

109 equal divisions of the 4th harmonic (abbreviated 109ed4) is a nonoctave tuning system that divides the interval of 4/1 into 109 equal parts of about 22 ¢ each. Each step represents a frequency ratio of 41/109, or the 109th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 22
2 44
3 66.1 26/25
4 88.1 41/39
5 110.1 33/31
6 132.1
7 154.1 47/43
8 176.1 41/37
9 198.2 28/25, 37/33
10 220.2 25/22, 42/37
11 242.2
12 264.2
13 286.2
14 308.3 37/31, 43/36
15 330.3 23/19
16 352.3
17 374.3 36/29, 41/33
18 396.3 39/31
19 418.3 14/11
20 440.4
21 462.4 17/13, 47/36
22 484.4 41/31
23 506.4
24 528.4 19/14
25 550.5
26 572.5
27 594.5
28 616.5
29 638.5
30 660.6
31 682.6 43/29
32 704.6
33 726.6 35/23, 38/25
34 748.6
35 770.6
36 792.7 30/19
37 814.7
38 836.7 47/29
39 858.7 23/14
40 880.7
41 902.8
42 924.8 29/17
43 946.8 19/11
44 968.8
45 990.8
46 1012.8
47 1034.9
48 1056.9 35/19, 46/25
49 1078.9
50 1100.9
51 1122.9
52 1145
53 1167
54 1189
55 1211
56 1233
57 1255 31/15
58 1277.1 23/11
59 1299.1 36/17
60 1321.1 15/7
61 1343.1
62 1365.1 11/5
63 1387.2 29/13
64 1409.2
65 1431.2
66 1453.2
67 1475.2
68 1497.2
69 1519.3
70 1541.3
71 1563.3 37/15
72 1585.3 5/2
73 1607.3 43/17
74 1629.4
75 1651.4
76 1673.4
77 1695.4
78 1717.4
79 1739.4 41/15
80 1761.5 36/13, 47/17
81 1783.5 14/5
82 1805.5
83 1827.5
84 1849.5
85 1871.6
86 1893.6
87 1915.6
88 1937.6
89 1959.6
90 1981.7
91 2003.7 35/11
92 2025.7
93 2047.7
94 2069.7 43/13
95 2091.7
96 2113.8
97 2135.8
98 2157.8
99 2179.8
100 2201.8
101 2223.9 47/13
102 2245.9
103 2267.9
104 2289.9
105 2311.9 19/5
106 2333.9
107 2356
108 2378
109 2400

Harmonics

Approximation of harmonics in 109ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +11.01 -8.38 +0.00 +10.02 +2.63 -0.02 +11.01 +5.26 -0.99 +10.15 -8.38
Relative (%) +50.0 -38.0 +0.0 +45.5 +12.0 -0.1 +50.0 +23.9 -4.5 +46.1 -38.0
Steps
(reduced)
55
(55)
86
(86)
109
(0)
127
(18)
141
(32)
153
(44)
164
(55)
173
(64)
181
(72)
189
(80)
195
(86)
Approximation of harmonics in 109ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +7.18 +10.99 +1.64 +0.00 +5.14 -5.74 +10.74 +10.02 -8.40 -0.86 +10.26
Relative (%) +32.6 +49.9 +7.4 +0.0 +23.3 -26.1 +48.8 +45.5 -38.1 -3.9 +46.6
Steps
(reduced)
202
(93)
208
(99)
213
(104)
218
(0)
223
(5)
227
(9)
232
(14)
236
(18)
239
(21)
243
(25)
247
(29)