69ed4

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← 67ed4 69ed4 71ed4 →
Prime factorization 3 × 23
Step size 34.7826¢ 
Octave 35\69ed4 (1217.39¢)
Twelfth 55\69ed4 (1913.04¢)
Consistency limit 1
Distinct consistency limit 1

69 equal divisions of the 4th harmonic (abbreviated 69ed4) is a nonoctave tuning system that divides the interval of 4/1 into 69 equal parts of about 34.8 ¢ each. Each step represents a frequency ratio of 41/69, or the 69th root of 4.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 34.8
2 69.6
3 104.3 35/33
4 139.1
5 173.9 21/19
6 208.7 35/31
7 243.5
8 278.3 34/29
9 313
10 347.8
11 382.6
12 417.4
13 452.2 13/10
14 487
15 521.7 23/17, 27/20
16 556.5 29/21
17 591.3 31/22
18 626.1 33/23
19 660.9 22/15
20 695.7
21 730.4 29/19, 35/23
22 765.2 14/9
23 800 35/22
24 834.8 34/21
25 869.6
26 904.3
27 939.1
28 973.9
29 1008.7 34/19
30 1043.5 31/17
31 1078.3
32 1113 19/10
33 1147.8 33/17
34 1182.6
35 1217.4
36 1252.2 35/17
37 1287 21/10
38 1321.7 15/7
39 1356.5
40 1391.3 29/13
41 1426.1
42 1460.9
43 1495.7
44 1530.4
45 1565.2 37/15
46 1600
47 1634.8
48 1669.6
49 1704.3
50 1739.1
51 1773.9
52 1808.7 37/13
53 1843.5 29/10
54 1878.3
55 1913
56 1947.8
57 1982.6 22/7
58 2017.4
59 2052.2
60 2087 10/3
61 2121.7 17/5
62 2156.5
63 2191.3
64 2226.1
65 2260.9
66 2295.7
67 2330.4
68 2365.2
69 2400

Harmonics

Approximation of harmonics in 69ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +17.4 +11.1 +0.0 -3.7 -6.3 +5.1 +17.4 -12.6 +13.7 -12.2 +11.1
Relative (%) +50.0 +31.9 +0.0 -10.7 -18.1 +14.6 +50.0 -36.2 +39.3 -35.0 +31.9
Steps
(reduced)
35
(35)
55
(55)
69
(0)
80
(11)
89
(20)
97
(28)
104
(35)
109
(40)
115
(46)
119
(50)
124
(55)
Approximation of harmonics in 69ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +11.6 -12.3 +7.4 +0.0 -0.6 +4.8 +15.5 -3.7 +16.2 +5.2 -2.2
Relative (%) +33.5 -35.4 +21.2 +0.0 -1.7 +13.8 +44.7 -10.7 +46.5 +15.0 -6.3
Steps
(reduced)
128
(59)
131
(62)
135
(66)
138
(0)
141
(3)
144
(6)
147
(9)
149
(11)
152
(14)
154
(16)
156
(18)