29ed11/5

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← 28ed11/529ed11/530ed11/5 →
Prime factorization 29 (prime)
Step size 47.0691¢ 
Octave 25\29ed11/5 (1176.73¢)
Twelfth 40\29ed11/5 (1882.76¢)
Consistency limit 3
Distinct consistency limit 3

29 equal divisions of 11/5 (abbreviated 29ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 29 equal parts of about 47.1 ¢ each. Each step represents a frequency ratio of (11/5)1/29, or the 29th root of 11/5.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 47.069
2 94.138
3 141.207 25/23
4 188.276 10/9, 19/17
5 235.346
6 282.415 13/11
7 329.484 17/14, 23/19
8 376.553
9 423.622 14/11
10 470.691 17/13, 25/19
11 517.76 23/17, 27/20
12 564.829
13 611.898
14 658.968 19/13, 22/15, 25/17
15 706.037 3/2
16 753.106 17/11
17 800.175
18 847.244
19 894.313 5/3
20 941.382 19/11
21 988.451 23/13
22 1035.52
23 1082.59
24 1129.659 21/11, 25/13
25 1176.728
26 1223.797
27 1270.866 23/11
28 1317.935
29 1365.004 11/5

Harmonics

Approximation of harmonics in 29ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -23.3 -19.2 +0.5 -9.2 +4.6 +20.2 -22.7 +8.7 +14.6 -9.2 -18.7
Relative (%) -49.4 -40.8 +1.1 -19.6 +9.8 +42.8 -48.3 +18.5 +30.9 -19.6 -39.7
Steps
(reduced)
25
(25)
40
(11)
51
(22)
59
(1)
66
(8)
72
(14)
76
(18)
81
(23)
85
(27)
88
(1)
91
(4)
Approximation of harmonics in 29ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -16.0 -3.1 +18.6 +1.0 -9.8 -14.6 -14.0 -8.7 +1.0 +14.6 -15.3
Relative (%) -34.1 -6.6 +39.6 +2.2 -20.8 -31.0 -29.8 -18.5 +2.0 +30.9 -32.6
Steps
(reduced)
94
(7)
97
(10)
100
(13)
102
(15)
104
(17)
106
(19)
108
(21)
110
(23)
112
(25)
114
(27)
115
(28)