39ed11/5

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← 38ed11/539ed11/540ed11/5 →
Prime factorization 3 × 13
Step size 35.0001¢ 
Octave 34\39ed11/5 (1190¢)
Twelfth 54\39ed11/5 (1890.01¢) (→18\13ed11/5)
Consistency limit 3
Distinct consistency limit 3

39 equal divisions of 11/5 (abbreviated 39ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 39 equal parts of about 35 ¢ each. Each step represents a frequency ratio of (11/5)1/39, or the 39th root of 11/5.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 35
2 70 23/22, 28/27
3 105
4 140
5 175.001
6 210.001 9/8, 17/15, 26/23
7 245.001 15/13, 23/20
8 280.001 20/17
9 315.001
10 350.001
11 385.001
12 420.001
13 455.001 13/10
14 490.002
15 525.002 23/17
16 560.002
17 595.002
18 630.002
19 665.002 22/15
20 700.002 3/2
21 735.002 23/15, 26/17, 29/19
22 770.002 14/9
23 805.002
24 840.003
25 875.003
26 910.003 22/13, 27/16
27 945.003 19/11, 26/15
28 980.003
29 1015.003
30 1050.003
31 1085.003
32 1120.003
33 1155.004
34 1190.004
35 1225.004
36 1260.004
37 1295.004
38 1330.004
39 1365.004 11/5

Harmonics

Approximation of harmonics in 39ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -10.0 -11.9 +15.0 +13.7 +13.1 -8.8 +5.0 +11.1 +3.7 +13.7 +3.1
Relative (%) -28.6 -34.1 +42.9 +39.1 +37.3 -25.2 +14.3 +31.7 +10.6 +39.1 +8.7
Steps
(reduced)
34
(34)
54
(15)
69
(30)
80
(2)
89
(11)
96
(18)
103
(25)
109
(31)
114
(36)
119
(2)
123
(6)
Approximation of harmonics in 39ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +4.5 +16.2 +1.7 -5.0 -4.9 +1.1 +12.5 -6.3 +14.2 +3.7 -3.3
Relative (%) +12.8 +46.3 +5.0 -14.2 -14.1 +3.2 +35.7 -18.0 +40.7 +10.6 -9.3
Steps
(reduced)
127
(10)
131
(14)
134
(17)
137
(20)
140
(23)
143
(26)
146
(29)
148
(31)
151
(34)
153
(36)
155
(38)