39ed11/5
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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
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← 38ed11/5 | 39ed11/5 | 40ed11/5 → |
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
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) |
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) |