44ed11/5
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Prime factorization
22 × 11
Step size
31.0228¢
Octave
39\44ed11/5 (1209.89¢)
Twelfth
61\44ed11/5 (1892.39¢)
Consistency limit
2
Distinct consistency limit
2
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44 equal divisions of 11/5 (abbreviated 44ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 44 equal parts of about 31 ¢ each. Each step represents a frequency ratio of (11/5)1/44, or the 44th root of 11/5.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 31.023 | |
2 | 62.046 | 26/25, 30/29, 31/30 |
3 | 93.068 | 18/17, 19/18 |
4 | 124.091 | |
5 | 155.114 | 12/11, 23/21 |
6 | 186.137 | 19/17, 29/26 |
7 | 217.16 | 17/15, 25/22, 26/23 |
8 | 248.183 | 15/13 |
9 | 279.205 | |
10 | 310.228 | 6/5, 31/26 |
11 | 341.251 | |
12 | 372.274 | 21/17, 26/21, 31/25 |
13 | 403.297 | 19/15, 29/23 |
14 | 434.32 | |
15 | 465.342 | 17/13, 30/23 |
16 | 496.365 | |
17 | 527.388 | 23/17 |
18 | 558.411 | 18/13, 29/21 |
19 | 589.434 | 31/22 |
20 | 620.456 | 10/7 |
21 | 651.479 | 19/13 |
22 | 682.502 | |
23 | 713.525 | |
24 | 744.548 | 23/15 |
25 | 775.571 | |
26 | 806.593 | |
27 | 837.616 | |
28 | 868.639 | |
29 | 899.662 | |
30 | 930.685 | 12/7, 29/17 |
31 | 961.708 | |
32 | 992.73 | 23/13 |
33 | 1023.753 | |
34 | 1054.776 | 11/6 |
35 | 1085.799 | |
36 | 1116.822 | 21/11 |
37 | 1147.844 | |
38 | 1178.867 | |
39 | 1209.89 | |
40 | 1240.913 | |
41 | 1271.936 | 23/11, 25/12 |
42 | 1302.959 | |
43 | 1333.981 | 13/6 |
44 | 1365.004 | 11/5 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +9.9 | -9.6 | -11.2 | +5.7 | +0.3 | +12.7 | -1.4 | +11.9 | -15.4 | +5.7 | +10.2 |
Relative (%) | +31.9 | -30.8 | -36.2 | +18.5 | +1.1 | +40.8 | -4.4 | +38.4 | -49.6 | +18.5 | +32.9 | |
Steps (reduced) |
39 (39) |
61 (17) |
77 (33) |
90 (2) |
100 (12) |
109 (21) |
116 (28) |
123 (35) |
128 (40) |
134 (2) |
139 (7) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -4.3 | -8.5 | -3.8 | +8.5 | -3.3 | -9.2 | -9.8 | -5.5 | +3.1 | -15.4 | +0.7 |
Relative (%) | -13.7 | -27.3 | -12.3 | +27.5 | -10.8 | -29.8 | -31.5 | -17.7 | +10.0 | -49.6 | +2.3 | |
Steps (reduced) |
143 (11) |
147 (15) |
151 (19) |
155 (23) |
158 (26) |
161 (29) |
164 (32) |
167 (35) |
170 (38) |
172 (40) |
175 (43) |