17ed11/5
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Prime factorization
17 (prime)
Step size
80.2944¢
Octave
15\17ed11/5 (1204.42¢)
(semiconvergent)
Twelfth
24\17ed11/5 (1927.06¢)
Consistency limit
8
Distinct consistency limit
4
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← 16ed11/5 | 17ed11/5 | 18ed11/5 → |
(semiconvergent)
17 equal divisions of 11/5 (abbreviated 17ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 17 equal parts of about 80.3 ¢ each. Each step represents a frequency ratio of (11/5)1/17, or the 17th root of 11/5.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 80.294 | 21/20, 22/21, 23/22, 24/23 |
2 | 160.589 | 11/10, 12/11, 23/21 |
3 | 240.883 | 8/7, 23/20 |
4 | 321.177 | 6/5, 17/14 |
5 | 401.472 | 5/4, 14/11 |
6 | 481.766 | 4/3, 17/13, 21/16 |
7 | 562.061 | 11/8 |
8 | 642.355 | 16/11, 19/13, 23/16 |
9 | 722.649 | 23/15 |
10 | 802.944 | 8/5 |
11 | 883.238 | 5/3 |
12 | 963.532 | 7/4 |
13 | 1043.827 | 11/6, 20/11 |
14 | 1124.121 | 21/11, 23/12 |
15 | 1204.415 | 2/1 |
16 | 1284.71 | 21/10, 23/11 |
17 | 1365.004 | 11/5, 20/9, 24/11 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +4.4 | +25.1 | +8.8 | +24.0 | +29.5 | +3.5 | +13.2 | -30.1 | +28.4 | +24.0 | +33.9 |
Relative (%) | +5.5 | +31.3 | +11.0 | +29.9 | +36.8 | +4.4 | +16.5 | -37.5 | +35.4 | +29.9 | +42.3 | |
Steps (reduced) |
15 (15) |
24 (7) |
30 (13) |
35 (1) |
39 (5) |
42 (8) |
45 (11) |
47 (13) |
50 (16) |
52 (1) |
54 (3) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -24.3 | +8.0 | -31.2 | +17.7 | -7.0 | -25.7 | -39.0 | +32.8 | +28.6 | +28.4 | +31.7 |
Relative (%) | -30.3 | +9.9 | -38.9 | +22.0 | -8.7 | -32.0 | -48.5 | +40.9 | +35.7 | +35.4 | +39.5 | |
Steps (reduced) |
55 (4) |
57 (6) |
58 (7) |
60 (9) |
61 (10) |
62 (11) |
63 (12) |
65 (14) |
66 (15) |
67 (16) |
68 (0) |