17edf
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Prime factorization
17 (prime)
Step size
41.2915¢
Octave
29\17edf (1197.45¢)
(semiconvergent)
Twelfth
46\17edf (1899.41¢)
(semiconvergent)
Consistency limit
6
Distinct consistency limit
6
| ← 16edf | 17edf | 18edf → |
(semiconvergent)
(semiconvergent)
17EDF is the Division of the just perfect fifth into 17 equal parts. It is related to 29 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 41.2915 cents. Unlike 29edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.
Intervals
| Degree | Cents | Approx. ratios of the 15-odd-limit |
|---|---|---|
| 0 | 0.0000 | 1/1 |
| 1 | 41.2915 | 25/24~33/32~56/55~81/80 |
| 2 | 82.5829 | 21/20 |
| 3 | 123.8744 | 16/15, 15/14, 14/13, 13/12 |
| 4 | 165.1659 | 12/11, 11/10 |
| 5 | 206.4574 | 9/8 |
| 6 | 248.7488 | 8/7, 7/6, 15/13 |
| 7· | 289.0403 | 13/11 |
| 8 | 330.3318 | 6/5, 11/9 |
| 9 | 371.6232 | 5/4, 16/13 |
| 10 | 412.9147 | 14/11 |
| 11 | 455.2062 | 9/7, 13/10 |
| 12· | 495.4976 | 4/3 |
| 13 | 536.7891 | 11/8, 15/11 |
| 14 | 578.0806 | 7/5, 18/13 |
| 15 | 619.3721 | 10/7, 13/9 |
| 16 | 660.6635 | 16/11, 22/15 |
| 17· | 701.9550 | 3/2 |
| 18 | 743.2465 | 14/9, 20/13 |
| 19 | 784.5379 | 11/7 |
| 20 | 825.8294 | 8/5, 13/8 |
| 21 | 867.1209 | 5/3, 18/11 |
| 22· | 908.4124 | 22/13 |
| 23 | 949.7038 | 7/4, 12/7, 26/15 |
| 24 | 990.9952 | 16/9 |
| 25 | 1032.3287 | 11/6, 20/11 |
| 26 | 1073.5782 | 15/8, 28/15, 13/7, 24/13 |
| 27 | 1114.8697 | 40/21 |
| 28 | 1156.1612 | 48/25~64/33~55/28 ~160/81 |
| 29 | 1197.4526 | 2/1 |
| 30 | 1238.7441 | 25/12~33/16~112/55~81/40 |
| 31 | 1280.0356 | 21/10 |
| 32 | 1321.3271 | 32/15, 15/7, 28/13, 13/6 |
| 33 | 1362.6185 | 24/11, 11/5 |
| 34 | 1403.9100 | 9/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.5 | -2.5 | -5.1 | -19.8 | -5.1 | +17.1 | -7.6 | -5.1 | +19.0 | +19.1 | -7.6 |
| Relative (%) | -6.2 | -6.2 | -12.3 | -47.9 | -12.3 | +41.4 | -18.5 | -12.3 | +45.9 | +46.3 | -18.5 | |
| Steps (reduced) |
29 (12) |
46 (12) |
58 (7) |
67 (16) |
75 (7) |
82 (14) |
87 (2) |
92 (7) |
97 (12) |
101 (16) |
104 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.0 | +14.5 | +19.0 | -10.2 | +8.7 | -7.6 | -18.7 | +16.4 | +14.5 | +16.6 | -19.1 |
| Relative (%) | +45.9 | +35.2 | +45.9 | -24.7 | +21.1 | -18.5 | -45.2 | +39.7 | +35.2 | +40.1 | -46.2 | |
| Steps (reduced) |
108 (6) |
111 (9) |
114 (12) |
116 (14) |
119 (0) |
121 (2) |
123 (4) |
126 (7) |
128 (9) |
130 (11) |
131 (12) | |