User:MisterShafXen/47edf: Difference between revisions
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Prime factorization
47 (prime)
Step size
14.9352 ¢
Octave
80\47edf (1194.82 ¢)
Twelfth
127\47edf (1896.77 ¢)
Consistency limit
3
Distinct consistency limit
3
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Latest revision as of 14:43, 1 August 2025
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47 equal divisions of the perfect fifth (abbreviated 47edf or 47ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 47 equal parts of about 14.9 ¢ each. Each step represents a frequency ratio of (3/2)1/47, or the 47th root of 3/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 14.9 | |
| 2 | 29.9 | |
| 3 | 44.8 | |
| 4 | 59.7 | 27/26, 29/28, 30/29, 31/30 |
| 5 | 74.7 | 22/21, 23/22 |
| 6 | 89.6 | 20/19, 21/20 |
| 7 | 104.5 | |
| 8 | 119.5 | 15/14, 31/29 |
| 9 | 134.4 | |
| 10 | 149.4 | |
| 11 | 164.3 | 11/10 |
| 12 | 179.2 | 21/19, 31/28 |
| 13 | 194.2 | 19/17, 29/26 |
| 14 | 209.1 | 9/8, 26/23 |
| 15 | 224 | |
| 16 | 239 | 23/20 |
| 17 | 253.9 | 22/19 |
| 18 | 268.8 | |
| 19 | 283.8 | 13/11, 20/17 |
| 20 | 298.7 | |
| 21 | 313.6 | |
| 22 | 328.6 | 23/19 |
| 23 | 343.5 | 28/23 |
| 24 | 358.4 | |
| 25 | 373.4 | |
| 26 | 388.3 | |
| 27 | 403.3 | 19/15, 29/23 |
| 28 | 418.2 | 14/11 |
| 29 | 433.1 | |
| 30 | 448.1 | 22/17 |
| 31 | 463 | 17/13, 30/23 |
| 32 | 477.9 | 29/22 |
| 33 | 492.9 | 4/3 |
| 34 | 507.8 | |
| 35 | 522.7 | 19/14, 23/17, 31/23 |
| 36 | 537.7 | 15/11, 26/19 |
| 37 | 552.6 | |
| 38 | 567.5 | |
| 39 | 582.5 | 7/5 |
| 40 | 597.4 | 31/22 |
| 41 | 612.3 | 10/7 |
| 42 | 627.3 | |
| 43 | 642.2 | 13/9, 29/20 |
| 44 | 657.1 | 19/13, 22/15 |
| 45 | 672.1 | 28/19, 31/21 |
| 46 | 687 | |
| 47 | 702 | 3/2 |