25edf
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Prime factorization
52
Step size
28.0782 ¢
Octave
43\25edf (1207.36 ¢)
Twelfth
68\25edf (1909.32 ¢)
Consistency limit
2
Distinct consistency limit
2
| ← 24edf | 25edf | 26edf → |
25 equal divisions of the perfect fifth (abbreviated 25edf or 25ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 25 equal parts of about 28.1 ¢ each. Each step represents a frequency ratio of (3/2)1/25, or the 25th root of 3/2. It corresponds to 42.7378 edo (similar to every fourth step of 171edo).
It is related to the regular temperament which tempers out 703125/702464 and 5250987/5242880 in the 7-limit, which is supported by 43edo, 128edo, 171edo, 214edo, 299edo, and 385edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.4 | +7.4 | -6.6 | +0.6 | +4.3 | -4.2 | +8.7 | +12.7 | -9.2 | +10.7 | +7.5 |
| Relative (%) | +26.2 | +26.2 | -23.4 | +2.0 | +15.2 | -14.9 | +31.1 | +45.3 | -32.7 | +38.1 | +26.9 | |
| Steps (reduced) |
43 (18) |
68 (18) |
99 (24) |
120 (20) |
148 (23) |
158 (8) |
175 (0) |
182 (7) |
193 (18) |
208 (8) |
212 (12) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.1 | +0.8 | +2.6 | -11.0 | +5.7 | -11.5 | -13.1 | -7.1 | +4.9 | +12.9 | -11.5 |
| Relative (%) | +36.0 | +3.0 | +9.3 | -39.1 | +20.1 | -41.1 | -46.7 | -25.1 | +17.3 | +46.1 | -41.0 | |
| Steps (reduced) |
223 (23) |
229 (4) |
232 (7) |
237 (12) |
245 (20) |
251 (1) |
253 (3) |
259 (9) |
263 (13) |
265 (15) |
269 (19) | |
Intervals
| Degree | Cents | Corresponding JI intervals |
Comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 28.0782 | 51/50 | |
| 2 | 56.1564 | 26/25 | |
| 3 | 84.2346 | 21/20 | |
| 4 | 112.3128 | 16/15 | |
| 5 | 140.391 | 13/12 | |
| 6 | 168.4692 | ||
| 7 | 196.5474 | 28/25 | |
| 8 | 224.6256 | 8/7 | |
| 9 | 252.7038 | ||
| 10 | 280.782 | 20/17 | |
| 11 | 308.8602 | pseudo-6/5 | |
| 12 | 336.9384 | ||
| 13 | 365.0166 | ||
| 14 | 393.0948 | pseudo-5/4 | |
| 15 | 421.173 | 51/40 | |
| 16 | 449.2512 | ||
| 17 | 477.3294 | ||
| 18 | 505.4076 | 75/56 | pseudo-4/3 |
| 19 | 533.4858 | ||
| 20 | 561.564 | ||
| 21 | 589.6422 | 45/32 | |
| 22 | 617.7204 | 10/7 | |
| 23 | 645.7986 | ||
| 24 | 673.8768 | ||
| 25 | 701.955 | exact 3/2 | just perfect fifth |
| 26 | 730.033 | 153/100 | |
| 27 | 757.1114 | 39/25 | |
| 28 | 786.1896 | 63/40 | |
| 29 | 814.2678 | 8/5 | |
| 30 | 842.346 | 13/8 | |
| 31 | 870.2452 | ||
| 32 | 898.5024 | 42/25 | |
| 33 | 926.5806 | 12/7 | |
| 34 | 954.6588 | ||
| 35 | 982.737 | 30/17 | |
| 36 | 1010.8152 | pseudo-9/5 | |
| 37 | 1038.8934 | ||
| 38 | 1066.9716 | ||
| 39 | 1095.0498 | pseudo-15/8 | |
| 40 | 1123.128 | 153/80 | |
| 41 | 1151.2062 | ||
| 42 | 1179.2844 | ||
| 43 | 1207.3526 | 225/112 | pseudo-2/1 |
| 44 | 1235.4408 | ||
| 45 | 1263.519 | ||
| 46 | 1291.5972 | 135/64 | |
| 47 | 1319.6754 | 15/7 | |
| 48 | 1347.7536 | ||
| 49 | 1375.8318 | ||
| 50 | 1403.91 | exact 9/4 | |