24ed5/4
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24 equal divisions of 5/4 (abbreviated 24ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 24 equal parts of about 16.1 ¢ each. Each step represents a frequency ratio of (5/4)1/24, or the 24th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 16.1 | |
| 2 | 32.2 | |
| 3 | 48.3 | |
| 4 | 64.4 | 23/22 |
| 5 | 80.5 | 26/25 |
| 6 | 96.6 | 18/17, 19/18, 20/19 |
| 7 | 112.7 | 15/14 |
| 8 | 128.8 | 13/12, 14/13 |
| 9 | 144.9 | 25/23 |
| 10 | 161 | 11/10, 12/11, 21/19, 23/21 |
| 11 | 177.1 | |
| 12 | 193.2 | 10/9, 19/17 |
| 13 | 209.3 | 25/22 |
| 14 | 225.3 | 17/15 |
| 15 | 241.4 | 15/13 |
| 16 | 257.5 | 7/6, 22/19 |
| 17 | 273.6 | |
| 18 | 289.7 | 13/11, 20/17 |
| 19 | 305.8 | 25/21 |
| 20 | 321.9 | 6/5, 23/19 |
| 21 | 338 | 17/14 |
| 22 | 354.1 | 11/9, 21/17 |
| 23 | 370.2 | |
| 24 | 386.3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.23 | -2.58 | -1.64 | -1.64 | +4.65 | -4.68 | +5.59 | -5.16 | +5.59 | +1.55 | -4.21 | +2.08 | +2.55 | -4.21 | -3.27 | +4.45 | +2.07 | +5.05 | -3.27 | -7.26 | -7.31 | -3.79 | +3.02 | -3.27 | -6.79 |
| Relative (%) | +44.9 | -16.0 | -10.2 | -10.2 | +28.9 | -29.1 | +34.8 | -32.0 | +34.8 | +9.7 | -26.2 | +12.9 | +15.9 | -26.2 | -20.3 | +27.6 | +12.9 | +31.4 | -20.3 | -45.1 | -45.4 | -23.5 | +18.7 | -20.3 | -42.2 | |
| Steps (reduced) |
75 (3) |
118 (22) |
149 (5) |
173 (5) |
193 (1) |
209 (17) |
224 (8) |
236 (20) |
248 (8) |
258 (18) |
267 (3) |
276 (12) |
284 (20) |
291 (3) |
298 (10) |
305 (17) |
311 (23) |
317 (5) |
322 (10) |
327 (15) |
332 (20) |
337 (1) |
342 (6) |
346 (10) |
350 (14) | |
| Harmonic | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.74 | -6.31 | -2.68 | +3.02 | -5.46 | +3.96 | -1.02 | -4.42 | -6.31 | -6.79 | -5.94 | -3.82 | -0.50 | +3.96 | -6.60 | -0.03 | +7.53 | -0.08 | -6.79 | +3.44 | -1.60 | -5.85 | +6.74 | +3.96 | +1.87 |
| Relative (%) | -48.1 | -39.2 | -16.6 | +18.7 | -33.9 | +24.6 | -6.4 | -27.4 | -39.2 | -42.2 | -36.9 | -23.7 | -3.1 | +24.6 | -41.0 | -0.2 | +46.8 | -0.5 | -42.2 | +21.4 | -9.9 | -36.3 | +41.9 | +24.6 | +11.6 | |
| Steps (reduced) |
354 (18) |
358 (22) |
362 (2) |
366 (6) |
369 (9) |
373 (13) |
376 (16) |
379 (19) |
382 (22) |
385 (1) |
388 (4) |
391 (7) |
394 (10) |
397 (13) |
399 (15) |
402 (18) |
405 (21) |
407 (23) |
409 (1) |
412 (4) |
414 (6) |
416 (8) |
419 (11) |
421 (13) |
423 (15) | |