256ed5
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Prime factorization
28
Step size
10.884¢
Octave
110\256ed5 (1197.24¢) (→55\128ed5)
Twelfth
175\256ed5 (1904.71¢)
Consistency limit
2
Distinct consistency limit
2
| ← 255ed5 | 256ed5 | 257ed5 → |
256 equal divisions of the 5th harmonic is an equal-step tuning where each step represents a frequency ratio of 256th root of 5, which amounts to 3.90625 millipentaves or about 10.884 cents. It is equivalent to 110.2532 EDO.
256ed5 combines dual-fifth systems with quarter-comma meantone.
Theory
In 256ed5, the just perfect fifth of 3/2, corresponds to approximately 64.5 steps, thus occurring almost halfway between the quarter-comma meantone fifth and it's next step.
Uniquely, 6/5 is nearly perfect.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.76 | +2.75 | +5.37 | +0.00 | -0.00 | +5.23 | +2.62 | -5.38 | -2.76 | -4.50 | -2.76 |
| Relative (%) | -25.3 | +25.3 | +49.4 | +0.0 | -0.0 | +48.0 | +24.0 | -49.4 | -25.3 | -41.3 | -25.4 | |
| Steps (reduced) |
110 (110) |
175 (175) |
221 (221) |
256 (0) |
285 (29) |
310 (54) |
331 (75) |
349 (93) |
366 (110) |
381 (125) |
395 (139) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.16 | +2.47 | +2.75 | -0.14 | +3.75 | +2.75 | -3.78 | +5.37 | -2.91 | +3.63 | +2.86 |
| Relative (%) | +1.5 | +22.7 | +25.3 | -1.3 | +34.4 | +25.2 | -34.8 | +49.4 | -26.7 | +33.3 | +26.3 | |
| Steps (reduced) |
408 (152) |
420 (164) |
431 (175) |
441 (185) |
451 (195) |
460 (204) |
468 (212) |
477 (221) |
484 (228) |
492 (236) |
499 (243) | |
Table of intervals
| Step | Name | Size (cents) | Size (millipentaves) | Associated ratio |
|---|---|---|---|---|
| 0 | prime, unison | 0 | 0 | exact 1/1 |
| 29 | classical minor third | 315.63710 | 113.28125 | 6/5 |
| 64 | minor fifth | 696.57843 | 250 | 3/2 I, exact 4th root of(5) |
| 65 | major fifth | 253.90625 | ||
| 128 | octitone, symmetric ninth | 1393.15686 | 500 | |
| 256 | pentave, fifth harmonic | 2786.31371 | 1000 | exact 5/1 |