45/28
| Interval information |
marvel-ptolemaic minor sixth,
aberschismic augmented fifth
45/28, conventionally known as the septimal wide minor sixth or marvel-ptolemaic minor sixth, is an interval that is sharp of the Pythagorean minor sixth by 3645/3584, i.e. a syntonic comma plus a marvel comma. However, it functions more commonly as an augmented fifth, sharp of the Pythagorean augmented fifth by an aberschisma. This gives rise to the more precise name aberschismic augmented fifth, and in fact it arises as the result of stacking certain 9-odd-limit consonances – of 5/4 and 9/7, and of 9/8 and 10/7.
Temperaments
Marvel tempering equates this interval with the classical minor sixth and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into essentially tempered chords.
Approximation
This interval is only a third of a cent sharper than 13\19, the minor sixth of 19edo.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | -21.40 | -5.35 |
| 16 | 11\16 | 825.00 | +3.60 | +4.80 |
| 19 | 13\19 | 821.05 | -0.35 | -0.55 |
| 22 | 15\22 | 818.18 | -3.22 | -5.90 |
| 32 | 22\32 | 825.00 | +3.60 | +9.61 |
| 35 | 24\35 | 822.86 | +1.46 | +4.26 |
| 38 | 26\38 | 821.05 | -0.35 | -1.09 |
| 41 | 28\41 | 819.51 | -1.89 | -6.44 |
| 51 | 35\51 | 823.53 | +2.13 | +9.06 |
| 54 | 37\54 | 822.22 | +0.82 | +3.71 |
| 57 | 39\57 | 821.05 | -0.35 | -1.64 |
| 60 | 41\60 | 820.00 | -1.40 | -6.99 |
| 70 | 48\70 | 822.86 | +1.46 | +8.51 |
| 73 | 50\73 | 821.92 | +0.52 | +3.16 |
| 76 | 52\76 | 821.05 | -0.35 | -2.19 |
| 79 | 54\79 | 820.25 | -1.14 | -7.54 |