56/45
56/45, conventionally known as the septimal narrow major third or marvel-ptolemaic major third, is flat of the Pythagorean major third by 3645/3584, namely a syntonic comma plus a marvel comma. However, it functions more commonly as a diminished fourth, flat of the Pythagorean diminished fourth by an aberschisma. This gives rise to the more precise name aberschismic diminished fourth, and in fact it arises as the interval between various 9-odd-limit consonances – between 5/4 and 14/9, between 9/7 and 8/5, between 9/8 and 7/5, and between 10/7 and 16/9 – with it also being 6/5 away from the marvelous fifth, 112/75.
| Interval information |
marvel-ptolemaic major third,
aberschismic diminished fourth
[sound info]
According to Ozan Yarman, the perde segah of Turkish maqam music should range from 56/45 to 5/4.
Temperaments
Marvel tempering equates this interval with the classical major third and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into essentially tempered chords.
Approximation
This interval is a third of a cent flatter than 6\19, the major third of 19edo.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 1\3 | 400.00 | +21.40 | +5.35 |
| 16 | 5\16 | 375.00 | -3.60 | -4.80 |
| 19 | 6\19 | 378.95 | +0.35 | +0.55 |
| 22 | 7\22 | 381.82 | +3.22 | +5.90 |
| 32 | 10\32 | 375.00 | -3.60 | -9.61 |
| 35 | 11\35 | 377.14 | -1.46 | -4.26 |
| 38 | 12\38 | 378.95 | +0.35 | +1.09 |
| 41 | 13\41 | 380.49 | +1.89 | +6.44 |
| 51 | 16\51 | 376.47 | -2.13 | -9.06 |
| 54 | 17\54 | 377.78 | -0.82 | -3.71 |
| 57 | 18\57 | 378.95 | +0.35 | +1.64 |
| 60 | 19\60 | 380.00 | +1.40 | +6.99 |
| 70 | 22\70 | 377.14 | -1.46 | -8.51 |
| 73 | 23\73 | 378.08 | -0.52 | -3.16 |
| 76 | 24\76 | 378.95 | +0.35 | +2.19 |
| 79 | 25\79 | 379.75 | +1.14 | +7.54 |