56/45
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| Ratio | 56/45 |
| Factorization | 23 × 3-2 × 5-1 × 7 |
| Monzo | [3 -2 -1 1⟩ |
| Size in cents | 378.60219¢ |
| Names | septimal narrow major third, marvelous major third |
| Color name | zg4, zogu 4th |
| FJS name | [math]\text{d4}^{7}_{5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 11.2992 |
| Weil height (log2 max(n, d)) | 11.6147 |
| Wilson height (sopfr (nd)) | 24 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.47261 bits |
[sound info] | |
| open this interval in xen-calc | |
56/45, the septimal narrow major third, or marvelous major third, is the interval between various 9-limit consonances- 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being 6/5 away from the marvelous fifth, 112/75. Marvel tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into essentially tempered dyadic chords. It is a third of a cent flatter than the 6\19 major third of 19edo, however, it functionally doubles as a type of diminished fourth. According to Ozan Yarman, the perde segah of Turkish maqam music should range from 56/45.