75/56
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| Ratio | 75/56 |
| Factorization | 2-3 × 3 × 52 × 7-1 |
| Monzo | [-3 1 2 -1⟩ |
| Size in cents | 505.75652¢ |
| Name | marvelous fourth |
| Color name | ryy3, ruyoyo 3rd |
| FJS name | [math]\text{A3}^{5,5}_{7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 12.0362 |
| Weil height (log2 max(n, d)) | 12.4576 |
| Wilson height (sopfr (nd)) | 26 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~3.92947 bits |
[sound info] | |
| open this interval in xen-calc | |
75/56, the marvelous fourth (505.8 ¢), is 225/224 (7.7 ¢) sharp of the just fourth 4/3. It often arises in just intonation scales. Tempering out 225/224 from the scale can be used to make it much less sharp, but it is usable as it is, being only half a cent sharp of the 19edo fourth of 8\19. Considered as a meantone fourth, it is approximately 5/14-comma meantone.
See also
- File:jid_75_56_pluck_adu_dr220.mp3 – another sound example
- 112/75 - its octave complement
- Gallery of just intervals