75/56
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Ratio | 75/56 |
Factorization | 2^{-3} × 3 × 5^{2} × 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 (log_{2} nd) | 12.0362 |
Weil height (log_{2} 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