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Interval information
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