75/56

Interval information

Ratio	75/56
Factorization	2-3 × 3 × 52 × 7-1
Monzo	[-3 1 2 -1⟩
Size in cents	505.7565¢
Name	marvelous fourth
Color name	ryy3, ruyoyo 3rd
FJS name	[math]\displaystyle{ \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]\displaystyle{ \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