112/75

Interval information

Ratio	112/75
Factorization	24 × 3-1 × 5-2 × 7
Monzo	[4 -1 -2 1⟩
Size in cents	694.2435¢
Name	marvelous fifth
Color name	zgg6, zogugu 6th
FJS name	[math]\text{d6}^{7}_{5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	13.0362
Weil height (log2 max(n, d))	13.6147
Wilson height (sopfr(nd))	28
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~3.6276 bits
[sound info]
open this interval in xen-calc

112/75, the marvelous fifth (694.2¢), is 225/224 (7.7¢) below the just fifth 3/2. It often arises in just intonation scales, for instance as the interval from 15/14 to 8/5, or 5/7 to 16/15. Tempering out 225/224 from the scale can be used to make it much less flat, but it is usable as it is, being only half a cent flat from the 19edo fifth of 11\19. Considered as a meantone fifth, it is approximately 5/14-comma meantone.

See also

• File:jid_112_75_pluck_adu_dr220.mp3 – another sound example
• 75/56 - its octave complement
• Gallery of just intervals