96/77

Interval information

Ratio	96/77
Factorization	25 × 3 × 7-1 × 11-1
Monzo	[5 1 0 -1 -1⟩
Size in cents	381.8112¢
Name	keenanismic major third
Color name	1ur3, luru 3rd
FJS name	[math]\displaystyle{ \text{M3}_{7,11} }[/math]
Special properties	reduced
Tenney height (log2 nd)	12.8517
Weil height (log2 max(n, d))	13.1699
Wilson height (sopfr(nd))	31
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.03021 bits
[sound info]
Open this interval in xen-calc

96/77, the keenanismic major third, is likely to occur in JI scales in the 11-limit, as it is the difference between 7/6 and 16/11, or 11/8 and 12/7. It is flatter than 5/4 by 385/384, the keenanisma.

It is at Ozan Yarman's preferred size of about 382 cents for perde segah, and is almost exactly the size of the major third of 22edo, being 0.007 cents flat of 7\22. It could conceivably be used to tune 22edo by ear, as a cycle of 22 of these intervals fails to close by [-103 -22 0 22 22⟩, about a sixth of a cent, and 96/77 could be tuned by taking a 12/7 up and an 11/8 down.

See also

• 77/48 – its octave complement
• 77/64 – its fifth complement
• Gallery of just intervals