80/63

Interval information

Ratio	80/63
Factorization	24 × 3-2 × 5 × 7-1
Monzo	[4 -2 1 -1⟩
Size in cents	413.5778¢
Names	hemifamity major third, 5/7-kleismic major third
Color name	ry3, ruyo 3rd
FJS name	[math]\displaystyle{ \text{M3}^{5}_{7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	12.2992
Weil height (log2 max(n, d))	12.6439
Wilson height (sopfr(nd))	26
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.25744 bits
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80/63, the hemifamity major third or the 5/7-kleismic major third, which is 5120/5103 (5.76 cents) sharp of 81/64 and 441/440 (3.9 cents) flat of 14/11 is the interval between 9/8 and 10/7, as well as 7/5 and 16/9. It is one of the ways approximate 11-limit harmony can appear in 7-limit scales.

Terminology

It could also be called werckismic major third if viewed as fudging from 14/11 instead. Wide major third, a less unique name, is attested in Scala.

See also

• Gallery of just intervals