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Interval information
Ratio 80/63
Factorization 24 × 3-2 × 5 × 7-1
Monzo [4 -2 1 -1
Size in cents 413.57781¢
Names hemifamity major third,
5/7-kleismic major third
Color name ry3, ruyo 3rd
FJS name [math]\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]\sqrt{nd}[/math])
~4.25744 bits
open this interval in xen-calc

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.


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