80/63
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Ratio | 80/63 |
Factorization | 2^{4} × 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 (log_{2} nd) | 12.2992 |
Weil height (log_{2} 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.
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.