80/63
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| 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{n\cdot d}[/math]) |
~4.56808 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.