96/77
Jump to navigation
Jump to search
Ratio | 96/77 |
Factorization | 2^{5} × 3 × 7^{-1} × 11^{-1} |
Monzo | [5 1 0 -1 -1⟩ |
Size in cents | 381.81115¢ |
Name | keenanismic major third |
Color name | 1ur3, luru 3rd |
FJS name | [math]\text{M3}_{7,11}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 12.8517 |
Weil height (log_{2} max(n, d)) | 13.1699 |
Wilson height (sopfr (nd)) | 31 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.46012 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 interval between 7/6 and 16/11 and 11/8 and 12/7.
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.