From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 50/33
Factorization 2 × 3-1 × 52 × 11-1
Monzo [1 -1 2 0 -1
Size in cents 719.35448¢
Names ptolemismic fifth,
undecimal imperfect fifth,
5edo-esque fifth
Color name 1uyy5, luyoyo 5th
FJS name [math]\text{A5}^{5,5}_{11}[/math]
Special properties reduced
Tenney height (log2 nd) 10.6883
Weil height (log2 max(n, d)) 11.2877
Wilson height (sopfr (nd)) 26
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.36129 bits

[sound info]
open this interval in xen-calc

50/33, the ptolemismic fifth, the undecimal superfifth or the 5edo-esque fifth, is an 11-limit interval. It is sharp of 3/2, the perfect fifth, by 100/99, the ptolemisma, hence the name. It is also flat of 32/21, the superfifth, by 176/175, the valinorsma. Being 16/11 augmented by 25/24, it is technically a semiaugmented fifth aka paramajor fifth.


Measuring about 719.4 ¢, 50/33 is very well approximated by 5edo and its supersets.

See also