50/33

Interval information

Ratio	50/33
Factorization	2 × 3-1 × 52 × 11-1
Monzo	[1 -1 2 0 -1⟩
Size in cents	719.3545¢
Names	ptolemismic fifth, 5edo-esque fifth
Color name	1uyy5, luyoyo 5th
FJS name	[math]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.09894 bits
[sound info]
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50/33, the ptolemismic fifth 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.

Approximation

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

See also

• 33/25 – its octave complement
• Gallery of just intervals