33/25

Interval information

Ratio	33/25
Factorization	3 × 5-2 × 11
Monzo	[0 1 -2 0 1⟩
Size in cents	480.6455¢
Names	ptolemismic fourth, 5edo-esque fourth
Color name	1ogg4, logugu 4th
FJS name	[math]\displaystyle{ \text{d4}^{11}_{5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	9.68825
Weil height (log2 max(n, d))	10.0888
Wilson height (sopfr(nd))	24
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.16894 bits
[sound info]
Open this interval in xen-calc

33/25, the ptolemismic fourth or the 5edo-esque fourth, is an 11-limit interval. It is flat of 4/3, the perfect fourth, by 100/99, the ptolemisma, hence the name. It is also sharp of 21/16, the subfourth, by 176/175, the valinorsma. Being 11/8 diminished by 25/24, it is technically a semidiminished fourth aka paraminor fourth.

Approximation

Measuring about 480.6 ¢, 33/25 is very well approximated by 5edo and its supersets.

See also

• 50/33 – its octave complement
• 25/22 – its fifth complement
• Gallery of just intervals
• File:Ji-33-25-csound-foscil-220hz.mp3 – another sound example