33/32

Interval information

Ratio	33/32
Factorization	2-5 × 3 × 11
Monzo	[-5 1 0 0 1⟩
Size in cents	53.27294¢
Names	al-Farabi quarter tone, undecimal quarter tone, undecimal comma
FJS name	[math]\displaystyle{ \text{P1}^{11} }[/math]
Special properties	superparticular, reduced, reduced harmonic
Tenney height (log2 nd)	10.0444
Weil height (log2 max(n, d))	10.0888
Wilson height (sopfr(nd))	24
[sound info]
Open this interval in xen-calc

33/32, the al-Farabi quarter tone, undecimal quarter tone, or undecimal comma, is a superparticular ratio which differs by a keenanisma (385/384), from the septimal quarter tone (36/35). Raising a just perfect fourth (4/3) by the al-Farabi quarter-tone leads to the undecimal super-fourth (11/8). Raising it instead by 36/35 leads to the septimal super-fourth (48/35) which approximates 11/8.

Arguably 33/32 could have been used as a melodic interval in the Greek Enharmonic Genus. The resulting tetrachord would include 32:33:34 within the interval of a perfect fourth. This ancient Greek scale can be approximated in 22edo and 24edo, if the comma 1089/1088 is tempered so that 33/32 and 34/33 are equated.

33/32 is significant in Functional Just System as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. Apart from the aforementioned relationship between 4/3 and 11/8, it is also the interval between 32/27 and 11/9, and between 9/8 and 12/11.

See also

• 64/33 – its octave complement
• Gallery of just intervals
• 32/31
• File:Ji-33-32-csound-foscil-220hz.mp3