33/32

Interval information

Ratio	33/32
Factorization	2-5 × 3 × 11
Monzo	[-5 1 0 0 1⟩
Size in cents	53.27294¢
Name	al-Farabi (Alpharabius) quarter-tone
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

The al-Farabi (Alpharabius) quarter-tone, 33/32, 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 11/8 super-fourth. Raising it instead by 36/35 leads to the septimal super-fourth (48/35) which approximates 11/8.

Arguably the al-Farabia quarter-tone 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 22-edo and 24-edo, if the comma 1089/1088 is tempered so that 33/32 and 34/33 are equated.

See also

• Gallery of just intervals
• 32/31