33/32
| Interval information |
undecimal quarter tone
al-Farabi (Alpharabius) quarter tone
reduced,
reduced harmonic
[sound info]
33/32, the undecimal comma, undecimal quarter tone, or al-Farabi (Alpharabius) quarter tone, 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.