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33/32 |-5 1 0 0 1>

53.2729 cents

sound sample

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 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 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.