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The 5-limit just diatonic semitone is the superparticular interval 16/15 -- the difference between the major third 5/4 and the fourth 4/3, and between 3/2 and 8/5.

When this ratio is taken as a comma to be tempered, it produces father temperament, where 4/3 and 5/4 are equated. In this temperament, major thirds and fifths become octave-inverses of each other.