Limma

Limma, an interval which, on account of its exceeding smallness, does not appear in the practice of modern music, but which, in the mathematical calculation of the proportions of different intervals, is of the greatest importance. The limma makes its appearance in three different magnitudes—viz. the great limma, which is the difference between the large whole tone and the small semitone, being in the proportion of 27 to 25; the small limma, which is the difference between the great whole tone and the great semitone, being in the proportion of 135 to 138; and the Pythagorean limma, which is the difference between the great third of the ancients (which consisted of two whole tones) and the perfect fourth, the proportion of which is as 256 to 243.