(Gk.: ‘segment’).
A chromatic semitone in the Pythagorean system of intervals, equal to the difference between seven pure 5ths and four pure octaves, amounting to 113·7 cents and with a theoretical ratio of 2187:2048. According to the definition of Gaudentius (ed. K. von Jan in Musici scriptores graeci, Leipzig, 1895–9/R, pp.317–56, esp. 344), by subtracting the Limma from the whole tone, i.e. (9:8) – (256:244), the apotomē may be obtained. The difference between the two semitones – i.e. between the apotomē and limma – is equal to the difference between 12 pure 5ths and seven pure octaves, the Pythagorean comma.
JULIAN RUSHTON