APOTOME

APOTOME, in Mathematics, the remainder or difference of two incommensurable Quantities. See INCOMMENSURABLE.

An Apotome is an irrational Residue, as CB, arising when from a rational Line AC, called ἄλφα (alpha), you cut off a rational part AB, called βῆτα (beta), only commensurable in power to the whole Line AC—It may be expressed thus, a—√b. Apotome, in Music, is the Part remaining of an entire Tone, after a greater Semi-tone has been taken from it. See TONE and SEMI-TONE.



The Proportion, in numbers, of the Apotome is, of 2048 to 2187. See DEGREE. The Greeks thought that the greater Tone could not be divided into two equal Parts; for which reason they called the first part λείμμα (leimma), and the other ἀποτομή (apotomē), in this, imitating Pythagoras and Plato.

The Word is derived from the Greek Verb ἀποτέμνω (apotemnō), to cut off.

APOTOME