Complement (music) - Definition and Overview

In traditional music theory a complement is the interval added to another, that is placed on top of another, so that their complete span is an octave. The complement of any interval is its inverse, except for the octave and the unison which are each others complements.

In musical set theory or atonal theory, complement is used in both the naïve set theory sense above, and in the additive inverse sense directly above as well. Using integer notation and modulo 12, any two intervals which add up to 0 (mod 12) are complements (mod 12). In this case the unison, 0, is its own complement, while for other intervals the complements are the same as above (for instance a perfect fifth, or 7, is the complement of the perfect fourth, or 5, 7+5 = 12 = 0 mod 12).