In traditional music theory a complement is the interval which, when added to the original interval, spans an octave in total. For example, a major 3rd is the complement of a minor 6th. The complement of any interval is its inverse (or inversion), except for the octave and the unison which are each other's complements. In musical set theory or atonal theory, complement is used in both the sense above, and in the additive inverse sense of the same melodic interval in the opposite direction - e.g. a falling 5th is the inverse of a rising 5th. 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).
