Complement
In biology, complement is a group of proteins found in blood serum which act in concert with antibodies to achieve the destruction of non-self particles such as foreign blood cells or bacteria.
The complement is a concept used in naive set theory. See Complement (set theory).
In mathematics, complement is an operation that transforms an integer into its additive inverse. It is useful for subtracting numbers when only addition is possible, or is easiest. negative numbers are one form of additive inverse; subtracting 5 from 8 is the same as adding -5 to 8. Another form of subtraction deals only with positive numbers, and is called the method of complements. One common form of this is the two's complement, which is often used in computer microprocessors which perform calculations using the binary numeral system.
In music a complement is used in the sense immediately above. 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 naive 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.
In optics, complement refers to complementary colors.
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