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Inlinguistics,complementary distribution (as distinct fromcontrastive distribution andfree variation) is the relationship between two different elements of the same kind in which one element is found in one set of environments and the other element is found in a non-intersecting (complementary) set of environments.
The term often indicates that two superficially-different elements are the same linguistic unit at a deeper level, though more than two elements can be in complementary distribution with one another.
Complementary distribution is the distribution of phones in their respective phonetic environments in which one phone never appears in the same phonetic context as the other. When two variants are in complementary distribution, one can predict when each will occur because one can simply look at the environment in which the allophone is occurring.
Complementary distribution is commonly applied tophonology in which similarphones in complementary distribution are usuallyallophones of the same phoneme. For instance, in English,[p] and[pʰ] are allophones of thephoneme/p/ because they occur in complementary distribution.[pʰ] always occurs when it is thesyllable onset and, most likely, when followed by astressedvowel (as in the wordpin).[p] occurs in all other situations (as in the wordspin, or insipping').
There are cases of elements being in complementary distribution but not being considered allophones. For example, English[h] and[ŋ] are in complementary distribution:[h] occurs only at the beginning of a syllable and[ŋ] only at the end. However, because they have so little in common in phonetic terms, they are still considered separate phonemes.[1]
The concept of complementary distribution is applied in the analysis of word forms (morphology). Two different word forms (allomorphs) can actually be different "faces" of one and the same word (morpheme). An example is the English indefinite articlesa andan. The usagesan aardvark anda bear are grammatical, but the usages*a aardvark and*an bear are ungrammatical (as is marked with "*" in linguistics).
The formsa andan encompass every environment in which the English indefinite article is used, i.e. there are two different "forms" of the same "word" instead of two different words.