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I'm not sure if I understood what complementary distribution and defective distribution mean.

I have a definition that complementary distribution is an automatic, i.e. obligatory positional variation of a certain phoneme that always occurs in a certain position. I'm not completely sure what defective distribution is though. I found that defective distribution is when a certain phoneme occurs only in some contexts.

If we take for example that in English, word-initial stops are always aspirated: e.g. pin [pʰ] as opposed to spin [p], then, would this be an example of complementary distribution or defective distribution?

Am I right in thinking this is complementary distribution? It can't be defective distribution since aspirated stops don't occur only word-initially. They can also occur inside words, e.g. potato.

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Complementary distribution is really mutual defective distribution of a set of sounds. You have complementary distribution if a sound does not appear in a specified environment X. If sound A appears everywhere but context X (defective distribution 1) and B only appears in context X (defective distribution 2), we say that A and B are in complementary distribution. (In your potato example, only the first t is aspirated: the distribution of aspiration is actually not in terms of word position, it's in terms of stress-foot position, but typically the intro linguistic story is that it's only about word-initial vs. elsewhere).

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