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Why some symbols in phonology charts are put in parentheses or brackets, such as (z), or [ɲ], and why there is a tilde ~ in some places, such as dz [dʒ ~ dz]. Wondering what that means exactly, if it just means that the sound represented by their alphabet dz is within the range between and dz in IPA terms.

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Not all symbols used in phonological and phonetic descriptions are letters of the IPA. The symbol "~" typically means "alternates with", for example "a~æ" could be that either a or æ would be possible in a given context (i.e. the sounds are in free variation). It also can be used to refer to contextual variation, for example "The plural suffix, s ~ z ~ ɨz...". Square brackets canonically refer to phonetic values, so [dz ~ dʒ] would be that the thing in question (perhaps phonemic /dz/) is realised either as phonetic [dz] or as phonetic [dʒ]). It does not mean "some value intermediate between", it means "either this value or that value". There is no notation for talking of ranges of realization that are finer-grained than two similar transcriptions. If the realization of a sound was "anything between [dz] and [dʒ]", you would have to say that in words.

Parenthesis has two different meanings. In a list of phonemes, it implies that there is something marginal about the item in parentheses, for example one might list "(x)" in a phoneme chart of English, since there are a few words which some people pronouns with the velar fricative [x] (Bach, loch, Chanukah, chutzpah, Khalil). However, in writing a rule, it means "0 or 1 occurrences of", so "a→b/_(c)d" means "a becomes b when followed by d with zero or one occurrence of c intervening".

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    A cleaner way to say "0 or 1 occurrences of" might be "optional", as in the syllable structure (C)V "a vowel preceded by an optional consonant".
    – Draconis
    Commented Sep 16, 2018 at 16:00

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