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What are the rules for bounding a syllable? I am trying to take IPA text and write software to automatically separate the syllables for the word. By trying I am still just thinking about how to do it. Wondering if there are clear rules for syllables or anything to look into.

For example, take the word "example", /ɪɡˈzæmpl̩/. It could be broken into multiple ways:

eg-zam-pl
egz-zam-pl
egz-am-pl
egz-zamp-l
...

It seems in some cases you want to end the previous syllable with a sound, and start the next syllable with the same sound, and in other cases you don't. In English specifically it seems casual how we pronounce syllables words, as opposed to what seems like in Arabic being a very specific way to pronounce them (always start with a consonant, etc.). For example, in Arabic, you have yad-ru-suu-na (يَدرُسُونَ). It at least from my little knowledge doesn't appear to be any of these instead:

ya-dru-suu-na
ya-drus-suu-na
ya-drus-suun-na
yad-drus-suun-na
....

How do you know where to break the syllables apart? What are the rules, or what field of study is this if there aren't a clear set of rules? How can you go from IPA to a sequence of syllables programmatically?

Another word, wedding:

wed-ding
we-ding
wed-ing
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It's also a widely-held axiom in linguistics (phonology, specifically) that segments are always syllabified, in all languages. But that is not an empirically well-supported claim. There are certainly a number of languages which provide various kinds of evidence that the syllable can be a thing, just as [ʕ] can be a segment of a language, but not every language has [ʕ], not every language has tone, and there isn't a compelling argument that every language must have syllables.

One solution to the problem, then, is to not assign a segment to a syllable unless you have an actual reason to do so, therefore in Polish [fstʂɔw̃s] ("shock") it's possible that some of those initial consonants are not in any syllable at all.

To resolve the question in a given language, you therefore have to (1) study the details of the language that might tell you whether in a string [abcdefgh] c and d are in the same syllable, in different syllable, or one or both of these segments are in no syllable. And (2) you also need a theory of syllables: that is part of what the theory of phonology is about. Since Daniel Kahn's 1976 dissertation about the syllable in autosegmental phonology, there have been zillions of works written, so it's kind of hard to summarize everything on the topic in one post. English is a good example albeit of how competing theories can give rise to contradictory empirical claims, which simply cannot be resolved by pointing to data, instead we have to depend on one theoretical postulate vs. another.

A simple analytical procedure is to not assign any segments to syllables unless you have good evidence for doing so.

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It's a widely-held axiom in linguistics that syllabification is never phonemic. In other words, words aren't stored in your brain pre-broken-down into syllables; that syllabification happens later according to regular rules. The reasoning behind this axiom is a bit circular, since it sometimes requires you to finagle your underlying phonemic forms to encode this information (in Japanese, for example, coda [n] and onset [n] need to be treated as separate phonemes), and it's not entirely clear that this axiom is worth keeping (Blackfoot is a famous point of contention). But the upshot is, when linguists write out phonemic representations, it's almost always possible to derive the syllabification from that through regular rule application.

Those regular rules, though, generally need to be learned separately for each language. There are some broad principles which some linguists claim are universal, but the fine details are generally agreed to be language-specific.

For English in particular, these rules are usually expressed as ranked constraints. You have a set of constraints about what makes a valid syllable, which allow /splu/ but forbid /uslp/ (the "phonotactics"). And ranked below these, you have the maximal onset principle, one of the rules that some linguists claim are universal: all else being equal, stick as many consonants in the onset as possible. This principle is why we say /ɪm.pruv/ instead of /ɪmp.ruv/, even though /ɪmp/ and /ruv/ are both valid syllables: /ɪm.pruv/ makes a larger onset.

This suggests a relatively straightforward algorithm for syllabifying English words. Start from the end, progressively add consonants to the syllable, and stop if you create an invalid syllable in the process. I've used this algorithm before for Latin and Greek with good success. (Deciding which syllables are valid versus invalid, though, is left as an exercise for the reader.)

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