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For an assignment in one of our classes, our teacher had directed us to analyze a set of french words, which included the word [fij] (fille). However, later, she instructed us not to analyze that word. Presumably, she concluded that [fij] would be too difficult a word for her linguistics 101 students to analyze.

Consequently, we never learned the syllable structure for that word.

I believe that [j] is a semi-vowel, and that [i] and [j] jointly constitute the nucleus of [fij], and that as such, [fij] is an open syllable.

Is that true?

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In transcribing the word as [fij], you are committed to saying that this is a closed syllable (unless you invoke dubious abstract structures where j is not syllabified, or is the onset of a syllable containing no vowel). The letter [j] is not a vowel, and under normal assumptions about syllabification, it would be part of the syllable defined by the preceding vowel i. That, by definition, makes the syllable closed. You have choices in transcriptions, which do not reflect some immutable phonetic absolute, they reflect phonological analysis. If you want to say that the syllable contains a diphthong, then you should transcribe the word as [fii] (which is different from disyllabic [fi.i]), and if you want to say that the syllable contains a monophthong and is open, then you should transcribe the word as [fi].

You should also look at actual practices for transcribing vowels of English, because the diversity of practices very clearly show how transcriptions are simply conventionalized and cannot be fully rationalized. The word "fee" can be transcribed many ways, for example [fi, fi:, fij, fɪj...] In general, i-ending diphthongs are written with final ɪ,i,j as well as raised versions of any of these letters. One is always free to write "car" as [kaɹ] and call it an open syllable by labeling the sequence a rhotic diphthong.

In this case your teacher presumably gave you a transcription, and wants you to come up with an analysis. The question you might later pose to the teacher is, why that particular transcription? If the answer is "because this is an closed syllable", then the follow-up question would be "How do you know that it's an open syllable?". If s/he thinks it is an open syllable, the the follow-up questio would be "why [fij] and not [fii] or [fi]?"

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    Why should Hal look at actual practices for transcribing vowels of English, when the question relates to the a French word (either fille or possible fil, I presume)? – Colin Fine Oct 25 '15 at 21:21
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    In order to understand the broader point that transcriptions are not automatic, and that they also reflect prior analytic choices which need to be justified. He doesn't have to be limited to considering only French, in order to understand the underlying reasons for an answer that apply to French. – user6726 Oct 25 '15 at 23:10
  • Right. I honestly thought you had missed the heading, and thought you thought he was talking about the word 'fee'. – Colin Fine Oct 25 '15 at 23:17
  • As a layman I'd say that this phonological analysis and the resulting syllable classification depends entirely on whether you recognise the closing "e muet" in this word ("fille"). The French tend to say it has been "dropped", but to me as a native speaker of a Germanic language it still appears to be mostly there. Hear for yourself: fille on Wiktionary; e muet – reinierpost Oct 26 '15 at 12:10
  • Well, as a specific example, in Radical CV phonology (Lowenstamm), all syllables everywhere are CV and any apparent coda consonant has an empty nucleus. This is entirely independent of "e muet" in French. I don't know whether the word in question is supposed to be "fille" or "fit". If it is "fille" and the instructor gives [fi] for passé simple of faire, then I would agree. – user6726 Oct 26 '15 at 16:08

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