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IPA purpose seems straightforward to me: map all the known ways to produce sounds using the mouth to symbols and, for a specific language standard/dialect, map the possible sounds of it to these symbols. Now it is possible to describe the pronunciation of any word of the language/dialect in written form.

However, teachers, dictionaries and phonetic descriptions often uses phonemic transcriptions. As each phonem may be rendered by different allophones, the whole original purpose of IPA is broken IMHO.

Example 1: why use /paɪ/ instead of [pʰaɪ] to describe the pronunciation of the word "pie"? How would a Spanish native know that the initial "p" should be aspirated (Spanish has no aspirated "p")? The same applies for the flap T / D in GA English.

Example 2: GA American phonology Wikipedia shows /ɑ/ (open back unrounded vowel) as a central vowel in its vowel trapezoid diagram. Why not use the allophone [ä] instead, making clearer which is the standard sound?

The distinction between phonems and allophones may be useful in linguistics discussions, but I really do not understand its usefulness in language learning. It seems to me it only adds an extra layer of complexity and ambiguity.

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    I think we need some clarity from you about what exactly you want to teach Spanish speakers about English pronunciation. Maybe you won't care whether they aspirate p's in exactly the way native English speakers do -- in that case, don't teach them that. If you do want them to know about when to aspirate, you have to give them some information about it, don't you? – Greg Lee Jun 5 '19 at 1:12
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    Shortest answer: because evidence shows that native speakers think in terms of phonemes, not phones. – Draconis Jun 5 '19 at 1:13
  • @Greg Lee, I'd like to teach them how to aspirate like English speakers only once and afterwards they will know if a "p" in any new word is aspirated or not just by reading the IPA transcription in the dictionary. Doesn't that make sense? By the way, that was just an example. – Alan Evangelista Jun 5 '19 at 1:32
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    You seem to be assuming that IPA is used only for phonetic transciption, but it is also used for phonemic transcription. It can be used for broader or narrower transcription, as required. – Colin Fine Jun 5 '19 at 14:24
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    Yes, that's very clear. So you;re not trying to teach your Spanish speakers the same control over aspiration that native English speakers have, since of course the latter do not need to look in the dictionary to find out whether to aspirate. Provided you can teach your Spanish speakers how to make aspirates or non-aspirates at any position, which neither ordinary Spanish speakers nor English speakers know how to do, that might work, eventually. – Greg Lee Jun 5 '19 at 19:37
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You say the original purpose is lost. I ask, what is the original purpose?

Evidence indicates that native speakers remember phonemes, not phones. That is, an English-speaker's mental representation of "pie" is something like /paj/; the aspiration isn't "stored" as part of the word. Instead, English-speakers just know (subconsciously) to aspirate voiceless stops in stressed onsets, as long as they don't come after /s/. (This varies by dialect: I aspirate even after /s/, for example.)

Most language-learning programs are based on the same principle. There's an enormous amount of phonetic information in any word, so it's far easier to learn by "compressing" it: remembering a set of phonemes for each word, and a set of rules to turn those into a phonetic realization.

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    He meant the original purpose of the IPA, I thought, and surely the IPA is a system of phonetic notation. I understand why dictionaries intended for native speakers strip out a level and repurpose it as a system of phonemic notation, but the question of whether this is helpful for language learners stands. I suspect User6726 is right on that, but I don't think it's a simple as saying that an English-speaker's mental representation is X, therefore X is what needs to be taught to someone learning English as a second language and therefore starting with a different set of mental representations. – user23078 Jun 5 '19 at 7:24
  • It seems to me that native speakers remember words by their sounds (allophones), not any written form of it. The written representation in a dictionary is just a tool to understand the sound. I doubt anyone (native or non-native) memorizes that written representation, so IMHO it should prioritize precision over conciseness. – Alan Evangelista Jun 5 '19 at 11:19
  • @AlanEvangelista, Then it seems to you wrong. Native speakers do not remember words by their sounds -- instead, they remember words by their phonemes. This is not necessarily a written representation to be found in a dictionary. Languages with no dictionaries, and even those with no conventional written form at all, work the same. It took a long time for linguists to figure this our -- around a century -- but now this view is almost universally held. It is not surprising that you don't know about it, but now is the time to learn. – Greg Lee Jun 5 '19 at 20:00
  • @AlanEvangelista Categorical perception is an amazingly powerful force! Humans generally aren't even aware of allophones in their native language. – Draconis Jun 5 '19 at 20:20
  • @Minty Surely the IPA's used the "phonemic principle" from the beginning (which is why e.g. there's a letter ɧ used for a Swedish phoneme but without any phonetic value of its own, or why taps and flaps are conflated just because no language makes a phonemic distinction between them)? – Draconis Jun 5 '19 at 23:03
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The distinction between allophone and phoneme is useful, because allophonic rules are ones that can actually be taught as general rules, whereas morphophonemic rules (neutralizing rules) generally are taught as "you just have to memorize it". However, actually teaching the technical terminology and giving phonemicization exercises is pretty useless.

If you present data in phonetic transcriptions, rather than phonemic transcriptions along side practice with contextual variants, you make it so much harder to learn the morphology and orthography of the language. The extent to which that actually matters depends on the language: aspiration alternations in English are not ubiquitous.

If you don't teach something like a rule of aspiration, then you will have to give phonetically transcribed data, which will confuse students into thinking that English is like Hindi; and you will have to explain why you get aspiration variation between appʰly vs. application. As for the symbol for the low back vowel, I suppose you do have to deal with Wikipedia which is likely to be a popular source of misinformation. There is no reason to transcribe that vowel as anything other than [a]. Most linguists don't truly understand the IPA, much less general language learners.

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    The Wikipedia article says that the relevant table is from Wells 1982. It might be outdated, or based on controversial principles, or Wikipedia editors might have miscopied it—but I don't think it can be right to call John Wells "misinformed" about the principles of the IPA, given that he has been a member of the Council of the IPA since 1970. – brass tacks Jun 5 '19 at 1:51
  • <ɑ> is well established as a symbol for North American LOT/PALM in linguistics literature, EFL dictionaries, etc. probably because it was the symbol for RP PALM. Using <a> instead now runs the risk of confusing learners because it is now often used for RP/Canadian TRAP. Also it is my understanding that the cot-caught merger often results in a low back vowel. – Nardog Jun 5 '19 at 7:28
  • I do not understand why phonetic transcriptions would make English students think that English is like Hindi. Regarding apply/application, I have never even realized there was difference regarding aspiration between both before. I am not sure I have to teach the aspiration rules, but even if I do, having a phonetic transcription would reinforce the rules. Whether learning by phonetic transcription is harder and confuses students, it is subjective IMHO. I as language student think the opposite. An alternative would be to include both in a dictionary. – Alan Evangelista Jun 5 '19 at 11:51
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    @AlanEvangelista I must be missing something: you say "Whether learning by phonetic transcription is harder and confuses students, it is subjective IMHO", but isn't that pretty much the core of your question? Is that saying your question can only be answered subjectively, and you already know what the "correct" answer is for you? Why ask then? – LjL Jun 5 '19 at 18:55
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    Sorry if it is a naive question, but what is the problem of focusing on GA and RP? Cambridge dictionary already does is, doesn't it? In my layman's ears, it approaches very well what I hear from most US and England natives, the English native speakers I have more contact with. – Alan Evangelista Jun 5 '19 at 23:07
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Broad transcription is meant to capture the difference between e.g. dead, deed, lad, lead "plumbum" and lead "guide, head" or whether ghoti is to be read as "fish". That can help a beginner, but no kind of transcription can help learning a perfect pronounciation. Have you taken a look at narrow transcription? It's a mess, and only useful for advanced linguists beginning to learn something new.

In short, native English listeners hardly even perceive the difference betwen e.g. /pʰɪt/ and /spɪn/, and if they do, they won't care much.

Otherwise, even if they noticed a foreign accent, the foreigner would need an introduction to phonetics, and a trainer to get rid of it. That would be too extensive to belong in a dictionary, or in an elementary class room.

A different dialect is noted differently in the respective dicts, which take a choice to note the allophone specifically, to present only one still mighty broad dialect--consider e.g. dance as the prime example for the difference between UK or US. You might ask why they don't note the aspirated labial plosive, too, but you'd have to make a case why they should. They have to limit the detail at some point. The prior answeres have already tried to point out that it is a reasonable decision.

Whether dictionaries noting narrow transcription of certain dialects exist and who should use them is a related, but different question. It rather seems that native speaker experience is required. Otherwise rule based descriptions are applied to broad description to yield a narrow dialect description, and the rules are inferred from example sets. The rules may differ depending on what is used as basis. So e.g. Spanish speakers necessarily build on Spanish. In principle, any learner tries to infer these rules, and only the important ones are noted in introductory classes.

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    Is allograph a proper word? Or is spelling reasonably standardized everywhere that it is not needed? – vectory Jun 5 '19 at 17:24
  • Allograph is indeed a proper word. Examples of allographs are a and ɑ, which are allographs of the grapheme <A>. There are also lexemes and morphemes, not to mention phonesthemes like KL-. – jlawler Jun 5 '19 at 19:49

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