Certainly the i in words like bite and fright represents an /aɪ/ diphthong.
Phonemically, I come up with these:
/aɪ/ as in price, my, high, flight, mice/aʊ/ as in mouth, now, trout/eɪ/ as in face, date, day, they, grey, pain, reign/ɔɪ/ as in choice, boy, hoist/oʊ/ as in goat, toe, tow, soul, rope, cold/juː/ as in cute, few, dew, ewe/jə/ as in onion, union, million, scallion, scullion
Most examples are taken from here. What those all actually work out to phonetically varies a great deal across dialects and speakers. For example, many and perhaps even most North American speakers raise the /aɪ/ in tight to [ʌɪ], but not the one in died. You may wish to check out SoundComparisons.COM, where you can both see and hear the phonetic transcriptions for speakers of many, many different dialects, including words like four, hear, eight, cold, cow, fight.
You could also analyse words like way, yay, wow, yow as triphthongs if you really wanted to, although we don’t tend to do so in English. Instead they tend to have an initial /w/ or /j/ followed by a diphthong in normal notation. (In Spanish though they’d be considered triphthongs, as in cambiáis, which has just two syllables, cam- and -biáis.)
Non-rhotic speakers claim to have others, but I have trouble thinking of those as diphthongs myself. I always analyse diphthongs as having a principal vowel to act as the syllabic nucleus and then a glide either before or after it. If the glide comes before the main vowel, as in /jə/, /juː/, it is a rising diphthong, and if the glide comes after the main vowel, as in /aɪ/, /eɪ/, /aʊ/, /oʊ/, /ɔɪ/, it is a falling diphthong. (Some people consider only the falling ones “real” diphthongs. I’m not sure why, since million has only two syllables for me, not three.)
I know of no diphthongs in English that have no glide in them, although whether you write your glides with /j/ and /w/ or as semivowels makes no great difference. This leads to alternate transcriptions, as in /eɪ/ for /ej/, and /aʊ/ for /aw/.
If there is no glide, I don’t count it as a diphthong. That means that I don’t read /ʊə/ as a single syllable. Rather, it has two syllables, as in the programming language named Lua /ˈlʊːə/. I guess I might write that /ˈlʊː.ə/ if I thought people might misunderstand me. And no, it is not homophonic with monosyllabic lure /ˈl(j)ʊːɹ/.
Non-rhotic speakers sometimes analyse words with words with ‹r› in them as diphthongs, where they substitute /ə/ for /ɹ/, but since that’s not a glide, it’s not going to make a new diphthong in my book; it might make a new syllable, though. Even though I say fire /faɪɹ/, I realize that they say /faɪ.ə/. For me that would then rhyme with the disyllabic maya /ˈmɑjɑ/, /ˈmaɪ.ə/, although it becomes challenging to assign the /j/ to one syllable or the other. I don’t see people writing fire /ˈfajəɹ/, but at least then it would seem like two syllables. But you end up reassigning the glide and changing the word from having an /aɪ/ diphthong in the first syllable to having a /jə/ syllable in the second.
For the record, here’s how I see the following r-bearing words:
- bearer
/ˈbe(ɪ)ɹəɹ/
- tourer
/ˈtʰʊɹəɹ/
- nearer
/ˈniːɹəɹ/
- curer
/ˈkʰjʊɹəɹ/
- layer
/ˈleɪ.əɹ/, /ˈle.jəɹ/
- lair
/leɪɹ/
- fiery
/ˈfaɪɹi/ (two syllables), /ˈfa.jəɹi/ (three syllables)
- fairy
/ˈfeɪɹi/
- Faëry
/ˈfe.jəɹi/ (for trisyllabic rhymes in poetry)
- more
/mo(ʊ)ɹ/, /mɔɹ/
- mower
/ˈmoʊ.əɹ/, /ˈmowəɹ/
In that analysis, ‹r› is never part of a diphthong because /ɹ/ is not a glide, and if you write it as a schwa, you’ve likely introduced another second syllable. Non-rhotic AmE speakers (such as those from the South) always sound like they have have more syllables in their words to those of us from the North. The joke is there is no such thing as a one-syllable word in “Suthun”. For example, more is one syllable in the North’s /mo(ʊ)ɹ/, but two in the South’s /ˈmowə/.
Lastly, I realize that you can write ‹-er› as /ɚ/ or /ɹ̩/, as in murder written as either /ˈmərdər/ or /ˈmɝdɚ/. The problem is that we have only two rhotacized IPA symbols, stressed /ɝ/ and unstressed /ɚ/; for anything else that you want rhotacized, you have to use U+02DE MODIFIER LETTER RHOTIC HOOK, which doesn’t look so hot in most fonts, and doesn’t count as a combining character.
Best Answer
Actually, it's "worse" than that. Nearly all the vowels of English have more than one possible representation in IPA. For example:
The vowel sound in "goose" can be written as [u], [uː], [uw], [ʉ], [ʉː], [ʉw] or [ɵw]
The vowel sound in "choice" can be written as [ɔɪ], [oɪ], [ɔj] or [oj]
The vowel sound in "face" can be written as [eɪ], [e], [ɛɪ], [ej] or [ɛj]
It's not really a matter of something special about the four cases that you mention. Quite simply, the IPA is not precise enough, and the phonetic positions of English vowels are not specific enough (variation in the realization of any particular vowel sound exists both between speakers and within the output of any individual speaker), for there to be a single unambiguous one-to-one mapping between English vowels and possible IPA representations. Therefore, consistency between different transcriptions is just a product of convention, and in fact different people have used different conventions for various reasons.
Some of the possible criteria that people have used to judge phonemic transcription conventions:
phonetic accuracy: how close are the characters to the phonetic definitions for the IPA symbols?
simplicity: how many unique characters are used in the transcription system? How many characters are used that are expected to be unfamiliar to people who are just starting to learn the system?
symmetry: how well does the transcription reflect the phonological relationships between sounds, and the way sounds behave phonologically?
redundancy: does the system distinguish different vowels in only one way (e.g. ɪ vs. i, or i vs. iː) or in two (e.g. ɪ vs. iː)? Are the vowels that occur in unstressed vowels identified with any of the vowels that occur in stressed syllables (e.g. is the vowel in "strut" transcribed the same way as the vowel at the end of the word "comma", since for most speakers, these do not contrast) or are reduced vowels transcribed with special symbols reserved for vowels in unstressed syllables?
conservatism: how similar is the transcription system to transcription systems that have been used in the past?
Actually, the issue of "conservative" phonemic transcriptions that don't use the IPA letter that is closest to the usual modern phonetic realization of a phoneme doesn't only come up with regard to English. The transcription of Danish vowels is similarly problematic (with the symbol ɛ being used to represent a vowel that many speakers pronounce more like [e], and the symbol æ being used to represent a vowel that many speakers pronounce more like [ɛ]). There is at least one similar case in the transcription of French: the nasal vowel found in words like vin is conventionally transcribed as /ɛ̃/, even though for many speakers it has a noticeably different quality from non-nasal /ɛ/.
The following blog posts may be illuminating:
"IPA transcription systems for English", by John Wells (KarlG's answer also links to this resource)
"IPA vowel symbols for British English in dictionaries", by Jack Windsor Lewis
"The British English Vowel System" by Geoff Lindsey -- an attempt proposal for a new system for transcribing Southern British English that Lindsey says more accurately indicates the phonetics used by most present-day speakers in this region
A response to Lindsey's proposal on John Wells's blog (note that Wells talks about an earlier, slightly different version of Lindsey's transcription than the one you can see currently on Lindsey's site)
I would say the best way to learn more about English phonetics is to
practice listening to the way various speakers pronounce the sounds
get feedback about your own pronunciation from a good teacher, if you can,
to learn about phonetic details, read* explanations from phoneticians. For example, the web sites I linked to have a number of additional posts about various aspects of pronunciation, and there are other good sites like Alex Rotatori's blog.
*(Or listen, I suppose--there seem to be a number of Youtube videos and so on nowadays that cover these topics, although I don't have much experience with using videos to learn about English pronunciation so I can't give any specific suggestions.)
As Windsor Lewis says in the post I linked to above, the kind of transcriptions you find in places like dictionaries are mainly for telling you the distribution of phonemes in a word--they won't tell you exactly how to pronounce a word in terms of phonetics.