the vowel system in my accent of english
There are 16 distinct phonemes, which fall into four natural classes:
Checked vowels: /ɪ o ɛ a ɑ/
Diphthongs: /ij ʉw oj ɛj əw aj aw/
These are distinguished on the following basis:
Checked vowels only occur immediately before a tautomorphemic consonant; schwa only occurs in unstressed syllables; long vowels and schwa never occur before a vowel; diphthongs can appear anywhere.
Checked vowels and schwa are always short, long vowels are always long, and diphthongs vary in length depending on the environment.
Diphthongs are phonetic diphthongs at least some of the time; the other vowels are always monophthongs.
The constraint that long vowels and schwa never occur before a vowel is enforced across morpheme and word boundaries, by insertion of /r/ between any long vowel or schwa and any following vowel. For example drawing /droːrɪng/, there it is /ðəːrɪtɪz/.
Geoff Lindsey's description of /ɪ ɛ a/ for SSB is also accurate my accent. For the LOT vowel, however, which Lindsey transcribes as /ɔ/, I don't see any rounding in my lips when I pronounce it, nor do I hear any difference in quality between it and the /ɑː/ vowel of START, so I transcribe it as /ɑ/. Admittedly, from listening to the bossy / posso recordings in that Lindsey blogpost it seems I am unable to distinguish [ɒ] from [ɔ] by ear, so it's quite possible there is a quality difference between /ɑ/ and /ɑː/ that I simply don't perceive.
As for /o/, this is quite different from either the /ʌ̈/ of SSB STRUT or the /ɵ/ of SSB FOOT. If I listen closely, I can perceive a slight quality difference between it and /oː/: it's a little higher and more centralized. So /ʊ/ would not be an unreasonable transcription either. But since I think length is the primary distinguishing factor between /o/ and /oː/ ([bod] sounds much more like bud than board, and [bʊːd] sounds much more like board than bud), it seems more appropriate to use the simpler symbol /o/ for both vowels.
/oː/ = THOUGHT, NORTH, FORCE, CURE
The qualities of the vowels are the same as in SSB, though note that SSB doesn't merge NURSE and SQUARE; my /əː/ is pronounced like SSB NURSE, rather than SSB SQUARE.
Some possible quality differences that may exist between /o ɑ/ and /oː ɑː/ were noted above, but they are so subtle compared to the quantity difference that it seems unreasonable to not consider this a principally quantity-based contrast, with at most a minor contribution from quality. Therefore I'd say that my accent pretty much has phonemic vowel length.
/əː/ is a slightly different case. The quality of /ə/ is pretty variable; I haven't considered it in much detail but I think it's generally low-mid word-finally, and higher elsewhere. The quality of /əː/ is more fixed: it's consistently low-mid, like word-final /ə/.
SSB has up to two additional long vowel phonemes /ɪː/ and /ɵː/ found in the NEAR and CURE lexical sets, respectively. But /ɵː/ has a strong tendency to merge with /oː/, and this merger is fully complete for me. As for /ɪː/, for me it corresponds to /ij/, realized as [iː], before /r/, and a sequence of two phonemes, /ijə/, realized as [ɪjə], elsewhere. The /ijə/ pronunciation can also be levelled into forms with a following /r/: for me nearer can be either /nijrə/ or /nijərə/, the latter based on near /nijə/. I would regard /ijə/ as occupying two syllables, but this is somewhat arbitrary (I don't believe that there is a context-independent phonetic definition of "syllable" that could decide this question).
The basic phonetic realizations are similar to SSB. One clear difference is that my PRICE is /aj/, rather than /ɑj/, with a first element identical in quality to that of MOUTH.
Unlike the monophthongs, which are all pretty much pronounced the same in all environments, except for schwa, the diphthongs tend to vary allophonically quite a bit.
As mentioned above, all diphthongs vary in length depending on the environment: each diphthong has a short allophone and a long allophone. Some diphthongs also vary in quality; the conditioning environments for lengthening, and the ways in which length manifests, also vary; on this basis, we can distinguish three overlapping subgroups:
the high diphthongs, /ij/ and /ʉw/
the centralized diphthongs, /ʉw/ and /əw/
the low diphthongs, /aj/ and /aw/
The distinctive feature of high diphthongs is that they aren't always diphthongs. They are clearly diphthongs word-finally, or before a vowel, where their first element is distinctly near-high in contrast to the fully high second element: key [kɪj], if you replace the [j] with a [d], would sound the same as kid. Elsewhere, however, I would describe them as phonetically monophthongs, [i ʉ] when short, [iː ʉː] when long. In Lindsey's blog post, the recording of big leaves from Watch With Mother doesn't sound that different from how I'd say it (though the word usually does sound different, because its [uː] isn't centralized, and so do the late Queen's least [liːst] and few [fjuː], since for me these would be [list] and [fjʉ̞w]). The transcriptions /ij/ and /ʉw/ are meant as a compromise between the diphthongal and monophthongal pronunciations. Note that regardless of the phonetics, I think it's clear that the phonemes /ij/ and /ʉw/ are phonologically diphthongs, because they behave like all other diphthongs in exhibiting allophonic length variation and being able to occur immediately before another vowel without /r/ being inserted in between.
The centralized diphthongs are centralized in most environments except before dark L, where they preserve their older fully back pronunciations: pool [puːɫ], pole [pɔwɫ]. The starting point of backed /əw/ is audibly somewhere between /o/ and /ɑ/. When the diphthongs are centralized, I think /ʉw/ centralizes a bit more than /əw/; the starting point of /ʉw/ is a bit more front than back, so precisely something like [ÿ] or [ʏ̈], while the starting point of /əw/ is a bit more back than front, so precisely something like [ʌ̈]. Also despite the transcriptions I just gave, I'm not sure there is any difference in rounding between the two diphthongs; I think for both the rounding is weak to nonexistent at the start, and only gets stronger towards the end.
The low diphthongs are distinguished by two features: first, they are long word-finally, whereas all other diphthongs are short word-finally; secondly, when low diphthongs are long, it's clearly their first element that's lengthened, while for other diphthongs, the lengthening is more spread out across both elements, and if anything is more on the second element. So pie is [paːj], pine is [paːjn], how is [haːw], loud is [laːwd]; but fade is [fɛjːd], noise is [nojːz], etc.
There is one odd exception: before dark L, /aw/ behaves like a non-low diphthong, having the second element lengthened instead of the first: howl is [hawːɫ]. As for /aj/, it doesn't occur before dark L at all: /ə/ has been inserted wherever a diphthong ending in /j/ historically preceded dark L, as in reel [rɪjəɫ].
So what determines the length of a diphthong? As noted already, in word-final position, low diphthong are long and the rest are short. Before a vowel, all diphthongs are short. Before a single voiceless consonant all diphthongs are short, and before a single voiced consonant all diphthongs are long. Before consonant clusters, it seems the voicedness of the last consonant is what determines the length. So bind is [baːjnd] but pint is [pajnt], despite both words having a voiced consonant immediately after the /aj/.
Note that the sonorant consonants /m n l/ seem to vary in length in a similar way, becoming long before a voiced consonant: sent is [sɛnt], but send is [sɛnːd]. But I think there can only be one long sound in a syllable rime, so the /n/ in bind is not lengthened. It seems clear to me that when there's a sequence of diphthong + sonorant + voiced consonant, the diphthong is lengthened rather than the sonorant when the diphthong is one of /ij ʉw aj aw/: fiend [fiːnd], boomed [bʉːmd], find [faːjnd], sound [saːwnd]. I'm less sure about what happens with the other diphthongs; maybe it isn't just one segment which lengthens in this case, so rained would be something like [rɛjˑnˑd].