[Edit Oct 08: For everyone who arrives here by a google search for Scottish English vowels, please please consult the updated version: A Better Vowel Chart for Scottish English. It really is better.]
To the best of my knowledge, the only published vowel chart for Scottish English is the one in Heinz Giegerich’s 1992 textbook, English Phonology, and the purpose it serves is to show, as a series of stylised diagrams, the difference between Scottish, American, and Southern British vowels in conventional terms.
It’s bothered me for a while that, although those diagrams make all the contribution they’re required to make for the theoretical arguments being presented in the book, they aren’t a particularly close reflection of the phonetic or acoustic properties of the vowels of any of those varieties, the Scottish one being obviously the most salient for me.
(This poses a number of potential practical problems – eg, for when you wanted to transcribe any words that a Scottish speaker might produce – transcription symbols are meant to match fairly specific characteristics, as you can see/hear for yourself on this chart. It would also be a problem for people learning a Scottish variety of English as a second or other language, etc.)
What I’ve produced below is a very rough first draft of a more detailed vowel chart for Scottish English. It’s so rough, in fact, that I’ve even put the word rough in its title – it should only be taken as a very very very preliminary first step in the direction of a more accurate and detailed chart.
Note especially that (a) it’s based on productions from only one speaker, (b) each datapoint in the chart is based on the reading of one word, and (c) the words differed in the consonants surrounding the vowels. This means that it’s very unscientific and should not be taken as definitive in any sense: the data were collected for a completely different purpose and by putting them into this format I’m asking questions of the data which they were never designed to answer. Okay, in all its glory, here it is.
(The symbol /E/ stands for IPA /ɛ/, and /c/ stands for IPA /ɔ/.)
The primary point of interest is that it shows the /u/ vowel (for this speaker, in this particular word!) is much more “front” than you’d be led to believe from extant descriptions of Scottish English. It also shows the vowel /ɪ/ as being lower and more centralised than even the /e/ vowel (something which I’ve been worried about in transcriptions before). The /ʌ/vowel is also less centralised and more back than otherwise expected. I should add that none of them sound odd to me as a phonetically trained native speaker of Scottish English, so that taking caveats (a)-(c) into consideration I think the values should be fairly representative.
For completeness, here are the words from which these vowels were elicited, along with their conventional IPA symbols. If anyone finds a better chart, I’ll be delighted to hear of it – meantime, please be assured I’m aware of the defects of this one and willing to collaborate with anyone to fix it if anyone’s looking for anything more definitive.