Following on from yesterday’s discussion of American æ before ŋ, perhaps we’d better have a brief mention of another mysterious matter in American English phonetics: the question of ɪ followed by ŋ.
The traditional view, and surely the correct view for most accents, is that iː, like other long vowels (see yesterday’s comments), does not occur lexically immediately before a velar nasal. The sequence iːŋ is impossible, unless it arises through alveolar-to-velar assimilation in items such as bean curd.
Traditionally, and for most of us, king is kɪŋ, string is strɪŋ, and link is lɪŋk, all with the short KIT vowel, ɪ.
However some Americans (they seem to be mostly Californians) report that they feel themselves to be using the FLEECE vowel in such cases: kiːŋ, striːŋ, liːŋk. (I transcribe with length marks in my usual way, although as we know American English does not really have a long/short contrast so much as a tense-lax one.)
I am not sure whether this extends to the position before ŋɡ, as in finger.
Again, you can argue that here we have a positional neutralization, this time of ɪ - iː, so that in a sense it is meaningless to ask which of the two vowels we have here. However speakers do generally seem to have pretty clear intuitions of a phonemic nature here: most of us are happy to identify the vowel of king with that of kin, while a minority identify it with that of keen. Are they all Californians?
Are these the same people who use an identical pronunciation for tin and ten, mini and many (another typical Californianism)? To judge by Wikipedia and Penelope Eckert’s webpage, probably not.