I realise that the cardinal vowels are supposed to be fixed points of reference, but then we don’t all have exactly the same equipment. I am wondering whether vowel frontness etc. is really defined (or should really be defined) relative to our individual vowel space. Are there any studies relating the extent to which an individual’s vowels deviate from the average to the physiology of that speaker? Also, is there any way to measure the physical extremes of your own vowel space, or would you just end up measuring the limits of your ability to use it?
Ladefoged studied the expert productions of cardinal vowels, and found that experts do not produce the same thing. I am currently analyzing IPA demo tokens from Esling, Ladefoged, Wells and House, plus numbers reported by Catford, and find that there is significant variation between individuals. This is without substantive data on vocal tract geometry for these speakers. As far as I know, there is not a systematic study of corner-vowel productions looking at multiple tokens by "recognized experts". The problem is that the pool of trained experts is small (and diminishing). There is a noticeable difference between what the British-trained experts do in producing [i,a,ɑ,u] in demo-recordings, versus others, which is about the mental target and not the individual's physiology.
Ideally, one could make some progress by analyzing defining productions by Daniel Jones. The problem is that there do not seem to be any high-enough quality recordings that allow formant extraction; the same plagues the Ladefoged samples (assuming that there aren't hidden recordings somewhere in the basement).