The Handbook of the International Phonetic Association (1999: 11–2) defines the values of cardinal vowels as follows:
[T]wo fully front vowels [e] and [ɛ] are defined between [i] and [a] so that the differences between each vowel and the next in the series are auditorily equal; and similarly, two fully back vowels [ɔ] and [o] are defined to give equidistant steps between [ɑ] and [u]. The use of auditory spacing in the definition of these vowels means vowel description is not based purely on articulation, and is one reason why the vowel quadrilateral must be regarded as an abstraction and not a direct mapping of tongue position.
But this begs the question as to how those supposed auditory equidistances are, or can be, determined. We know they do not correlate exactly to the formant frequencies: the acoustic distances between [i u] and [e o] are smaller than those between [e o] and [ɛ ɔ] or between [ɛ ɔ] and [a ɑ].
Is there a way to measure auditory distances of vowels? Is it possible to (re)define the values of the close-mid and open-mid cardinal vowels based on any acoustic or auditory measures?
In his 1967 Three Areas of Experimental Phonetics, Peter Ladefoged speculated that, since the technology available back then was unable to determine the formants of high and back vowels, humans also lacked the ability to determine them, hence the discrepancy between acoustics and perception.
From pp. 132-3:
(1) The acoustic quality of most vowel sounds can be conveniently specified by stating the frequencies of their first two or three formants.
(2) This is not true of vowels which are called in traditional terms close vowels, nor of so-called back vowels. It is not at all easy to analyse these vowels in terms of their formants.
(3) The perceptual quality of a vowel usually depends on the relationship between the pitches of the formants of that vowel and the pitches of the formants of other vowels pronounced by the same speaker.
(4) The listener to speech uses his past experience to form an adaptation level, the immediate past experience of a particular voice being the most important factor in this process.
(5) Neither of points 3 and 4 above has been shown to be true for the vowels mentioned in 2 above.
But now computers can extract the formants of high and back vowels just as easily as any other vowels, and I've never seen Ladefoged's speculation (in 1967) repeated in more recent literature, including his. Has this speculation turned out to be true, false, or just less likely? Can one devise a means to confirm or deny it?