thanks and this isn't what I'm asking about, I'm aware of all of this (background in physics and in music performance).

of course people can hear and distinguish mathematically pure intervals especially if demonstrated in these ways.

you said,

> This brings some practical musical advantages, but even the average listener can hear the difference, the loss of purity of harmony

which I interpreted as meaning that average listeners are both hearing and actively aware of this difference in their day-to-day exposure to equal-tempered music.

I am very skeptical of this claim, but perhaps this is not what you intended to imply? I can understand why my question would lead to yours and geofft's answers.