skilled instrumentalists are quite capable of consistently reproducing intervals in a given tuning system. particularly thirds in just intonation. it’s not an approximation. it’s one of the reasons we spend so much time learning ear training in conservatory.
I argue all just about all intonation is some sort of approximation, unless you're playing an electronic instrument that doesn't allow pitch adjustments! And it does surprise me how little my ears seem to notice despite having zero tolerance for people singing even slightly off-key.
relative to mathematical perfection, of course it’s all an approximation when a human instrumentalist is involved. that’s the nature of our physical reality.
the most important element here is how it sounds to our ears. not how closely it tracks to an equation.
