Everything a human can hear can be measured, no ifs, ands or buts. There is no equivocation, no in principle, it's a simple fact. Plain and simple everything we hear is a physical phenomena transferred via the air around us.Something tells me you don't fully understand what you wrote.
There is a difference between measuring sound pressure which anybody can measure.
But it's difference from measuring how human perceive music. No instrument on earth that I know of can do that.