In addition to
@MaxwellsEq 's comments:
You do realise that every tiny detail of the "complex auditory signals"** in recorded music
HAVE been measured.... by the very microphone that was used to record them - otherwise they wouldn't be in the signal in the first place.
Yet we have measuring gear (such as the Analogue Precision analyser used by Amir) that are orders of magnitude better (more sensitive, lower noise, lower distortion, higher resolution, higher bandwidth) than the best studio mic.
I mean - hell - I can spend about £200 and get an E1DA cosmos ACD which is way better than the best studio mic, and perform my own measurements if I wish.
So, to answer your question, yes we do.
*******
** they are really not all that complex, in terms of modern electronics.