Listen to old/early blues recordings and you'll notice that they are tuned to the "how the most difficult to tune is right now", so it can be anything and even, to modern, ears, totally out of tune, but as they were all untuned to the same frequency, everything works.
The "worst" are the solo guitarists, who were very often totally untuned, but they were making music without any problem as their instrument had strings tuned to themselves.
Also learn Indian music or go to an Indian music concert, and you'll notice that first the pitch is decided by the singer and second he/she exposes the intervals which are never fixed and decided by the singer just before the event.
In their music theory, the notes in their multiple scales all have the same name (sa ri ga ma pa dha ni), but the intervals and the pitch are not fixed, which is very clever and that's the reason of the adjustable (moveable?) frets on the sitar.
Tuning to a fixed frequency is just for the ease of interpreting "classical" music the same way anywhere in the world.