[bigtech]

It's an interesting history, better explained here: https://en.wikipedia.org/wiki/12_equal_temperament but in short, prior tuning systems were more mathematically correct, but an instrument would be tuned for a particular key and playing in other keys would sound (to us, anyway) like the instrument was out of tune.

[rgrieselhuber]

But if a piece was written for a specific key and the instrument was tuned to that key for that piece, that would be both more mathematically correct and also matching the original intent of the composer? What is the rationale for equal temperament?