Yeah, pianos deal with both the tuning inaccuracies that are inherent to 12-tone equal temperament in addition to piano-specific oddities like having to stretch

Yeah, pianos deal with both the tuning inaccuracies that are inherent to 12-tone equal temperament in addition to piano-specific oddities like having to stretch the octave. Basically, the harmonics that rise off of piano strings aren't exact multiples of the fundamental -- they're a little bit off, because piano strings don't behave entirely like ideal strings, they behave like metal cylinders. In the mid-range they're pretty pretty close to plain equal temperament, but in the high treble the strings get shorted but the string gauge stays almost the same, which means the ratio of diameter to length increases and they act less like strings and more like cylinders. The bass has similar issues with single and double wound strings. So, the fix is to just stretch the octave enough so that the harmonics of low notes line up better with the fundamentals of higher notes, and so on. (What we perceive as "out of tune-ness" is the wobbly sound of two frequencies played together that almost but don't quite line up, creating a beat frequency.)