I've seen the phrases "said my peace", "say your peace" etc. but just recently I read "said my piece."

I always thought "peace" was correct--or maybe I should say more common--and it made sense to me. But, "piece" makes sense, also. As in, "a piece of my mind" or something like
that.

However, it seems like the context of the phrase is one where the speaker is searching for the resolution of a dispute or is at least trying to mitigate the contentious nature of their opinion so "peace" seems more appropriate even if it's odd.

Which do you think is more common in the phrase? "Peace" or "piece?" Is there an origin to the phrase that make the answer to that question clear?