I never quite grasped this until I saw a plot of the tuning of a piano, all 88 notes.
As you said, only the a below middle C was a spot-on 440hz. Looking at the plot, the lower you went from there it was progressively / fractionally flatter the lower you went, and going up from there was the same incremental curve, reversed, going sharp. Yet to play it upon completion, it sounded perfectly in tune. Tuned in perfect mathematical increments, and it would sound beyond bizarre, according to the tech that was giving me the USA TODAY short course in 'Piano Tuning for Dummies'. Some keyboard synths allow for 'unlatching' the standard tempered tuning and going to alternates tuning methodologies, if you want to experience this yourself. You won't want to do it twice . . .