I listened to the Clara Schumann piece and I thought the low notes have a "perfectly tinny" sound, as if they were computer-generated on MATLAB. Or like a harpsichord. I assume that's the difference?
A pure treble note like from a computer wave form does not rattle like that, to my ears.
A normal piano is supposed to have impure frequencies, it's part of the timbre and what gives it warmth.
Like a chocolate or winey kind of muddy. Artistically I much prefer that.