That's the ideal, given infinitely long and infinitely bendable strings. Reality is that a tuner works from a certain key and tunes in equal temperament the oth

That's the ideal, given infinitely long and infinitely bendable strings. Reality is that a tuner works from a certain key and tunes in equal temperament the other keys. Since the piano and the tuning is a compromise and there is limited time, the piano will always sound slightly better in one key than another. As most people play in keys close to the C major scale, this usually gets most attention. Also, pianos rely on resonation. I would not be surprised that the sound board and resonant cavity is designed to favour certain tones. I'm not certain about this though.