The whole idea of the piano involves sound that cannot be identified: one can name the keys but not the sound they produce. It is a big mistake to lead children to believe otherwise.
Once restricted to easy definitions and limitations the ear is relegated to replay as opposed to play. One of my students complains of having melodies that go round and round inside her head in a most maddening way. She feels powerless to stop this. Her field is science, a discipline that requires the ability to reproduce consistently and accurately the experiment of yesterday or last year.
Music is quite the opposite. If it were a question of accurate repetition I would do something else--anything else. Yet for many years it seemed that that was the goal of the classical music establishment, a goal very much suggested and furthered by recording techniques that stressed perfection above all else.