Ooh, interesting! I'm a pianist and a mother, and I have a daughter and a son, and have been observing with interest how each responds to music from an early age. We've always had a piano in the house and there's always been music going on, so they've had similar exposure since birth. My daughter never showed much interest in it at all as a very young child. She's always had a bit of difficulty holding a tune - once any interval gets beyond a fourth she finds it difficult to reproduce it singing, so that if the interval is, say, a sixth or seventh, she'll sing only a fourth or fifth and the song will end up gradually descending in key. However, when she was nearly eight she decided she wanted piano lessons, because one of her friends was learning and she thought it might be fun. She goes to the same teacher as her friend. She's working steadily for her teacher and is making progress and enjoying it, which I'm pleased about. She's very good at the theory, as she's bright and learns quickly. But she can only play what's on her sheet music - she has great difficulty picking out even simple tunes without music in front of her. She's learning Alfred's at the moment with her teacher, and I think this method is quite good for her as it teaches chords in each key. That means that with a bit of work and explanation, she can manage to improvise. She can't do it at all by ear, but she can do it from her theoretical knowledge, although it's very hard work.
My son has been entirely different and it's been so interesting to watch this! From a very early age he's been able to sing anything perfectly in tune. He's now five, and is getting interested in the piano and asked me if I would teach him. He can pick out tunes by ear and annoys his sister by playing her pieces although he can't read the music yet.
My son has inherited my musical abilities - I have good pitch and have been able to improvise from a very young age. My husband is verging on tone deaf, can't reproduce a tune singing, and like my daughter can't distinguish between intervals beyond about a fourth or a fifth. My daughter seems to have his genes!
I'm going to be so interested watching how both children progress musically as they grow. My son seems to have more innate musical talent. But my daughter works hard, so maybe she can turn into a reasonably competent musician because of that. Maybe both of them will hate the piano and give up in their teens. I'll post back in 20 years with the results....
Kathryn