The Importance of Singing
There is a strong connection to ones abilities on their instrument and the ability to sing whatever they are trying to do with their voice.
The best musicians I know have a strong musical sense with their voice.
You can hear Glenn Gould, Oscar Peterson, or Keith Jarrett singing while they play.
The piano can be a detached instrument because you play a key, which then moves a lever, which then strikes the string. This is much more disconnected than say a violin where you feel the instrument vibrate against your body and the bow causes the string to vibrate.
1st order — voice, body rhythm (ala Bobby McFerrin)
2nd order — violin, clarinet, drums, ..
3rd order — piano
4th order — computer programmed music
The first and best place to start learning music is through singing. Ideally you start singing as a child.