Smoothing out the rough edges

When you normally play, the human ear is unable to pick up the exact timing you hit a chord. However, because you rarely strike all notes at the same time, the recording into the app picks up each specific instance that the note was struck, thus creating a sort of "rough" edge to the music that is less smooth than a real experience when listening first hand.

Is there a way to smooth out these rough edges? Is there a way to create a better recording experience or perhaps shift the notes after the fact in the program in order to create this smoother sound?

Appreciate any thoughts. Thanks!