Hi Mansun,
Looks to me like all the races played musical instruments-
Esty's Music Thread
(and links within)
Though the orcs seemed fondest of percussion and braying horns, so exactly how musical that was I don't know
.
The dwarves seem to be the only clarinet-ists, those metal keys and twiddly bits look tricky to make so perhaps only they had the necessary metal-working skills?
The Saucepan Man reckoned Gandalf was a demon on the Hammond Organ, but I'd take that with a pinch of salt if I were you.
Oh, and Elrond was a harpist. It often used to be reckoned a useful accomplishment for men and women of 'noble birth' to learn an instrument, perhaps Elrond had harp classes back in the the First Age?
Was thinking on the more general education question and apprenticeships seems to be how trades and skills were learnt in the Shire. Wasn't the Gaffer 'prenticed to Old Holman to learn his gardening?