The short answer
In unmodded Build 42 you cannot sit down and play a guitar, keyboard, horn or drum kit for fun. The big instruments are coded as InstrumentWeapon items: you can swing them at zombies, and that is all. There is no play action, no song, and no boredom or unhappiness effect attached to them in the item data we checked.
Three things in the music space do work in vanilla. Whistles and the harmonica replace your shout with a louder sound. CDs played in a CD player are the vanilla way to use music for mood. Radio stations broadcast in the first days, though their main value is information, not music. Everything else on this page, from drum kits to pianos, is decoration or a mod feature.
If you want a real music system, it comes from Workshop mods, covered in the last part. For the moodles that music is supposed to fix, see mood and boredom and the moodles list.
