tune + neanderthal: Someone whose music taste didn't evolve beyond Pat Boone/Perry Como.
A (singing): So you think you can tell/heaven from hell/blue skies from pain...
B: Wo dat?
A: Pink Floyd.
B (clueless): Pink...
A: Just cut it, man, stick with Perry Como - you know, catch a falling star...(to himself) Such a neanderthal, tuneless...yesss, that's it, tuneanderthal, difficult to say though.