OK 
I'm half tone deaf... maybe 3/4 even.
AHHhhh I see what you're picking out now....The melody there is very similar to Zelda's lullaby, but not quite the same. You're not tone deaf.

Zelda's lullaby: In relative key is "Mi Sol Re" (notes are B D A)
Conan Song: In relative key is "Ti Do La" (note are B C A)
They even start on the same note, and the instruments sound the same, but the melodies are just a bit different - and where those notes lay within their respective keys and applications is very different. I see what you're saying now, but nope, not exactly from Zelda, but pretty similar. Nice ear!