Without a written notational system, something that did not exist in Dovid’s time, it is nearly impossible to preserve a melody.
I’ve not done any research into the age of the melodies we use for things like the leining, so I may be mistaken, but it’s seems that they’ve survived hundreds if not thousands of years. If we could manage to pass them along generation to generation, why didn’t those of Dovid HaMelech get passed down, as well?
You are mistaken. I’m not sure where the origins of the musical notes that we use in leining are, but it’s fairly clear that it has morphed and changed over time. I’ve been teaching leining to bar mitzvah boys for over 20 years and I can tell you that none of the boys I taught lein exactly the same way that I do — nor do I lain exactly the way my teacher did. Much as word pronunciation changes over time*, I would expect a musical “language” used by far fewer people to experience an even greater “drift” over the generation.
The Wolf
* An excellent book on language that covers, among other things, how word pronunciations in the English language have drifted over the years and locations is Bill Bryson’s “The Mother Tongue.”