What is a melody?

Well, I suppose we can reduce it to a list of numbers, where 1 corresponds to the note of the key and then up through to 12 for the other semitones.

It is a matter of common experience that some sequences of notes, or numbers, are melodies, but different sequences are not.

Is there some rule for this? How might we derive it? Why does it exist?

And I am not talking about sequences of notes which are not in any key. If I had, for example, the chords G, D, C, C, and I only played random notes within that chord sequence, the vast majority would be still meaningless. One, however, would be There She Goes by the La's. Another would be Waterloo Sunset by the Kinks. This is what I am talking about.

Why do they form qualia? Why is there an inherent meaning to the sequence of notes/numbers {1 5 1 7 1 4 1 5 1 3 1 3 1 3 1 -7 1} of joy and optimism? Why is there a different quale associated with Waterloo Sunset, of peace, apathy, and contentment?

Is there some sort of evolutionary advantage to this? It is extremely hard to see why. So is there some sort of objective pattern to melodies?

I don't have any clear answers.