As many melodies as there are pretty girls

How many melodies are possible? I was thinking about this recently. Mark Steyn's Song of the Week a while back was "Moonglow." He writes:
"Moonglow" is a conventional 32-bar AABA song - main theme, repeated, middle eight, back to the main theme. But the main A theme is very repetitive: Betraying its theme-tune origins, it's more like a riff than the principal building block of a song. It's not just that the first and third lines are identical, and that the second is all but. It's that the entire eight-bar phrase only has three notes: E, G and B. The odd bars are seesaws between E and G, and the even bars get the B. "It", "have", "way", "in", "it", and "have" are all on E. "Must", "been", "up", "the", "must", and "been" are all on G. "Moonglow" and "blue" are on B. And then for the heavy-footed fourth line Hudson goes back to the G: G-G-G-G-G-G. One note.
I can Name That Tune in one note, Johnny! So, have all the melodies been written? It doesn't sound like it.