I think we need some clues. Another bit of mine goes:
Daa daaaa, da da-da-da daaaaaa, da daa daaaa, da da-da-da daaaaaaa,
da daaaa, da da-da-da daa daaaa, da daa daaaa, da DA-DA-DA DAAAAAAA.

[Raak] I think it's Star Trek (original series).

[Darren] That's it!

*Clue* The answer to mine was put forward by someone else as a suggestion to ZK's No.9, also a cartoon, which turned out to be "Dangermouse".

The only cartoon guess I can see is The Tom and Jerry Show, but listening to the theme I'm doubtful.

[Kim, rab] Ooooh - y'know ... I think rab has picked up the right clue. Weren't there TWO different Tom & Jerry productions? Each with its own tune? Is this the Fred Quimby one?

[rab] I can only surmise that you're either not listening to the tune properly (doubtful) or listening to the "other" tune, because, as Chalks says, this is the tune to the Tom & Jerry cartoons from the unsurpassed Fred Quimby. Joint honours to rab and Chalky! Sing it now with me: "Pa-pa-pa paaah, paaah pah-pa paaah...."