>>16020331And, I guess it also represents Travis's own mind, if I could stretch it.
At the end of the movie, he goes back to doing what he does without a shred of care about it all or change shown. I assume that you know how it's clearly implied that he hasn't changed at all and would simply go back to being a timebomb after the final scene, just not sung as a hero the next time he explodes. It was simply a fluke, this time around. Again, hearing the jazz tricks you into thinking that it's all okay and you should feel romanticized towards the things that are going around, and that you should keep calm and carry on. Nothing wrong.
That's the state his mind is in, just flowing on, with zero attention to whatever is it that's happening around him. Not exactly to the depravity of the city, he himself is proud in seeing that and making a stand against it, but rather himself. He'll never have that tune stop playing in his head, telling him that it's all okay and he should go on with how he is. I feel that as long as you have that music playing, you're just not capable of feeling like anything that you're doing is wrong or should change, you get absorbed in the mood of it all. The worst thing about it is how it makes everything feel alright, while it's not.
And, so, yeah, maybe that's how it represents the state of Travis. It's all kind of dreamlike, and he won't ever truly realize what he's doing until it's too late.
Therefore, you get a bit of a look into his sense of mind every time that you listen to the theme, and that's what it gives it that sinister feeling, along with everything from before. It tells you that it's okay despite, and that's a bit scary.
Anyhow, I guess that's enough rambling about the theme of a movie I watched probably over half a decade ago, now. Character limit, I'll see if there's more.