Probably "Sesame Street"; this is basically an old "Sesame Street" thing but improved for adult sensibilities.

I heard nobody singing. It's likely not a song.

I thought it was early hip hop.

Yeah, I know what you mean, the music sounds really, really familiar and very reminiscent of classic SESAME STREET live-action filmed-on-location segments.

I'll give three possibilities in declining order of probability:

1) It's stock royalty-free music from a music library that you might have heard as background music in a local TV commercial.
2) TV Funhouse had it composed for them specifically in the style of classic SESAME STREET.
3) They licensed music, possibly composed by Joe Raposo, from SESAME STREET.

No, I didn't spend hours fruitlessly watching every SESAME STREET live-action segment that I could find with music by Joe Raposo to see if I could find a match just to end up watching the full TV FUNHOUSE "Western Day" episode and see "Original Music: Compositions Inc, Steven Gold, Adam Schleisinger" in the end credits.

Just kidding, I totally wasted most of my day doing all that. Not that I was going to do anything productive on Thursday.

Joe Raposo's background music track for "Primates on Film" isn't identical but it's pretty close: starts with a piano and features a jazz flute:

http://youtu.be/RE1g8gTYSG0

Like, I wouldn't be surprised if that's one of the classic SESAME STREET segments Compositions Inc, used as inspiration for creating the music, although they composed it pre-Youtube so I guess their inspiration would have been limited to whatever old SESAME STREET clips they could tape off Noggin.

This show still makes me laugh. I was just enrolled in college and finally had cable TV so it was this and Space Ghost Coast to Coast. I don't think we'd have things like Adult Swim without this.

There's a lot of things I can say the 18 year-old me would laugh at that the 32 year-old me would not, this isn't one of them.