Lots of times when a musician wants to play an instantly-identifiable “Oriental” musical riff (this is too stereotypical to be “Asian,”) he’ll play a particular short tune. IIRC it’s present in “Limehouse Blues” and that “I really do believe that I am turning Japanese” song. If you’ll pardon the ASCII rendering of musical notes, it goes like this: “chinga-chinga ching ching, choong choong CHING.” It’s the kind of thing they played in madcap seventies comedies when a ninja appeared out of nowhere. “Oh no- the man in the ape suit has stolen the diamond!” <enter ninja> <cue music> “chinga-chinga ching ching, choong choong CHING, chinga-chinga choong choong ching. BONNNNNNNG!”
Then there’s the stereotypical Egyptian music (I suppose it’s also used for India, especially snake charmers.) I can’t do an ASCII rendering, but I’ve heard it put to the following lyrics:
There’s a place in France
Where the naked ladies dance
And there’s a hole in the wall
Where the men can see it all.
The “Egyptian” tune is sometimes called “The Snake Charmer” and is sometimes found in books of piano instruction. Among other uses, i serves as the last few bars of the long-lived but obscure Colon Sphincter Band’s piece You Can’t Outrace the Mummy. There the band joins the vocalist to sing "nyah-nyah-nyah, nyah, nyah-nyah-nyah-nyah n’nyah…
I recall hearing the late Steve Allen talk about how it fell to him to once entertain a group of Asians. I believe it may have been a delegation from the People’s Republic of China. He started off by playing the traditional “Oriental” piece, and got nothing but blank stares. Not only was it unfamiliar to them, but the whole sound of it seemed foreign to them. Allen admitted he had no idea where that tune came from, or where we got the idea that it was Chinese, anyway.
Rightly or wrongly, I associate it with silent films, and suspect it goes back at least to that era.
I recall that Jay Leno once observed that one frequently heard that tune played whenever a Chinese character toddled onto the screen in an old TV show, possibly because the producers feared the audience would otherwise think they had a Klingon on their hands. He went on to ask: when Clint Eastwood walks on screen in a movie dubbed into Chinese, do they play How Much Is That Doggy in the WIndow?