Thanks, all, for telling me about Bix Biederbecke.

I found a great recording of a 1927 jazz tune in the belly dance minor here:

http://www.youtube.com/watch?v=ZxP0cf1bpTM&feature=related

It got my husband up from his sick bed to ask with pleasure what it was.

I can just imagine Bertie Wooster, in London, 'swinging a swift shoe' to it.

Next I expect somebody to tell me that it's New Orleans jazz. But it's not.