from 1902 and again in 1973

Using the commenters clues, I poked around the intertubes (oops: my internet, youtube contraction) and found it. It's what I thought it was, but I'd forgotten about the intro part, and I couldn't remember what it was called, and I couldn't remember quite how it went. Other than those minor details, I knew what it was. :))
Now it will be rolling through my head all day! Definitely entertaining!

Well, I found all your comments very Entertaining, too. Thanks.

sbemus-- I grinned at the tie-in with Joplin! Scott woulda liked that, too, I'm sure.

david-- Obviously a page for cello and clarinet, or such. Sharp catch!

PotatoMum-- with my humming, you would still be scratching your head!

If you keep this up I'm going to have to call you and have you hum it for me over the phone!

(in 1973 there were too many people who thought Marvin Hamlisch wrote this)

Kind of cruel to the amateurs, putting up the B-flat part for the melody and the C part for the bass!

Yes, very entertaining, says this member from near Joplin!

Sure is entertaining! :) Thanks, Oddio!