Sing Sing Sing

Dear reader,
James is moving house and using this as an excuse not to do anything else.
Dear James,
Not the Carpenters song. Or the Travis song. Sorry. This Benny Goodman 1936 piece is one we're using in the opening sequence to episode one, though we still need to find out if the copyright has expired and we can use it for free. Otherwise I'll just compose a similar work myself, but we'd rather use this one.

I like this because Keith Moon's granddad plays drums on it. It's also very amusing to watch with the sound turned off. It all goes very nicely up until (3:22) and the vibraphone kicks in and we have ourselves an entirely different animal. They say the piano solo is very special too. It's a "four chorus, highly chromatic masterpiece". What does that mean, James?

This song featured in three Woody Allen films. Can you name them without looking at the wikipedia page? More importantly, can you tell me which British ice dancers used this for their winning 1981 routine?

There's also an even longer version but without the piano solo, notable for the looks on the audience's faces, as if Carnegie Hall were Benny Goodman's Free Trade Hall moment. There's also a woman at (0:49 who appears to have eaten her husband.