I remember that Ken Colyer made an impressive recording of it long ago.
I have listened to it and note that it's essentially a 16-bar tune with some lovelier-than-usual harmonies. It's a useful tune because you can play it at slow-to-medium tempo, thereby creating a contrast with some of the quick numbers we all love to play.
This is how I've worked it out and this is how I shall try to play it, unless anyone supplies me with a more accurate version.
(Insertion: Henry - banjo from Germany - has just told me it should be B7. I think he's right.)
In some performances on record, free-style solos on a straightforward 12-bar blues progression are played after the above, before returning to the 16-bar theme to finish.
What exactly was a 'Saturday Night Function'? Most probably it was a means of paying the rent. You invited people to buy tickets for a Saturday-night party at your house; and the admission charges covered the cost of your rent.
There's another Duke Ellington tune with the same sociological background - Rent Party Blues.