Having heard for the past few years at various conventions, players noodling around the chord sequence and calling their efforts "Sweet George Brown" I felt that I should at least ATTEMPT to establish what the ACTUAL melody is. !

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Be aware of the lyrics.. there are more but just these are relevant:-
Sweet Georgia Brown
Words by A. Ken Casey, Music by Maceo Pinkard
Chorus
No gal made has got a shade on Sweet Georgia Brown.
Two left feet, but oh, so neat has Sweet Georgia Brown.
They all sigh and wanna die for Sweet Georgia Brown,
I'll tell you just why, you know I don't lie (not much!).
It's been said she knocks 'em dead when she lands in town.
Since she came why it's a shame how she's cooled 'em down.
Fellas that she can't get Must be fellas that she ain't met.
Georgia claimed her, Georgia named her, Sweet Georgia Brown. I'm not sure of the chord on the words "not much" (Bars 23-24) but the Ab-E7 feels right for the melody notes, also the half diminished chords (m7b5) may seem over elaborate but they are in keeping with the era and genre'.
(Please excuse the non syncopation in the notation, I just can't get around how to do it in Tabledit.)
All corrections GRATEFULLY and graciously accepted..
I also can't figure out why the program misses out the crotchet rests (F minor section) in the notation on page 2 ? It's displaying on the screen !!
AND the hi-resolution pdf is
HERE