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Ahhh. But while it's the first music score for "St. James Infirmary," the sheet music for "Gambler's Blues," an earlier title for the song, had been printed four years earlier. The composer credits were to, not Joe Primrose, but Phil Baxter and Carl Moore. I wrote a bit about it here: The Golden Grail - you'll find more in the book.
"St. James Infirmary" aka "Gambler's Blues" had been around for many years before being taken into a recording studio. There were a ton of variations. There were many verses. The song, chameleon-like, changed its colour for the environment it stumbled into. The sheet music below, the first of its kind, gives us a taste of the song. But the song was more than this. It assumed many shapes; there were many versions.
This was just one of them.