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Sinatra liked to think he naturally belonged to the brotherhood of jazz musicians. Norvo opens the show with a number and then introduces "a new boy singer we've added". This is clearly a gag but it's also a recognition that Norvo and his musicians aren't just there to provide a foil for Sinatra's celebrity.
What ensues is both a band gig and also one of those performances where the musicians don't seem to be troubled by the worry of who might be listening. It's not just the way Sinatra plays with the lyrics or the inclusion of on-tour gags like "On The Road To Mandalay" (lyrics by Kipling). It's the serene, carefree bounce of the way he leans on the drummer's roll underpinning the line "when I get you up there" in "Come Fly With Me".
The performance, which is frictionless throughout, is beguiling enough to make you forgive the tape hiss. The show was only recorded because somebody in the venue's sound booth decided to press "record" just as it got under way and it wasn't released until the late 90s.
As Adam Gopnik points out, the downside of Sinatra's perfectionism could be a tendency to chide musicians to the point of bullying. When the pianist gets the wrong chord at the beginning of "All The Way" Sinatra sings deliberately off-key. I'm trying to imagine the rock singer who'd have the nerve to do that.