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This CD cover image released by Interscope shows “Cheek to Cheek,” by Tony Bennett and Lady Gaga. (AP Photo/Interscope) Image Credit: AP

By any standards, it is an improbable alliance. In one corner, the last man standing from the golden era of crooning — a singer who has spent years interpreting the tunes of the big band years.

In the other, the madcap pop diva famous for outrageous wigs, over-the-top concerts and dresses made from slabs of meat ...

But Tony Bennett and Lady Gaga are not quite the strange bedfellows they might seem.

Despite a 60-year age gap, the King of Cool and the Queen of Drama have a good deal in common. Both are Italian New Yorkers with a flair for live performance, and both cut their teeth singing the Great American Songbook.

The classy Bennett, 88, served his apprenticeship learning the standards at New York’s Paramount Theatre before going on to duet with Frank Sinatra and Ella Fitzgerald. Gaga, 28, won a New York state jazz competition in her teens before being swept away by the throbbing rhythms of the Manhattan club scene.

Now they’ve teamed up on Cheek To Cheek, a covers collection of classics by George Gershwin, Cole Porter and Irving Berlin.

It reiterates Bennett’s easy charm and flawless pitch — and shows Gaga in a fascinating new light: as an authentic jazz vocalist with decent phrasing and a winning appetite for playful, sassy interjections.

Bennett knows the secret of a good duet lies in a contrast of styles, adding the right amount of tempo to the title track and some tit-for-tat exchanges on Jerome Kern’s I Won’t Dance.

Refreshingly, without all the electronic bells and whistles that usually submerge her natural talent, Gaga enjoys herself.

In fact, Cheek To Cheek serves both singers well. For Bennett, it continues a process of introducing the classics of yesteryear to a younger audience that began with 1994’s MTV Unplugged; for Gaga, it puts music above her desire to shock. And that, perversely, is the most surprising move she has made in ages.