Did the world demand more jazz from Lady Gaga and Tony Bennett? Well, that’s what the world’s gonna get. Cheek to Cheek, out September 23, will have a slew of classics (including “It Don’t Mean a Thing [If It Ain’t Got That Swing],” “Bewitched, Bothered, and Bewildered,” and “Lush Life”) and one original song written by Gaga called “Paradise.” First, their cover of “Anything Goes,” done as traditionally as Gaga can — although she does wear a piano caftan at 0:26.