In the annals of music so bad it’s good, Florence Foster Jenkins stands as a towering example. A New York socialite who fancied herself an opera singer, Foster Jenkins had a voice of weapons-grade awfulness — shrill, piercing, miles off-key — and yet in her own ears she was a coloratura to rival Lily Pons. Thanks to a handful of self-financed 78 rpm discs, Foster Jenkins became a cult hit, and in October of 1944 she became surely the worst singer ever to sell out Carnegie Hall.

Meryl Streep plays the great lady in “Florence Foster Jenkins,” and the moment she first appears — wearing an absurd angel costume with a straight face — we know we’re in for a treat. With Hugh Grant as St. Clair Bayfield, her devoted yet unfaithful husband, and Simon Helberg as Cosme McMoon, an unwitting young pianist for hire, “Florence Foster Jenkins” is a terrific screwball comedy with just the right touch of tenderness from director Stephen Frears (“The Queen”). Nearly everything about it, from Nicholas Martin’s sharp script to Alexandre Desplat’s lovely score, is pitch-perfect.

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“Florence Foster Jenkins” gets plenty of mileage from its heroine’s earsplitting voice — Streep clearly did her research, which couldn’t have been easy — but Frears is also interested in Jenkins as a person. Famed conductors such as Arturo Toscanini (John Kavanagh) and Carlo Edwards (a very funny David Haig) flatter her vanity and take her checks but conveniently disappear when she sings in public. Meanwhile, St. Clair bribes critics, bars them from entry or buys every paper to protect his wife from bad reviews.

St. Clair is the film’s most fascinating character, a smooth-talking scoundrel (he keeps a mistress, played by Rebecca Ferguson) who nevertheless dotes on his dowdy wife. Grant isn’t just good here, he’s dazzling. It’s as if he’s been rehearsing his whole life to play this charming, good-hearted adulterer. Surely the 55-year-old actor has just sealed his first-ever Oscar nomination.

Like Tim Burton’s “Big Eyes,” about kitschy painter Margaret Keane, “Florence Foster Jenkins” focuses on a figure of fun but locates something brave and noble inside her. As one of her mocking yet devoted fans insists: “The lady is a lesson in courage, and that’s why we love her.”