Among the many bad movie genres spawned by Hollywood — geezer capers, biblical epics — the musical theater biopic may be the worst. Purporting to tell the life stories and celebrate the genius of classic American songwriters like George Gershwin and Cole Porter, these films, which flourished in the 1940s, instead offer tin-eared portraits of the men and their methods. If you watch a lot of them in sequence, as I recently did in a fog of disbelief, you might conclude that the greatness of Broadway’s golden age was the result of dumb luck, random inspiration and down-home values.

“Those ’40s biopics are fascinatingly, violently bad,” Ethan Hawke told me.

“A loser genre,” Richard Linklater added.

They have reason to be interested in the matter. In Linklater’s new biopic, “Blue Moon,” Hawke plays Lorenz Hart, the tiny, gay, alcoholic wordsmith whose hundreds of songs with the composer Richard Rodgers defined the caustic charm (“The Lady Is a Tramp”) and bittersweet balladry (“My Funny Valentine”) of the 1920s and ’30s. Avoiding hagiography along with garbled then-I-wrote timelines, “Blue Moon” offers a corrective to the biopic disease.

The biopic it particularly corrects is “Words and Music,” an eye-poppingly spurious 1948 portrait of Rodgers and Hart in which Hart is smallish (he’s played by Mickey Rooney) but neither gay nor alcoholic. He spends much of the story courting a made-up chorus girl whose rejection is said to be the “spark that was to affect everything.” Great Hart lyrics like those for “Spring Is Here” are plucked effortlessly from the ether when in truth they were harder than diamonds to mine.

The portrait of Rodgers (Tom Drake) is no more realistic. Far from the single-minded scold he was in real life, he is lovingly indulgent and apparently amnesiac. “I’m almost sorry to say there were none of the standard trials and tribulations you’d ordinarily expect,” he asserts at the start of the film, despite their famously tortured collaboration.

“Blue Moon” goes everywhere “Words and Music,” subject to the Motion Picture Production Code, could not. Hawke’s Hart may say he’s on the wagon, but he longingly sniffs at full glasses of bourbon. He also longingly sniffs at young men, making no secret of his predilections. If he is genuinely witty and believably artistic, neither of which qualities Rooney got near, he is also frankly pathetic.

That’s historically likely, at least on the day Linklater, working from a screenplay by Robert Kaplow, depicts. Not even a whole day, in fact: just a real-time 100-minute slice of it, much of it a monologue.

But what a crucial slice that is! It’s March 31, 1943, the opening night of “Oklahoma!” — the first musical Rodgers (Andrew Scott) has written with his new partner, Oscar Hammerstein II. Good sport that he is, Hart awaits the celebratory party at Sardi’s, steeling himself to offer false praise while enduring the shipwreck of his career that the new show represents.

“This circumstance is astonishing,” Hawke says. “It’s like being with Lennon and McCartney on the night they’re breaking up, and one of them is going to start a new band that’s bigger than the Beatles and the other is going to be dead.”

Though Hart did attend that party, “Blue Moon” doesn’t stick religiously to history. The New Yorker writer E.B. White shows up at the bar — an invention, if a plausible one. Hammerstein brings the 13-year-old Stephen Sondheim to the party. (He’s obnoxious.)

More significantly, Kaplow extrapolates a romantic interest for Hart from actual letters written to him by a young woman named Elizabeth (Margaret Qualley). Having him propose to her at Sardi’s is a fantasia, certainly, but unlike the absurd cover-ups in “Words and Music,” it reveals a deeper truth: that for an artist like Hart, even an impossible love is less painful than having lost Rodgers forever.

“The facts can’t be cement shoes,” Hawke said.

That the ’40s biopics are so bad on the facts as well as the spirit doesn’t render them entirely worthless. Created in part to take advantage of performers the studios had under contract while musicals were still big box office, they function like human jukeboxes. “Hey, here’s Judy Garland! Here’s Lena Horne!” as Linklater put it. “They may be patch jobs, but they are sometimes records of great performers giving it hell.”

So yes: Horne shows up to sing “Can’t Help Lovin’ Dat Man” in “Till the Clouds Roll By” (1946), the otherwise stultifying Jerome Kern biopic. Mel Torme gorgeously croons “Blue Moon” in “Words and Music.” The Cole Porter story “Night and Day” (1946) engages in another gay whitewash but includes Estelle Sloan performing an astonishing tap number to the tune of “Just One of Those Things.” Oscar Levant’s bravura renditions of Gershwin’s piano music are a highlight of “Rhapsody in Blue” (1945). And in “Yankee Doodle Dandy” (1942), Jimmy Cagney records for posterity the headlong, stiff-legged dancing of George M. Cohan.

On the other hand: “Till the Clouds Roll By” ends with “Ol’ Man River” — sung by Frank Sinatra and a thousand all-white extras. You may never recover.

“Blue Moon” has none of that. “In our movie, instead of a bunch of numbers we have a handful of people,” Linklater said. “We’re interested in them as artists.”

Artistry is what the ’40s biopics get most wrong. Not just the facts, though the depictions of composition, collaboration and show-making are boldly inaccurate. “Rhapsody in Blue” makes a fuss about Gershwin’s use of a diminished-ninth chord in “Swanee,” a chord that appears nowhere in it. In “Till the Clouds Roll By,” Kern, who wrote only music, is seen improvising the lyrics to “They Didn’t Believe Me,” his first hit. (The lyrics are actually by Herbert Reynolds.) In “Night and Day,” Porter comes up with “Begin the Beguine” while serving in the French Foreign Legion during World War I, just before an explosion crushes his leg. Nice, though he wasn’t in the French Foreign Legion, he wasn’t wounded in World War I and he wrote “Begin the Beguine” in 1935, on an ocean liner to Fiji.

But the real harm is to the bigger picture of creativity. These movies portray musical theater artists as average, upbeat American types, though in fact these men were, if not bohemians, nonconformists. (All but Cohan were either gay or Jewish or both.) That Porter’s long marriage to Linda Lee was sexless yet loving is an idea that Hollywood could not even contemplate. (A 2004 biopic, “De-Lovely,” did a better job.) That Hart joined Rodgers and his wife on their honeymoon, living one floor above them in London, is the act of an extreme personality, not the goofball little-brother leprechaun Rooney portrays.

As it happens, Hart forgot to turn off his tub, immediately flooding the newlyweds’ apartment — an apt image for the mutual inundation of his art and Rodgers’s. That’s the key thing “Blue Moon” corrects about Hollywood’s portrayal of the great American songwriters as lucky burghers sailing on happy clouds of easy inspiration and ambient romance. For the first time in film, we see where all that seemingly effortless art came from: from the endless brain work and bullheadedness of craft, fighting to stay afloat on a sea of mediocrity.