The United States vs. Billie Holiday starring Andra Day is the third film adaptation drawn from Holiday’s life story—and the third that looks at Holiday through a prism of sensationalism, sordid or heroic, rather than as a groundbreaking musician who expanded and refined the possibilities of jazz.

Originally, there was Lady Sings the Blues (1972), starring Diana Ross and directed by Sidney J. Furie, followed by a play by Lanie Robertson, Lady Day at Emerson’s Bar and Grill (1986), eventually produced as an HBO film (2016) starring Audra McDonald and directed by Lonny Price. There may be some merit to these movies, but the music in them takes a distant second place to Holiday’s drug use, arrests, troubles with men, difficult childhood, etc.

Anyone hoping The United States vs. Billie Holiday would be any different need only note that, according to a recent NPR profile of soundtrack composer Kris Bowers, “One of the first things director Lee Daniels told his composer was that he doesn’t care for jazz.” Hilton Als, in a scathing review in The New Yorker, called The United States vs. Billie Holiday “an illustration of the nasty impulses that spell out Daniels’s interest in degradation.”

Forget the movies. If you do care about jazz, Billie Holiday is simply in the firmament, someone whose technical contribution made the music possible.

Two of Holiday’s obvious inspirations are Louis Armstrong and Bessie Smith. Armstrong gets credit for being one of the first (and certainly the most influential) to create swinging improvisations on pop songs from Tin Pan Alley. This is the whole universe of “standards”—George Gershwin, Cole Porter, the “Great American Songbook,” the hefty stack of tunes your grandma can sing and that are still kept in rotation by many contemporary jazz practitioners.

When Billie Holiday performed those standards, she went further than Armstrong. Holiday didn’t invent the torch song, but she came to define it. This deep melancholy came in part from Bessie Smith, the master of early blues, who delivered each earthy line with devastating conviction. Everyone believed Bessie Smith when she sang her downhearted truth. Everyone believed Billie Holiday when she reinvented glamorous standards with a rough-hewn bluesy edge.

Even at a bright dance tempo, Holiday offered a complex emotion, the tear beneath the smile. She really improvised; the melancholy was always fresh. While Holiday was a composer—one of the few singers who added active standards to the repertoire, including “God Bless the Child,” “Don’t Explain,” and “Lady Sings the Blues”—any piece performed by Holiday was recast as a Holiday original, with some now existing in the public consciousness as “by Billie Holiday”: “My Man,” “Good Morning, Heartache,” and of course the epochal “Strange Fruit.”

One of Holiday’s key associates was Lester Young, often considered the second-most-important jazz soloist after Louis Armstrong. Young famously named Holiday “Lady Day.” In return, she named Young “Pres” (short for “President of the Tenor Saxophone”). Before Pres met Lady Day, his saxophone lines bobbed and swung with effortless grace. After studying Holiday’s approach, Young darkened his tone and added more ballads to his repertoire.

Miles Davis also studied Billie Holiday. They were friends. He talked about her a lot over the years, including for several pages of his autobiography. Davis said she sounded like a horn, and in a 1958 interview he drew a direct line from Lady Day to his famous moody interpretation of “My Funny Valentine”:

I’d rather hear her [Holiday] now. She’s become more mature. Sometimes you can sing words every night for five years, and all of a sudden it dawns on you what the song means. I played “My Funny Valentine” for a long time—and didn’t like it—and all of a sudden it meant something.

Holiday’s affect is not just bluesy or melancholy. It is also jagged, even surreal. When forming his aesthetic, the greatest jazz surrealist of them all, Thelonious Monk, would lie in bed for hours, staring at a photo of Holiday taped to his ceiling and illuminated by a single red lightbulb. Monk’s unforgettable cubist performances of sentimental standards like “Just a Gigolo” and “Don’t Blame Me” would be unthinkable without Lady Day in the background.

One of the first people to offer a systematic approach to studying jazz was Lennie Tristano. Tristano made his piano, trumpet, and saxophone students sing along to Holiday records, attempting to get each inflection exactly right. In time, star Tristano pupil Lee Konitz also enforced the same discipline with the next generation. It’s not just the Tristano school. For over 50 years, Ran Blake has been teaching the practice of emulating Billie Holiday solos at the New England Conservatory of Music, and if you take a lesson with Wynton Marsalis tomorrow, he’s going to tell you to listen Holiday, especially for rhythm.

Rhythm is very important, for jazz is the American mixture of European classical music and African classical music. From Africa comes the rhythmic information. Much of the time, duple and triple meter exist simultaneously, a basic polyrhythm that musicians who only know European information simply can’t get right. Of the earlier jazz masters, Billie Holiday has the most advanced polyrhythmic phrasing, outdoing both Louis Armstrong and Lester Young in metrical complexity. It’s hard to notate, which is one reason Tristano advocated singing along with the records, but that doesn’t mean it isn’t precise. It is precise, just as precise as the lead conga drum in an Afro-Cuban ensemble.

Lady Day’s phrasing is sometimes described as “late” or “behind the beat,” but that’s hardly the whole story. In the same interview, Miles Davis explained further:

She sings way behind the beat and then brings it up—hitting right on the beat. You can play behind the beat, but every once in a while you have to cut into the rhythm section on a beat and that keeps everybody together. A lot of singers try to sing like Billie, but just the act of playing behind the beat doesn’t make it sound soulful.

A good beat brings out Holiday’s rhythmic expertise. One of her best drummers was Jo Jones, known as “Papa” Jo Jones, for every significant American drummer followed in his wake thanks to the rhythmically revolutionary music Jones played with the Count Basie band. Papa Jo is present on most of the sessions with Billie Holiday and Lester Young together, all of which belong in the time capsule documenting the finest of human achievement.

“He Ain’t Got Rhythm” is a novelty number of no social import whatsoever, written by Irving Berlin in 1937 for the movie On the Avenue, and an obvious response to Gershwin’s big hit “I Got Rhythm” from a few years earlier. Berlin’s song would have have sunk without a trace—except that Billie Holiday lavished upon it a peerless vocal performance.

In the first chorus, clarinetist Benny Goodman and pianist Teddy Wilson peacefully intertwine. Listen to Jo Jones. He’s mainly playing a two-beat feel on the high hat, with a kind of irresistible momentum that is also phenomenally relaxed. The technical term might be, “going backwards and forwards at the same time.” Lady Day appears in the second chorus. It’s profoundly ironic that this trivial ditty is about not having rhythm, for she demonstrates the absolute polar opposite. The third chorus offers a tenor saxophone solo that has gone into the books as quintessential Pres. Trumpeter Buck Clayton takes it home.

If there had been another take, Holiday would have done it differently, offering another aspect of her technical excellence as an improviser and jazz musician. Sublime vocal control, playful, a bit sad, swinging like crazy: The timeless Billie Holiday. Maybe someday they’ll make a movie about her.