In the new film Save the Last Dance, Roy Johnson is a white jazz trumpet player who lives on the black South Side of Chicago. He has a goatee, he wears a weathered Lester Young hat and faded green cardigan sweaters, and he mumbles more than he talks in a voice made gruff and gravelly by too many late-night gigs in too many smoke-filled clubs. A deadbeat dad, he has a poster of black avant-garde Chicago trumpeter Malachi Thompson hanging in his kitchen.

There was a time, in the ’40s and ’50s, when Roy would have epitomized cool, the outcast white boho who chooses to live on the jazz margins of after-hours urban blackness. But now he’s just a relic — crusty, outmoded, and irrelevant, a specter creeping in an Eminem world.

Roy’s ballet-dancing daughter, Sara, whose story Save the Last Dance tells, has just moved in with him after the death of her mother, has just started attending the local black high school in Roy’s neighborhood, and has just realized that in order to be cool — or, as we’re told, “slammin’ ” — she must be schooled in hip-hop. Before long, she’s rehearsing ballet moves to Biggie and dropping beats on a Juilliard audition. That Roy plays jazz doesn’t make him cool to Sara. When Sara’s black boyfriend, her hip-hop tutor, comes over to Roy’s rundown apartment, he wrinkles his brow at the music and tells her he’s not a fan.

The tenets of American cool have always been rooted in blackness and brokered by whiteness — both Roy and Sara are who they are because of their involvement with black music — but as Sara’s coolness eclipses Roy’s, we also see that the tenets always change: from trumpets to turntables, from the white and black men typically at the center of cool’s histories to the white and black girls at the center of cool’s futures (Save’s opening weekend audience was estimated at 80 percent female, 30 percent of whom were black). One of the numerous points Lewis MacAdams makes about the cultural history of cool in his new book Birth of the Cool: Beat, Bebop, and the American Avant-Garde (Simon & Schuster) is that it is mercurial, hopping from outsider locale to outsider locale, always on the run from squares and Gap ads.

No matter what citizen of cool MacAdams gets to know — Jackie McLean or Jack Kerouac, Chano Pozo or John Cage — it remains a stylistic space of kinship where avant-minded whites take cues from blacks who had to be avant-minded to survive, who had to strike a cool pose (in Amiri Baraka’s wonderful phrase “silent, yet knowing”) as armor in a war of dehumanization they were never supposed to win. MacAdams, a white poet and journalist from Texas who lit out for the cool of New York, is part of it too. Cool, he says of himself, was “a ticket out of the life I felt closing in all around me.”

Birth of the Cool takes its title from the 1949-1950 recordings, originally released as 78s, that were collected in an album as Birth of the Cool in 1957 — a “cool jazz” classic (just reissued yet again by Capitol) produced by the pairing of black trumpet player Miles Davis and white arranger Gil Evans. MacAdams tells us that by 1957 Davis had already been to Paris and had fallen in love with Juliette Greco, a white chanteuse who sang to clubs full of Europe’s version of cool — Sartrean existentialists. The pairings of Davis and Evans and then Davis and Greco are foundational, exemplary moments for MacAdams’s trajectory of cool as an American margin marker, the secret bonding code between black and white avant-gardes of artistic innovation.

No matter where cool goes in the book of Birth, it always resonates with jazz. But the jazz of cool is not Ken Burns’s PBS jazz, not the from-Louis-Armstrong-to-Duke-Ellington tradition that Burns and his chief ideologue, Wynton Marsalis, have boxed up and institutionalized as the music of the “American gumbo.” Cool’s jazz is the Minton’s agit-bop of Miles Davis, Dizzy Gillespie, Thelonious Monk, and Charlie Parker. It’s the jazz of shadow dwellers and basement scientists, of heroin highs and tilted berets and Yoruba chants, of playing “out” as a way of living out — jazz that peeps into the gumbo pot but wants to make a bowl of its own instead.

The Burns/Marsalis/Lincoln Center refrain is that jazz is “America’s music”; they stamp national ownership on an art created by post-slavery American blacks precisely because they weren’t allowed full participation in America. When heard through the ear of cool, though, jazz is music in response to America, in the face of America, music that instead of accepting the America in front of it created (to borrow a phrase from cool guru William Burroughs) a “potential America” instead.

“Whose foot has been in my ass?”, Dizzy Gillespie asked himself when the government tried to draft him. “The white man’s foot has been buried in my asshole up to his knee.” It’s what Burns misses, MacAdams gets, and Save the Last Dance ignores. The art of jazz is removing that foot. The art of cool is making it look as if it had never been there.

In the new film Save the Last Dance, Roy Johnson is a white jazz trumpet player who lives on the black South Side of Chicago. He has a goatee, he wears a weathered Lester Young hat and faded green cardigan sweaters, and he mumbles more than he talks in a voice made gruff and gravelly by too many late-night gigs in too many smoke-filled clubs. A deadbeat dad, he has a poster of black avant-garde Chicago trumpeter Malachi Thompson hanging in his kitchen.

There was a time, in the ’40s and ’50s, when Roy would have epitomized cool, the outcast white boho who chooses to live on the jazz margins of after-hours urban blackness. But now he’s just a relic — crusty, outmoded, and irrelevant, a specter creeping in an Eminem world.

Roy’s ballet-dancing daughter, Sara, whose story Save the Last Dance tells, has just moved in with him after the death of her mother, has just started attending the local black high school in Roy’s neighborhood, and has just realized that in order to be cool — or, as we’re told, “slammin’ ” — she must be schooled in hip-hop. Before long, she’s rehearsing ballet moves to Biggie and dropping beats on a Juilliard audition. That Roy plays jazz doesn’t make him cool to Sara. When Sara’s black boyfriend, her hip-hop tutor, comes over to Roy’s rundown apartment, he wrinkles his brow at the music and tells her he’s not a fan.

The tenets of American cool have always been rooted in blackness and brokered by whiteness — both Roy and Sara are who they are because of their involvement with black music — but as Sara’s coolness eclipses Roy’s, we also see that the tenets always change: from trumpets to turntables, from the white and black men typically at the center of cool’s histories to the white and black girls at the center of cool’s futures (Save’s opening weekend audience was estimated at 80 percent female, 30 percent of whom were black). One of the numerous points Lewis MacAdams makes about the cultural history of cool in his new book Birth of the Cool: Beat, Bebop, and the American Avant-Garde (Simon & Schuster) is that it is mercurial, hopping from outsider locale to outsider locale, always on the run from squares and Gap ads.

No matter what citizen of cool MacAdams gets to know — Jackie McLean or Jack Kerouac, Chano Pozo or John Cage — it remains a stylistic space of kinship where avant-minded whites take cues from blacks who had to be avant-minded to survive, who had to strike a cool pose (in Amiri Baraka’s wonderful phrase “silent, yet knowing”) as armor in a war of dehumanization they were never supposed to win. MacAdams, a white poet and journalist from Texas who lit out for the cool of New York, is part of it too. Cool, he says of himself, was “a ticket out of the life I felt closing in all around me.”

Birth of the Cool takes its title from the 1949-1950 recordings, originally released as 78s, that were collected in an album as Birth of the Cool in 1957 — a “cool jazz” classic (just reissued yet again by Capitol) produced by the pairing of black trumpet player Miles Davis and white arranger Gil Evans. MacAdams tells us that by 1957 Davis had already been to Paris and had fallen in love with Juliette Greco, a white chanteuse who sang to clubs full of Europe’s version of cool — Sartrean existentialists. The pairings of Davis and Evans and then Davis and Greco are foundational, exemplary moments for MacAdams’s trajectory of cool as an American margin marker, the secret bonding code between black and white avant-gardes of artistic innovation.

No matter where cool goes in the book of Birth, it always resonates with jazz. But the jazz of cool is not Ken Burns’s PBS jazz, not the from-Louis-Armstrong-to-Duke-Ellington tradition that Burns and his chief ideologue, Wynton Marsalis, have boxed up and institutionalized as the music of the “American gumbo.” Cool’s jazz is the Minton’s agit-bop of Miles Davis, Dizzy Gillespie, Thelonious Monk, and Charlie Parker. It’s the jazz of shadow dwellers and basement scientists, of heroin highs and tilted berets and Yoruba chants, of playing “out” as a way of living out — jazz that peeps into the gumbo pot but wants to make a bowl of its own instead.

The Burns/Marsalis/Lincoln Center refrain is that jazz is “America’s music”; they stamp national ownership on an art created by post-slavery American blacks precisely because they weren’t allowed full participation in America. When heard through the ear of cool, though, jazz is music in response to America, in the face of America, music that instead of accepting the America in front of it created (to borrow a phrase from cool guru William Burroughs) a “potential America” instead.

“Whose foot has been in my ass?”, Dizzy Gillespie asked himself when the government tried to draft him. “The white man’s foot has been buried in my asshole up to his knee.” It’s what Burns misses, MacAdams gets, and Save the Last Dance ignores. The art of jazz is removing that foot. The art of cool is making it look as if it had never been there.