The headline blared: “Why Women Musicians Are Inferior.” It was cringe-inducing even in 1938, when the respected jazz publication DownBeat printed the essay. A rebuttal from a female saxophonist — a “skirt swinger” — was further ridiculed when DownBeat slapped on the title “How Can You Blow a Horn With a Brassiere?”

Two generations passed before female bandleaders, instrumentalists and composers — long ensconced in jazz history but often marginalized or maligned — began being saluted at “women-in-jazz” festivals.

The highest-profile example is the Kennedy Center’s Mary Lou Williams Women in Jazz Festival. But organizers in Washington have decided that this year’s undertaking, running Thursday through Saturday, will be the last to focus exclusively on female headliners. Next year, it will be rechristened the Mary Lou Williams Jazz Festival, keeping the name of the venerated pianist, composer, arranger and all-around jazz lodestar, but featuring at least one all-male act for the first time.

Kennedy Center programmers said the emphasis on women was too limiting and might at this cultural moment have the unintended negative effect of raising the question of its performers: Is she a great musician, or a great female musician?

Center officials characterize their decision as a victory for female jazz artists. After all, they said, women have proliferated at all levels in jazz since the late pianist and educator Billy Taylor founded the festival in 1996.

“I believe that with the current role of women involved in music, the designation may seem a bit pejorative,” said Kevin Struthers, the Kennedy Center’s director of jazz programming who has overseen the festival since 1997.

“With the name change,” Struthers said, “we’re not going to diminish the opportunities for women to perform here. I hope the impact will be a fulfillment of Billy’s vision that we don’t need to designate these wonderful women by gender. Talent is talent is talent.”

The decision to redefine the Kennedy Center’s jazz festival was urged by Jason Moran, the 38-year-old pianist and composer who began working as a jazz adviser to the arts center in 2011. A year earlier, he received a MacArthur Foundation “genius grant” in part for opening the boundaries of jazz to include hip-hop and other musical expressions.

Moran said his musical development was “inspired by everyone,” including women such as the jazz pianist Geri Allen, so he did not place a stark emphasis on gender. In his mind, the Kennedy Center’s festival would benefit by concentrating instead on the legacy left by Williams, who died in 1981 at 71.

Although she remains largely obscure to non-jazz followers, Williams enjoyed a sprawling career that included writing hits for the big bands of Benny Goodman, Duke Ellington and Dizzy Gillespie. Her apartment in Harlem had an open-door policy for musicians seeking her guidance, among them pianist Thelonious Monk, saxophonist Charlie Parker and trumpeter Miles Davis.

“Mary Lou Williams is such a pivotal figure to the music — her mentoring of modernist jazz artists,” Moran said. “Her relationship to the music — to think she’s only important to female musicians would be to limit her importance to the world of music.”

There has long been a strong political undercurrent associated with music festivals honoring women, and the jazz circuit was no exception. The first-known large-scale women-in-jazz event took place in March 1978 in Kansas City, Kan., a site chosen by the organizers because Kansas was among the first states to ratify the Equal Rights Amendment.

The festival drew national coverage and 2,000 ticket buyers to see performers such as pianist Marian McPartland, guitarist Mary Osborne and bandleader Toshiko Akiyoshi.

The Kansas City event, which shuttered by the mid-1980s, begat others in New York, Seattle and eventually Washington, where institutional backing of the Kennedy Center has kept it afloat.

Taylor half-jokingly worried at first about the ability to fill the roster of performers and attract an audience. But it soon became apparent the problem was one of bounty. There were too many musicians and not enough spots.

Those featured that first year included McPartland, bandleader Maria Schneider, trumpeter Ingrid Jensen, flutist Dotti Anita Taylor and the dexterous singer Dee Dee Bridgewater. This year, Bridgewater, a Tony- and Grammy-winning entertainer, is marking her fifth consecutive year as host, and the event is taped so that she can rebroadcast it on her National Public Radio show “JazzSet.”

For female musicians, the world has changed in a way those Depression-era DownBeat editors would never have imagined. Whether there remains a glass ceiling still in need of shattering with a High C is much debated among musicians and aficionados.

Lee Mergner, publisher of JazzTimes, said his magazine stopped running an annual women-in-jazz issue years ago but then recently revived the concept, “not because they’re underappreciated but because they are great artists.”

“Our first thought was, it’s silly — we [are] covering women throughout the year,” Mergner said. “And we came back to the women-in-jazz issue because it’s great to celebrate women. It was about more than just having it serve as advocacy.”

McPartland, 95, who helped inaugurate several of the women-in-jazz festivals, discounted the importance of gender entirely over her eight-decade career. “I never focused hard on being a woman in jazz,” she said. “I was glad to be in the business.”

Of the 1978 Kansas City event, she recalled, “I particularly didn’t think of it being a women’s festival. I was there because these were my friends.” And she said Williams, with whom she shared that stage, felt similarly: It was to them strictly a job, no different from a club date or an appearance on television or the radio.

Whatever happens at the Kennedy Center, the District remains home to another women-in-jazz festival. It was started in 2011 by Amy K Bormet, a garrulous and gifted 28-year-old pianist whose interest in music was piqued by the free Kennedy Center tickets she used to get while attending the Duke Ellington School of the Arts.

She subsequently performed at the Mary Lou Williams event, which she called “one of the most important festivals that really believed in female instrumentalists.”

She called Moran, the Kennedy Center’s jazz adviser, “inventive” and someone who can “spice up” the festival in the aftermath of Billy Taylor’s death in 2010. But she expressed concern about dropping “women” from the title.

“I’m glad the Kennedy Center has finally decided women have reached equality in jazz and across the board,” she said, somewhat caustically. “I don’t understand where that is coming from. I don’t see the need to move away from it, and I know plenty of women who need that space to show their music.

“It’s disappointing to me to move the focus away from being for just women, but I can understand their need to react. Maybe it’ll be like New Coke.”