All the regulars at the Village Vanguard know the rules: no photography, no texting, no talking or unnecessary noise during a performance. Operating in the same location since 1935 and virtually unchanged over those years, the Vanguard is the closest thing to a holy space in the world of jazz. The prestige of being booked at the club is tantamount to sanctification, and the experience of seeing musicians play there has a quality of bearing witness. There’s quiet and stillness and an air of reverence in the room, no matter who’s onstage—or so there had been at the dozens of shows I’ve attended at the Vanguard until this fall, when I saw Cécile McLorin Salvant.

A full month before the event, I started to notice that something extraordinary was in the works. As soon as I got the announcement that Salvant would be playing a week of duo shows at the Vanguard, accompanied by the pianist Sullivan Fortner—two sets a night for six nights—I logged on to the club’s website to make a reservation, only to find that all 12 shows were sold out. News of this sort would be the opposite of news for Beyoncé or Taylor Swift, but it’s rare for even the biggest stars in jazz, the bigness of their stardom being a relative matter. I e-mailed the club manager, asking if there was standing-room space available, and was told my only option would be to arrive early and get in line with the people hoping for cancellations. I did just that and waited on the sidewalk on Seventh Avenue for nearly an hour—and then everyone on the line was sent away. There were no cancellations for this show.

Two nights later, after going through the same routine twice more, I finally got in through the door and squished my way into a seat in the grossly, thrillingly overpacked space. The crowd was a mix of smartly put-together millennials and jazz bigwigs. I spotted Renee Rosnes and Bill Charlap, two pianists who have also headlined the Vanguard this year, a few feet from the stage. Off to one side of them, there was the jazz singer Catherine Russell, and not far behind her was a table full of musicians from the Jazz at Lincoln Center Orchestra. It was like a summons had gone out to assemble people certified as cool.

I had seen Salvant perform once before, a year and a half earlier, in a one-off night with Fred Hersch in his annual “Duo Invitation Series” at the Jazz Standard, another New York club. Salvant was 26 at the time; she was celebrated for having won the Thelonious Monk Institute of Jazz International Vocals Competition and had already released three albums—including one, WomanChild, for which she’d earned her first Grammy nomination. I found her impressive overall but a bit tentative onstage, and I thought she sounded too much like Billie Holiday. She sat on a stool, nearly motionless, for most of that show, and closed her eyes or looked down at the floor much of the time she was singing. For the ballads that dominated the set, Salvant’s minimalism came across as internalism—rumination appropriate to the material. I walked away thinking of her as a promising young heir to the Holiday tradition.

What I experienced at the Village Vanguard in October was something more than the fulfillment of that promise: I saw Salvant transcend the conventions of multiple traditions in jazz singing, including Holiday’s, without abandoning the tenets of emotional maturity, deep musicality, and rhythmic drive that distinguish jazz. Onstage at the Vanguard, as well as on her latest album, Dreams and Daggers, Salvant made a kind of jazz that honors the history of the music while speaking with ringing, stinging cogency to a 21st-century audience.

In place of reverence, quiet, and stillness, there was an atmosphere of shared excitement. If the regulars remembered the rules about keeping quiet, it didn’t show. And there seemed to be many more newcomers than regulars in the place—unbridled fans cheering in full voice during a song, picking up on Salvant’s cheeky humor and laughing along, even calling out requests, an act of apostasy at the Vanguard. About halfway into the set, someone yelled for “I Didn’t Know What Time It Was,” the Rodgers and Hart ballad that Salvant reconsiders on Dreams and Daggers—a double-CD set of standards, vintage obscurities, and new songs written (or co-written) by her, including some tracks recorded at a show at the Vanguard in late 2016 that I didn’t attend. Salvant’s pianist responded, “You read our mind,” and a woman in the audience called back to them, “You’re reading mine!”

At the end of the set, about half the audience rose to give Salvant a standing ovation, something I had not seen in the venue in years—not since the first show that the pianist Barry Harris played after suffering a stroke. On my way out, I saw the Vanguard’s longtime owner, Lorraine Gordon, sitting near the exit with her daughter Deborah, who has taken over the club’s day-to-day operations. “It hasn’t been so hard to get into this place since Barbra Streisand,” I said, referring to the evening in 2009 when Streisand booked the Vanguard for a show recorded and filmed for a live album and DVD. (The room was stocked that night with the likes of Bill and Hillary Clinton and Barry Diller.) Lorraine, now 95, smiled a little smile and said, “I like this girl better.”

Deborah, gesturing to the line of people waiting to enter for the second set, added, “And look—she’s a star!”

There are jazz singers today more famous than Cécile McLorin Salvant: Diana Krall headlines major theaters like the Beacon in New York City and performing-arts centers around the country, and others like Kurt Elling, René Marie, Dianne Reeves, Janis Siegel, Esperanza Spalding, and Cassandra Wilson are all established success stories in vocal jazz. (I’ve put Elling first on this list going alphabetically, not because he’s one of a small handful of men to rank among the most popular singers in jazz.) Quite a few young or youngish singers have gotten serious critical attention in recent years: Laila Biali, José James, Jo Lawry, and Jen Shyu, among others. And a group of gifted lesser-knowns have the potential to break through next: Nancy Harms, Aubrey Johnson, and Camila Meza, among those I’ve seen and admired thus far. So what does Salvant have, what does she do, to earn her status as jazz’s most exciting new star?

A major element of her success in this taxing discipline is her unfailing technical proficiency. A singer since childhood, Salvant took lessons in both voice and piano and went on to study music at the Darius Milhaud Conservatory in France. (She also took some classes in law.) She has superb intonation and can hit a note dead on. She also understands the greater wisdom in varying her pitch for expressive purposes—for instance, lowering a tone to communicate misgivings or regret. At the Vanguard, she did this deftly at multiple points in Billy Strayhorn’s “Lush Life,” for instance, singing the last word in the phrase “I was wrong” so low on the register that you could see her there in that small dive.

Salvant has superb breath control and command of dynamics. She knows how to lower her voice to a near-whisper to draw listeners into her inner world, or belt out a phrase with full lung power. Even more impressively, she uses these techniques only for their emotive capacity—never merely to demonstrate how fancy she can get. And she rarely scats; Salvant gives the impression that music is important to her as a vehicle for bringing out the meaning of words.

The marvel of Cécile McLorin Salvant is the complexity of her point of view as an artist. Like most jazz and cabaret singers, she works in a milieu that is essentially interpretive rather than expressive. She sings songs that others wrote at various points in the past, including material that a great many other singers have sung and continue to sing. While she has written or co-written some songs, the bulk of her repertoire consists of popular standards (“The Trolley Song,” “You’re My Thrill”) and deeper cuts (“Growlin’ Dan,” “Tell Me What They’re Saying Can’t Be True”). But she chooses her material so astutely, and interprets it so adroitly, that the songs come across like the personal expression of an idiosyncratic individual with an utterly contemporary sensibility.

Salvant has a gift that I’ve never seen developed so well in a singer of vintage material. She accomplishes two seemingly incompatible feats simultaneously: taking on a standard with a palpable respect for the intention of the material and bringing forth the essence of the song, while at the same time communicating a second meaning, an analytical or ironic commentary. It’s almost as if she has two selves, the first one singing for all she’s worth and the other standing alongside, offering her own thoughts.

Among the highlights of the Vanguard set I saw was a torch song called “Gone Again,” best known, to the degree that it’s known at all, through a recording by Dinah Washington (under the title “He’s Gone Again”). The lyric, co-written by Gladys Hampton, wife of the legendary vibraphonist Lionel Hampton, is a plainspoken statement of regret for hanging on to an unreliable man. Salvant put the idea across clearly and potently, seeming to embody the song’s ill-treated woman, while—with no more than a slight squint as she sang “I’m his completely” and an arched eyebrow for the words “I miss him”—she sent out another set of meanings.

With her ability to tease out such complexity in every song, Cécile McLorin Salvant has created a repertoire twice as deep as other singers’. How wonderful, and strange, that a singer can nowadays achieve a kind of stardom for such a thing.