Back in the day, the path of a musician from sideman to leader was more clear-cut: Players who had star quality, a talent for composition, and natural leadership qualities eventually graduated to the front ranks. Call it the “trickleup” theory. In the millennial era, there are many other factors at work, so much so that a player who has all these qualities may find himself struggling to rise through the ranks.

Today, a lot of important musicians remain on the margins: They lead their own groups in the more peripheral clubs, but when they play the major rooms, it’s never with their own names on the marquee.

I’ve heard the tenor saxophonist Joel Frahm with dozens of groups in every club across the city, most recently with the singer Rondi Charleston at Dizzy’s and the fine, swing-oriented septet Waverly 7 at Jazz Standard. And yet for all the times I’ve heard Mr. Frahm, in every context from traditional big bands to avant-garde groups, I would be hard-pressed to tell you what he sounded like — other than very good. The diversity that’s expected of contemporary musicians is generally a good thing, but it makes it hard to get a handle on what a player’s individual sound is.

This week the 37-year-old Mr. Frahm is having a sort of coming out party. He is releasing a new album, “We Used To Dance” (Anzic), on which he fronts a quartet of heavyweight veteran players who are also supporting him this week at Sweet Rhythm. They are pianist Kenny Barron, bassist Rufus Reid, and drummer Victor Lewis, and it’s safe to say that Mr. Frahm would feel honored to play for them in any of their own groups. Having seen his performance at Sweet Rhythm this week, I at last feel I know what Mr. Frahm sounds like: He has a big, buzzy, bear-like sound that seems to match his extra-musical personality.

As for forebears, his all-star rhythm section is the same trio that accompanied Stan Getz in the final phase of that giant’s career. But the presence of Mr. Reid suggests that if Mr. Frahm sounds like anyone, it’s the great Dexter Gordon, with perhaps hints of Don Byas and Ben Webster here and there — an imposing, aggressive, straight-downthe-middle sound, immediately notable for its warmth, energy, and sheer size.

Mr. Frahm’s second tune of the opening set on Wednesday was “Nad Noord,” sections of which sounded like an invocation or prayer, others like a love song. It must not be a coincidence that the title is similar to Miles Davis’s “Drad Dog” (“Goddard” spelled backward). The piece is complex and somewhat cerebral, in the fashion of some of Davis’s more experimental music of the 1960s. Other than “Nad,” the rest of the set and most of the album exalt in the basic four B’s of contemporary jazz: boppers, ballads, blues, and bossa nova. Mr. Frahm showed where he was coming from right away with “Bob’s Blues,” a rollicking 12-bar line named for his father that makes me wish his next album will be a tenororgan combo. He also transformed the chords to Victor Schertzinger’s “I Remember You” into a fast and dazzling bebopper titled “A Whole New You,” and reconfigured the opening notes of “You and the Night and the Music” into a fast, bouncy bossa. He titled this piece “Jobimiola” because, he explained, it superimposes a 5/8 melody over a 4/4 beat — i.e. the classical ideal of hemiola. In the actual playing, it comes off more like Dexter Gordon’s “Soy Califa.”

Mr. Frahm didn’t play the album’s title track, “We Used To Dance,” in the opening set, but everything he did play had a bubbly, dancing quality. The album also has two excellent ballads, “My Ideal,” which he also played at Sweet Rhythm, and “Spring Can Really Hang You Up the Most,” a timely tune that everybody seems to be doing all of a sudden. Mr. Frahm’s previous album, “Don’t Explain,” an excellent set of duets with the pianist Brad Mehldau, was, because of the nature of the beast, heavy on ballads. In both contexts, he is especially good at slow love songs, but whatever he plays, it’s Frahm the heart.

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Like his contemporaries Jimmy Scott and the late Arthur Prysock, the jazz singer Ernie Andrews is one of the grandfathers of soul music. All three were among the first to sing sophisticated ballads with the force and feeling of the blues and vice versa, to merge the Mississippi Delta with Tin Pan Alley in a way that eventually became its own category of pop music. Mr. Andrews had one early R&B hit, the irresistible “Soothe Me” in 1945, then spent much of his career on the West Coast; if he has ever had a week-long gig in a major New York club, I don’t know about it. In more than 60 years of singing, Mr. Andrews has done fewer than a dozen albums, half of them for producer Joe Fields (the latest of which is the excellent “How About Me”); most of the rest have not been made available in the digital age.

This week the good news is that Mr. Andrews is appearing at Dizzy’s Club Coca-Cola, but the bad news is that he’s only doing half the show (although it’s good news again that the rest of the set is given to the Juilliard Jazz Orchestra playing Duke Ellington).

With his throaty chestnut-colored baritone, which still sounds remarkably rich and plummy even though he’ll turn 80 this Christmas, Mr. Andrews fits in nicely between Mr. Scott’s tenor and Prysock’s bass. The man has made history himself, and his act is a repository of musical lore, book-ended by a collage of blues themes (including “Parker’s Mood,” Ellington’s “Rocks in My Bed,” and Jay McShann’s “Confessin’ the Blues”) building up to a long medley of Ellington classics. Having never seen a whole show by Mr. Andrews in person (I still haven’t, come to think of it), I was most surprised by his physical presence, his constant gesturing and grimacing, equal parts Cab Calloway and Al Jolson, matching his ultraprecise articulation.

I was disappointed only with the duration of the set, which lasted only about 30 minutes. I wanted to hear him sing the two slices of Ellingtonia from the new album — “Monday Every Day” and “It Shouldn’t Happen to a Dream ” — not to mention “Soothe Me.” I only wish that every singer in New York would stop by the club and, as the late Cannonball Adderley advised, “get with Ernie Andrews right down to the middle of the nitty-gritty.”

wfriedwald@nysun.com