Bill Charlap has performed with many of the leading artists of our time including Phil Woods, Tony Bennett, Gerry Mulligan … Video

When jazz is played well enough, it becomes conceptual art without really trying. There’s so much there: the idea of improvisation; the idea of what a song is; the idea of (in some cases) an American style, and the disappearance or persistence thereof; repertory versus imagination; received wisdom versus innovation; concision versus the big statement.

All this emerged during the first set by the pianist Bill Charlap’s trio at Dizzy’s Club Coca-Cola on Tuesday. But the music wasn’t programmatic: None of these ideas were out on stalks, and the set, 10 songs in a little more than an hour, didn’t feel like a lecture.

Mr. Charlap started with two bebop tunes from the 1950s that, generally speaking, you never hear: “Odd Number,” by Hank Jones, and “Simplicity,” by Al McKibbon. They were clean and fast, and both drew from Bud Powell in the drive and tension of their melodic lines. They had lightness, character, inner purpose, strength of design; they were good enough to make you go home and listen to old records — by Powell, by Sonny Clark, by the young Hank Jones — to find out if jazz was really like this once.

It was — even better in fact — and the trouble with playing this way is how to do it without seeming deluded and ultimately fatalistic. Mr. Charlap’s gigs get around this problem with hard work and craft, but more important because he seems less interested in stylistic eras of jazz than its ever-relevant ideal of melody and efficacy.

The process whereby an American theater song turns into jazz fascinates Mr. Charlap; he’s a student of these transformations, and has done it himself, with songs like George Gershwin and Irving Caesar’s “I Was So Young (You Were So Beautiful),” which came next in the set, arranged simply as a ballad with brushed drums. Because the song is basically unknown to jazz audiences, he could pour his own style into it, trickling out his phrases, making them sound like vocal runs.

But with two better-known songs, “The Way You Look Tonight” and “It’s Only a Paper Moon,” Mr. Charlap took pains to make a statement with form. The first was almost comically fast and frenetic, with layers of different tempos for piano and drums. And the second was super-slow, a set piece of counterintuition. The song almost lost its recognizability and identity, but that was the point. He leaned into his experiment, taking the harmony apart and putting a quiet semi-gospel arrangement on the song’s ending.

In almost every case Mr. Charlap, with the bassist Peter Washington and the drummer Kenny Washington (they’re not related), used an arrangement to bracket songs at the beginning and end, or to aerate them in the middle. His arrangements are usually built on short unison passages, and they never use a splattering drum fill when a single hit will do. And they’re almost archaic. (They didn’t seem so much this way 10 years ago, when Mr. Charlap’s trio was just beginning, and Tommy Flanagan, his supreme stylistic model, was still alive and working.) But they’re superbly scaled; they’re of a piece with the concision and craft of the rest of the music.

Simultaneous with the last piano chord of “It’s Only a Paper Moon,” Kenny Washington struck the middle of his cymbal once with the handle of his wire brush. In the context of the set, it was enough, and a lot.