Vijay Iyer Trio
Dizzy’s Club, Through June 18
‘Uneasy’ (ECM Records)

People talk about improvisation as if it were the most important thing in jazz, but I would make the case that interpretation is at least as significant. To clarify: Improvisation, by and large, is making up an entire new melody (usually based on existing harmonies) and interpretation is taking a tune and personalizing it, rendering it in a distinctly individual and personal way, such as no one has ever done before. The lines between the two approaches are often blurred, but the greatest musicians are invariably masters of both.

Pianist Vijay Iyer, who is appearing as part of his outstanding trio with bassist Harish Raghavan and drummer Tyshawn Sorey at Dizzy’s this weekend, reminds me that jazz is also the major music where it’s possible to have an interpretation of an interpretation. There’s a famous arrangement of “Honeysuckle Rose” with a classic shout chorus, as musicians call it, that’s sometimes attributed to Benny Carter, but may go back even earlier. Also, Ahmad Jamal’s 1958 recording of the 1936 song “Poinciana” has become so iconic that it’s hard to imagine the melody being played any other way.

In 1964, tenor saxophonist Joe Henderson recorded Cole Porter’s “Night and Day” on “Inner Urge,” a classic Blue Note album co-starring pianist McCoy Tyner, bassist Bob Cranshaw, and drummer Elvin Jones. The 1932 song was already one of the most performed in all of jazz, but Henderson’s version proved to be, as they say, a game-changer. 

He interprets the melody mostly straight, and certainly recognizably. After a delightfully florid intro, Henderson dances into the tune with a grace suggesting Fred Astaire, for whom the song was written (in the Broadway musical “Gay Divorce”), and treats the tune respectfully, goosing it with a minor flourish here and there. He improvises energetically in his second chorus, and Tyner’s piano solo is equally impressive.

Younger musicians have come to regard Henderson’s version as the essential template for “Night and Day.” Pianist Renee Rosnes, who played in one of the late saxophonist’s final bands, included it in her 2009 album “Black Narcissus (A Tribute to Joe Henderson).” Mr. Iyer, too, uses it as the jumping off point for his treatment of the song, which served as the centerpiece of his opening set at Dizzy’s on Thursday as well as on his current album, “Uneasy” (ECM Records).

In fact, in Mr. Iyer’s version, there’s just as much Henderson and Tyner as there is Porter; he too opens with a brief, understated flourish, similar to the one from 1964, that gracefully introduces the familiar melody. He gives us just enough of the tune for us to get our bearings, and then goes off on his own. 

There are eight bars we can recognize, then eight bars of variations, a pattern that is then repeated and that allows him to render the bridge for us more or less as Porter composed it. In his own improv, he seems to be Henderson and Tyner at the same time, spinning elaborate lines in his right hand and painting supportive splashes of color in his left.  

The bassist (Linda May Han Oh on the album) takes the spotlight for a chorus, as does Mr. Sorey on drums, and when Mr. Iyer frames the drum solo with piano interjections, it again has the feeling of choreography, as if Mr. Iyer were taking a great big balletic leap into the middle of the drum solo. 

At Dizzy’s, “Night and Day” arrived right in the middle of the set, following what from a distance seemed to be two longish numbers but were actually sequences of songs that flowed uninterrupted, one into the other. The first such block began with a few short sequences of notes interspersed with longer pauses as the melody of the album’s title track, “Uneasy,” comes into focus. The piece isn’t entirely accurately named: There are aspects of it, like a rumbling bass and drum part underneath, that do suggest a kind of unease, but the melody itself is soft and warm and even easy on the ear.  

The second tune at Dizzy’s — which came directly out of the first without a break — was a standard of a different stripe, Stevie Wonder’s “Overjoyed.” As far as I can see, Mr. Iyer and company have not yet recorded this, but his approach to the tune was angular in a way that again put me in mind of McCoy Tyner.  

The rest of the set was mostly Mr. Iyer’s originals as well as a piece by the late Geri Allen. Perhaps Mr. Wonder knows Mr. Iyer better than he knows himself; his music gives us many more reasons to be joyful than it does to be uneasy.