Since his death in 1967, the composer Billy Strayhorn has come to represent a lot of things. As the drummer Chico Hamilton puts it in a new PBS documentary called “Billy Strayhorn: Lush Life,” which makes its premiere tonight, “Billy Strayhorn was a sound, he was a time, and he was a movement, which anybody around him would embrace. That’s saying something, you know?”

One thing on which everyone can agree is that Strayhorn (1915–67) was one of the greatest writers in all of American music: His compositions were at once highly sensual and contagiously swinging, rich in complex harmonies and rife with unforgettable melodies; like his mentor and partner, Duke Ellington, he wrote for the heart, he wrote for the head, and he wrote for the feet — and other parts of the human anatomy as well.

Strayhorn essentially wrote two kinds of music. First, he was expected to function as Ellington’s alter ego, extending and enhancing the Maestro’s ideas, finishing what the bandleader either couldn’t or wouldn’t. When he wrote in Ellington’s shadow, the results were indistinguishable from the Master — neither man could tell where one’s work began and the other’s ended. Yet Strayhorn also wrote for himself, in his own style, which reflected his extensive classical training as well as his own firsthand familiarity with what he called “the intimacy of the Blues.”

Strayhorn’s legacy can get a bit complicated when one considers that he wrote both of these strains of music — Strayhorn as Ellington and Strayhorn as Strayhorn — for the Duke Ellington Orchestra. Several of his compositions were registered as Ellington/Strayhorn pieces, while collaborations between the two were listed only under Ellington’s name.

Factor in Strayhorn’s struggles with racism and his sexual orientation — he was a serious black composer and an openly gay man at a time when neither role was considered acceptable — and you have both a life story and a musical legacy of amazing richness. The filmmaker Robert Levi tells that story in the excellent “Lush Life.” Equally important, the documentary is accompanied by a new album with the same title from Blue Note, containing performances by Bill Charlap, Elvis Costello, Hank Jones, Joe Lovano, and Dianne Reeves, all of whom also perform in Mr. Levi’s documentary.

“Lush Life” employs a skillful balance of interview material (including several key subjects who are either recently or long gone, such as Stayhorn’s personal partner Aaron Bridgers and Ellington’s son Mercer), combined with archival footage of the Ellington band (in a few cases with Strayhorn at the piano), vivid home-movie footage, and the new performances from the album. It’s a fast-moving, intensely compelling production that tells Strayhorn’s story with a surprising amount of depth and detail crammed into 90 minutes. “Lush Life” also deftly accomplishes the difficult task of addressing the central event in Strayhorn’s life: his complex relationship with Duke Ellington.

The only objectionable moment in the film occurs in the first few minutes, when the narrator states that “few people know his work” and wonders “why he is so little known.” Nothing could be further from the truth. Strayhorn is hardly a neglected or little-known figure; he is surely one of the five most performed composers in the entire history of jazz, along with Ellington, Thelonious Monk, and Fats Waller. There are at least threedozen CDs devoted to Strayhorn’s music by different artists in every conceivable subgenre of jazz, and virtually everybody is familiar with his three most famous songs: “Lush Life,” “Take the A Train” and “Satin Doll.” There are also two well-known and excellent books on Strayhorn, David Hajdu’s groundbreaking biography, “Lush Life,” and Walter Van De Leur’s full-length musical study, “Something To Live For: The Music of Billy Strayhorn.”

In fact, Mr. Levi’s film benefits tremendously from Mr. Hajdu’s presence as the most prominent of his interview subjects and as the guide to Strayhorn’s life: his early life in Dayton, Ohio; his epochal meeting with Ellington backstage at the Stanley Theater in Pittsburgh; his increasingly important role in the Ellington organization; his conflicts with Ellington, which resulted in his leaving the band for a few years in the early 1950s; and his own inner struggles. As the singer-songwriter Jon Hendricks says in the film, “He was taken care of. His whole life was laid out for him. All he had to do was what he loved to do — so where else would he go? He was truly a prisoner of love.”

Likewise, Mr. Levi’s liner notes for the Blue Note CD contain one bizarre line: “Had Strayhorn lived, he might have produced and recorded for Blue Note Records.” Obviously, Strayhorn lived (he was not a fictitious character) and the three decades of his career run almost exactly parallel to the great years in which Alfred Lion and Frank Wolff ran Blue Note Records. The only other thing to gripe about is that there appear to be at least two performances sampled in the film that are not included on the album — Mr. Lovano playing the rapturous “Star-Crossed Lovers” and Mr. Charlap’s piano feature, “Sprite Music.” Incredulously, the album does not include Strayhorn’s single most famous jazz classic, the one offering instructions on which particular subway line will deliver one to Harlem in a hurry.

As for the music on the album, the only shortcoming is that there shoud be more of it. The CD opens with one of two piano solos by Mr. Charlap, both of which showcase the two main sides of Strayhorn’s influences: the stride-bassed “Fantastic Rhythm” (one of the composer’s earliest known pieces) and the impressionistic “Valse.” The album is especially valuable for several tracks by the Lovano-Hank Jones quartet, in which the great tenor evokes the feeling of the most famous Ellington tenor, Ben Webster, while at the same time remaining himself. There are also four standards by Ms. Reeves, including an insidiously rhythmic “Something To Live For,” with her straight-ahead quartet, always a good thing. “Lush Life” has already been recorded 70 trillion times, but Ms. Reeves’s duet on the song with the guitarist Russell Malone is a worthy contribution to its legacy. Normally, she brings a lot of highly entertaining and very musical mishegoss to a melody, but here she knows that to pull off “Lush Life” you have to sing it practically “straight” as written.

Billy Strayhorn burned himself out by age 51, committing suicide slowly with alcohol and tobacco, turning the lyrics of his most famous ballad into a self-fulfilling prophecy. It was an ironic, tragic ending for a composer who had given so many musicians, singers, and listeners something to live for.

wfriedwald@nysun.com