The tenor saxophonist Benny Golson, who is currently playing a rare week in New York at Dizzy’s Club Coca-Cola, represents a unique and fascinating generation of jazz musicians and, especially, composers. Mr. Golson, who turns 79 this month, was originally inspired to play by such big-band leaders as Duke Ellington and Lionel Hampton. But by the time he and his fellow Philadelphian saxophonists, such as John Coltrane and Jimmy Heath, reached musical maturity in the late 1940s, there had been a sea change in the music. The swing bands were dying out and the modern jazz of Charlie Parker and Dizzy Gillespie (whom Mr. Golson first heard in a life-altering experience in 1945) was taking over.

The transition from swing to bop was particularly crucial to the young Mr. Golson in his development as a composer: It meant a severe curtailing of possibilities in terms of his overall sonic palette — one can never do as much with five musicians as one can with 15 — but at the same time, bebop offered a greater range of harmonic and melodic options than had previously been possible. As one part of the canvas contracted, another expanded, and writers such as Tadd Dameron, Gigi Gryce, Mr. Heath, and Mr. Golson were up to the challenge.

The best-known part of Mr. Golson’s career is actually bookended by big-band work: After studying classical composition at Howard University, and before serving as an apprentice in rhythm-and-blues groups, Mr. Golson took a huge first step into the jazz world when he joined Gillespie’s legendary orchestra of 1956. A decade later, he gave up the road and, following in the footsteps of Benny Carter and Quincy Jones, he went to work full-time as a composer-arranger for the commercial music industry in Hollywood. But in the period between those two points, Mr. Golson made his reputation in the jazz world as an outstanding composer, musical director, and saxophonist who, among other things, helped Art Blakey create the entire hard-bop idiom, assembled the first definitive edition of the Jazz Messengers, and wrote most of the band’s book. He then was almost as successful when he fulfilled the same function with his own Jazztet, the cooperative combo he co-led between 1959 and 1962 with the trumpeter Art Farmer.

In writing for those three ensembles — Gillespie, Blakey, and the Jazztet — Mr. Golson wound up composing more all-time great jazz standards than any player still alive. Even in an age when the jazz repertoire includes Björk and Bob Dylan, I pity any musician who shows up for a gig without knowing the changes and melodies to “I Remember Clifford,” “Stablemates,” “Along Came Betty,” “Are You Real,” “Blues March,” and “Killer Joe.” Indeed, Mr. Golson wrote so many classics that he doesn’t even attempt to include all of his greatest hits in his current live sets.

At Dizzy’s, he played two relatively new songs and two all-time classics. He is leaving the bulk of his older compositions in the care of Joel Frahm, the fine young saxophone star who is playing the After Hours sets at Dizzy’s this week with the quartet, led by the pianist Adam Birnbaum, in a program called “The Music of Benny Golson.”

For the last 40 years, Mr. Golson has been able to pick his spots and only plays live when he feels a hankering to do it (as in a famous reunion with Farmer in the mid-1980s). He has appeared in New York on just a few occasions in the 21st century, which explains why it was so tough to get into Dizzy’s for Wednesday’s opening show. The quintet is the same one that appeared on Mr. Golson’s most recent album, 2004’s “Terminal 1”: the trumpeter Eddie Henderson, who is cast from a similar mold as Mr. Golson’s longtime collaborator, the late Lee Morgan, and whose bright and attractive tone came through on the first two tunes in particular, even though he was playing with a mute; the bassist Buster Williams, who has worked with Mr. Golson in various editions of both the Jazz Messengers and the Jazztet going back 45 years; the drummer Carl Allen, who played a pivotal role on “Terminal 1,” and Michael LeDonne, a neo-bop pianist who has made a career specialty of working with living legends such as Mr. Golson, James Moody, and the late Milt Jackson. On his solo feature, “I Didn’t Know What Time It Was,” Mr. LeDonne laid down dark, angular chords and percussive notes that recalled Mr. Golson’s fellow Philadelphian McCoy Tyner, who actually began his career in the original Jazztet.

Mr. Golson opened with “Horizon Ahead” (from his 1998 record “Remembering Clifford”), a memorable melody in ABAB song form. At 79, he still shows why he is in demand as a soloist as well as a musical director, displaying a smooth tone with just enough grit in it. Mr. Golson wrote “Terminal 1” to commemorate his speaking role (opposite Tom Hanks) in Steven Spielberg’s “The Terminal.” The piece depicts the hustle and bustle of a modern airport, with Mr. Allen’s drums serving as a sort of voice-over.

Mr. Golson, who was named an NEA Jazz Master in 1996, also played what might be his first great tune, the ballad “I Remember Clifford,” with just the rhythm section. He ended with his quintessential fast-bop number, “Stablemates,” which was made into a jazz standard by Coltrane and Miles Davis in 1955; it’s the one that starts like “Alone Together” for the first few notes and then quickly goes off on its own. (In 1962, Mr. Golson even recorded a version of the Arthur Schwartz show tune for comparison.)

Throughout his performance, Mr. Golson also entertained the crowd with his verbose and articulate anecdotage; he’s so good with words, it’s surprising he has traditionally relied on others to write the lyrics to his songs. On the way out of the Jazz at Lincoln Center complex, I noticed the American Songbook series is just about to start, and I couldn’t help but think that Benny Golson has written so many classic tunes that he belongs in that lineup as well.

* * *

Not long after Frank Sinatra’s death 10 years ago, three friends of mine mounted a tribute to the master, which they called “Our Sinatra.” Since then, that production, which blurs the boundaries of cabaret and off-Broadway-style revue, has become the little show that could, running almost constantly in various venues across New York and touring the country several times.

“Our Sinatra” is now back for this month at a new venue, the Songbook Theatre at the Broadway Comedy Club. It co-stars Christopher Gines, of the original cast, along with the young pianist-singer Elliot Roth and the impressive Harmony Keeney. In keeping with the show’s history, no one attempts a Vegas-style imitation of Sinatra — thank God — or even tries to replicate his essence, but “Our Sinatra” does convey a sense of the scope of the giant shadow that Francis Albert cast over the whole of the American musical landscape, and underscores, in Pete Hamill’s phrase, why Sinatra continues to matter.

wfriedwald@nysun.com