Phil Woods likes to tell a story about his fellow alto saxophone virtuoso and longtime musical partner, the late Gene Quill. One night, Quill played what Mr. Woods described as a “blazing solo” to wild reception from the audience — with the exception of one finger-waving self-appointed critic, who walked up to Quill and declared, “All you’re doing is imitating Charlie Parker.” Quill removed his saxophone from its strap, handed it to the guy, and said, “Here, you imitate Charlie Parker.”

Mr. Woods’s point is well taken. Imitating Charlie Parker is hardly the same as imitating Groucho Marx or Jimmy Durante. Yet the anecdote doesn’t do justice to the music of Quill, Mr. Woods, or even Parker. It was Bird who exerted the dominant influence on Mr. Woods throughout a career that’s spanned 55 years. But as audiences at the 92nd Street Y will hear tomorrow night in a special concert by Phil Woods and his Little Big Band, the saxophonist has never imitated Parker or anyone else. It seems impossible to imagine, in fact, that he would justify rote imitation, or any other artistically specious act on the grounds that it was technically difficult.

Mr. Woods, now 75, was raised amid the first flowering of modern jazz and grew to be, as per his own song title, among “All Bird’s Children” (he was, for a time, even married to Parker’s widow, Chan, and helped raise Parker’s actual children). Although few could challenge him for the title of best living bebop alto saxophonist, Mr. Woods often plays with a vibratorich tone that sounds more like a product of the swing era, an idea underscored when he plays clarinet. One of Mr. Woods’s signature tunes, “Song for Sisyphus,” opens with a ballad introduction that rings with the influence of Johnny Hodges as a player and Billy Strayhorn as a composer. He also enjoyed a long musical relationship with the other great big band alto giant, Benny Carter.

It was perhaps Carter’s influence that led the National Endowment for the Arts to name Mr. Woods a Jazz Master in the category of “composer-arranger.” When that announcement was made late last year, I thought the organization was bending its criteria a little — surely Mr. Woods is better known as a solo instrumentalist than a writer; but he has, in fact, enjoyed quite a distinguished career as a composer. He’s written at least two full-length extended works for large ensemble — 1961’s “Rights of Swing” and 1978’s “I Remember” — he almost always tours with a five-piece group to give himself the challenge of an additional horn to write for, and he works consistently with octets and nonets that he calls his “Little Big Band.”

Mr. Woods’s orchestral side has been the focus of attention for a series of recent releases by the Colorado-based label Jazzed Media, one of several “boutique” record labels to build much of their catalogues around Mr. Woods (another is Philology, the Italian label named after him). In the last few years, Jazzed Media producer Graham Carter has released six albums by Mr. Woods (three more are scheduled in the next year), three of which are large-format projects that concentrate on the altoist’s own past as well as shed light on neglected areas in the history of orchestral jazz.

On Tuesday, the pianist Bill Charlap, who served an apprenticeship in Mr. Woods’s bands, will launch this year’s Jazz in July series with a program of music from one of those albums, 2004’s “This Is How I Feel About Quincy.” Mr. Woods and Mr. Charlap will also feature the music of Oliver Nelson, another distinguished composer with whom the saxophonist enjoyed a long musical relationship.

Quincy Jones has made such a gigantic career as a pop producer and music industry factotum that it’s difficult to remember that he started as a humble jazz arranger, putting together scores for Lionel Hampton and Count Basie one note at a time. But he realized early on that his gift was in production, overseeing the work of other arrangers. Even by the time Mr. Jones was leading his own big band at the start of the 1960s, most of what he played was by other writers.

Most of the pieces on “This Is How I Feel About Quincy” are Jones compositions newly arranged for the Little Big Band (nine pieces) by Mr. Woods. There are echoes of Basie throughout, as well as the “cool” West Coast style of the mid-’50s: “For Lena and Lennie,” a dedication to the power couple Horne and Hayton, is a sultry, slow dance number with a twinkling melody that is enforced by Mr. Charlap at the piano. Mr. Charlap also kicks off the up-tempo flag waver “Birth of a Band,” with plenty of gusto before it builds to a chase chorus between Tom Hamilton on tenor sax and Nelson Hill on baritone. There are two pieces named for little girls on the album: the gently rocking “Jessica’s Day,” written for Dizzy Gillespie but adopted by Basie, and the sweet and tender “Lullabye for Jolie” (Jones’s daughter), which spotlights flute and Mr. Woods’s clarinet.

For all Mr. Woods’s recent big band activity, my dream project for the saxophonist would be a set of duets with Mr. Charlap titled “Phil and Bill”; it’s hard to believe they haven’t done that yet—which isn’t to say that you can’t play romantically and intimately with a larger ensemble. The prettiest piece in the “Quincy” collection is “The Midnight Sun Will Never Set,” easily Mr. Jones’s best composition, which he adapted from a Swedish folk song. Mr. Woods was already featured on both of the song’s most important recordings — with Mr. Jones in 1959, and with Benny Carter on “Further Definitions.” But the performance on “This Is How I Feel About Quincy” takes a backseat to neither, revealing the depth of feeling and full emotional wisdom that Phil Woods has spent the last 45 years accumulating.

wfriedwald@nysun.com