Of all the living legends of jazz certified by the National Endowment for the Arts, Joe Wilder is at once among the least known to the general public (he has made only six albums as a leader, three from 1956–59 and three for Evening Star Records between 1991 and 2002) and the most prized by musicians, especially his fellow trumpeters. I’ve heard Wynton Marsalis play Mr. Wilder’s arrangement of “Cherokee” many times, and even though it’s not much of an “arrangement” per se, it’s clear that Mr. Marsalis is using Mr. Wilder’s performance as a starting point. Jon Faddis has acknowledged that “Cherokee” (and the album it comes from, “Wilder N’ Wilder”) was a solo that he played over and over as a young trumpet student.

“He’s very smooth; there aren’t a lot of rough edges in his playing,” Mr. Faddis said. “He reminds me of Thad Jones in that his playing is extremely logical; his solos are like compositions unto themselves.” Mr. Wilder turned 85 in February, and was named a Jazz Master by the NEA last month. This Friday, he will headline in a concert titled “Legacy: Three Generations of Jazz Trumpet,” as part of the ongoing Jazz Spectrum series at Symphony Space, in which he’ll co-star with Mr. Faddis (the series’ director) and Mr. Faddis’s young protégé, Max Darché.

Mr. Wilder was raised in Philadelphia, where he studied at the Mastbaum School of Music. His first recording, according to Tom Lord’s Jazz Discography, was a New York session by a Los Angeles-based band, Les Hite and his Orchestra. The date, in April 1942, produced what is commonly regarded as the first genuine bebop solo on record: Dizzy Gillespie’s statement on “Jersey Bounce.” It was a fitting time and place for Mr. Wilder, whose mature music would soon draw on elements of both swing and bop. He had already shown a similar duality even as a student, in that he was equally versed in the European classical tradition and in jazz. As Mr. Faddis points out, “One of the amazing things about Joe is that, well before Wynton got his rep for playing for both jazz and classical, Joe was doing that back in the 1950s. He was playing trumpet concerti with symphony orchestras.”

Mr. Wilder’s early professional experiences were all extremely challenging: During World War II, he was one of the first black Americans to serve in the Marines, where he eventually served in a military orchestra. After his service stint, he returned to work with the vibraphonist Lionel Hampton, a bandleader who was notoriously tough on his sidemen. Then, after a rewarding sixmonth stint with Count Basie, Mr. Wilder again found himself in the vanguard of the integration movement. He played in the pit bands of several important Broadway shows, including “Guys and Dolls” and “Silk Stockings,” for which he required the personal approval of composer Cole Porter. In the mid-1950s, Mr. Wilder joined the staff orchestra at ABC-TV at a time when network and studio bands were almost exclusively Caucasian. “There has to be a tough side to Joe, although I’ve never seen it, to go through what he went through,” Mr. Faddis said.

In 1956, Mr. Wilder, along with his fellow studio stalwart Hank Jones (who, like Mr. Wilder, is still playing at the peak of his powers in his 80s), recorded his first album as a leader, “Wilder N’ Wilder.” At that point, the 12-inch LP was new, and it’s hard to think of another trumpeter of the era who recorded a whole album with just a rhythm section. Apart from “Cherokee,” the 10-minute opener, and an expressive blues piece, the bulk of the album consists of four standards upon which Mr. Wilder revealed that he is even better at expressing a melody in ballad tempo than he is at blowing on changes.

Mr. Faddis’s favorite Wilder track is “Day Dream,” a sublime duet with the pianist Bobby Tucker from the 1993 album “No Greater Love,” which he describes as “absolutely gorgeous — one of those songs that just reaches into your heart.” But my own prize ballad is “Prelude to a Kiss,” from “Wilder N’ Wilder.” The leader plays the words no less than the notes, putting as much feeling into them as would any great singer, stretching some notes, bending and caressing others, but never distorting anything. Even when he plays a run of a dozen notes where Duke Ellington had originally written only two or three, he never loses the thread of the narrative. When he creates certain effects, buzzes, smears, rasps, which can only be done on the horn, he does them all in the service of the words and the music, enhancing what Ellington left him to work with, rather than going into business for himself.

In 2002, Mr. Wilder celebrated his 80th birthday by co-headlining a JVC Jazz Festival Concert (with Frank Wess, who was also born in 1922) and, last year, almost 65 years after he first arrived in New York, he led his own band for the first time here at the Village Vanguard. In September, Messrs. Wilder and Faddis were asked to play at a reception at the Louis Armstrong Center for Music and Medicine (at Beth Israel Hospital), honoring the benefactress, Phoebe Jacobs.

“He reached into his trumpet case,” Mr. Faddis said, “and he says, ‘Oh no! I forgot my mouthpieces, and I know right where I left ’em!’ He was cleaning out his horn before he came down. His wife got up and took the train home to where they live, around 140th Street, but then she called him and she says, ‘I can’t find them!’ So I handed Joe my horn to play, and he sounded better than I did on it. He is, in every way, the musician that I aspire to be when I grow up.”