One of the more common figures in jazz lore (and in arts writing in general) is the neglected genius — a musician or composer who does amazing work and sets new standards in his or her craft but is generally unknown to the public, and sometimes even to critics. Residing at the opposite end of the spectrum are those towering figures who are so overwhelmingly famous that their work is taken for granted, and it’s often forgotten what they did to earn their celebrity in the first place. With a pair of new releases — “The Quincy Jones ABC/Mercury Big Band Jazz Sessions” and “Mosaic Select: Onzy Matthews” — Mosaic Records is exploring both sides of this equation, documenting two figures of the 1950s and ’60s who may well be the most and least famous jazz arranger-composers of all time.

How famous is Quincy Jones? It’s one of those Johnny Carson-esque setup lines, but Phil Woods, Mr. Jones’s longtime colleague, once uttered this answer: “Quincy is so big these days that the pope tries to get an audience with him.” No doubt when Mr. Jones was named, a few months ago, as an NEA Jazz Master, the selection wrinkled some brows; after all, Quincy Delight Jones, who turns 75 next month, is universally lauded as one of the most successful pop producers of all time. He is practically the Donald Trump of music, except that virtually nobody has anything bad to say about him, including all the sidemen who may have cringed when he moved to the greener pastures of mainstream pop. “Quincy more than paid his dues to jazz,” Mr. Woods said in a concert spotlighting Mr. Jones’s early orchestrations last summer. “He did everything he could to keep his big band together, and really put everything he had on the line.”

Mosaic’s five-disc set focuses on the climax of Mr. Jones’s jazz career, namely between 1959 and 1961, when he tried to lead his own touring jazz orchestra, made up of the best veteran players he could find. In assembling the group, Mr. Jones utilized everything he’d learned as a trumpeter and arranger for Count Basie and Lionel Hampton, and as a musical director for Ray Charles and Dinah Washington. By the end of the 1950s, he’d already made substantial contacts in Europe, and that was where his big band was destined to spend most of its brief existence.

The Mosaic box begins with a prelude — Jones’s brilliant 1956 album, “This Is How I Feel About Jazz” — before resuming with the initial sessions by Mr. Jones’s first working orchestra, fittingly released as “Birth of a Band” in 1959 on Mercury Records (the label that would soon hire him as vice president, making him the first black upper-level executive at a major label). The label also recorded the Jones orchestra in two live concerts.

There’s more than a technological difference between the live material and the studio recordings: Mr. Jones’s regular, commercial Mercury sessions packaged the band’s freewheeling energy, specifically its whimsical arrangements and audacious solos, into safe, three-minute tracks that seemed designed for AM radio airplay. Listening today, a number of the pieces amount to a jazz history lesson, in that Mr. Jones (and such arrangers as Ralph Burns, Al Cohn, Melba Liston, and Billy Byers) reorchestrated such jazz and blues classics as Don Redman’s “Chant of the Weed” and Bud Powell’s “Parisian Thoroughfare.”

The two concerts, however, featured the soloists stretching out and showcasing the band’s full potential as a hard-swinging unit in the tradition of Basie, Duke Ellington, and Woody Herman. A set from the Newport Jazz Festival in 1961 climaxes with Lester Young’s jam session classic, “Lester Leaps In,” which opens with the guitarist Les Spann expressing the tune before the fine, Basie-associated tenorist Eric Dixon embarks on the solo of a lifetime, an extended wailing interval with the energy of Ellington’s “Diminuendo and Crescendo in Blue.”

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Unlike Mr. Jones, the Texas native Onzy Matthews (1930–97) didn’t come up through the ranks of established big bands, but, as producer Michael Cuscuna shows in his thoughtful and well-researched annotation for the Mosaic Select box, more or less showed up out of nowhere in Hollywood in the hopes of making it as an actor, singer, and orchestrator. Matthews finally broke through when he was hired to arrange Lou Rawls’s 1962 album “Black and Blue,” just as the former gospel singer was poised to make his name as a pop music hit maker. On the strength of his work with Rawls, Capitol let Matthews try a series of instrumental sessions of his own.

Capitol released only two albums by Matthews, but Mosaic’s new three-disc package contains 51 tracks, mostly unreleased to this point. The centerpiece of the set is the closest thing Matthews had to a well-known album, his 1964 “Blues With a Touch of Elegance.” Like that of Mr. Jones, Matthews’s music is swinging, saturated with the blues, and thoroughly accessible. Whether working with his own original 12-bar themes (such as his memorable “Blues Non-Stop,” heard here in three different versions) or rearranging standards, Matthews packed a powerful amount of music into three-minute tracks.

Matthews made the most of both Capitol’s state-of-the-art recording facilities and his brilliant group of Los Angeles-based musicians, which featured the likes of trumpeter Dupree Bolton, saxophonists Curtis Amy (who takes the melody on soprano in “I Should Care”) and Earl Anderza, and trombonist Lou Blackburn (who moans meaningfully on “I Cover the Waterfront”). On “Dallas Blues,” Matthews built an intriguing set of contrasting themes, using the soul-jazz organist Richard “Groove” Holmes as a focal point.

Matthews’s best work showcases outstanding soloists in brilliantly copacetic backgrounds, and for a virtual unknown, he had full command of scintillating rhythms and gorgeous tonal colors. On one hand, it’s exciting to hear this much first-rate music by a relatively anonymous figure; on the other, it’s somewhat depressing to realize that the set constitutes nearly the sum total of Matthews’s output. With any luck, Mosaic’s new release will go some distance toward rescuing him from obscurity, just as the label’s Quincy Jones package might help resuscitate the arranger from his own celebrity.

wfriedwald@nysun.com