Ask any baritone saxophone player, and he’ll tell you that the hardest part of his job is showing up at gigs without anybody getting hurt. Perhaps jazz’s most unwieldy instrument, the baritone sax is even more awkward to transport than a bass fiddle; attempting to march with it in a parade amounts to an exercise in musical masochism. Partly as a result, it was overlooked by the jazz world for decades: In the big-band era, Duke Ellington was the only major arranger-bandleader to even include a baritone in his reed section, and the instrument didn’t gain its first celebrity – Gerry Mulligan – until the 1950s.

Ten years after his death at age 68, Mulligan remains the biggest superstar the instrument has known. Mulligan was celebrated internationally in his lifetime, and his star has continued to rise in recent years. The distinguished boutique label Mosaic Records has put together no less than three box sets of his music, the third of which, “Mosaic Select: Gerry Mulligan” (Mosaic Select 21, www.mosaicrecords.com), has just been released. Tonight he will be feted in a much-anticipated concert at Symphony Space, where the outstanding baritone saxophonist Gary Smulyan will play Mulligan’s compositions and arrangements with Jazz Band Classic, a 16-piece big band.

The new box includes 50 tracks recorded in December 1957, when Richard Bock, the producer and owner of Pacific Jazz Records, came east for a series of sessions. Bock worked on four projects with Mulligan: a spectacular album with an unusual saxophone ensemble; a reunion with trumpeter Chet Baker; a team-up with the vocalist Annie Ross; and an experimental date with a small string section.

The sax project, originally released as “The Gerry Mulligan Songbook, Vol. 1,” would turn out to be one of Mulligan’s most enduring accomplishments. It includes nine astounding tracks Mulligan recorded with four fellow saxophonists – Zoot Sims, Al Cohn, Lee Konitz, and Allan Eager – and a three-piece rhythm section composed of bassist Henry Grimes, drummer Dave Bailey, and guitarist Freddie Green.

For the album, Mulligan asked his fellow saxophonist and orchestrator Bill Holman to provide new charts of nine Mulligan compositions. Mr. Holman outdid himself. “Disc Jockey Jump,” which Mulligan first wrote for Gene Krupa a decade earlier, swings in the best big-band manner. “Crazy Day” is more relaxed and tranquil, yet this five-man super-sax team sounds urgent and in-your-face even while chilling out.

“Turnstile,” which is heard in two versions, is the climax of the set. As the title suggests, the song’s unison playing quickly gives way to a long series of short solos. After beginning with a simple line, the five saxophones trade eight-bar phrases, then fours. One great phrase quickly blends into another, and at times it seems like a single monster solo planned by a mythological creature with five mouths and 10 hands.

The box set’s 16 titles featuring the Mulligan-Baker duo compare in quality to the groundbreaking recordings the two cut together in Los Angeles five years earlier. (Mulligan and Baker had stopped working together after Mulligan was arrested for drug possession in 1953, and their 1957 recordings were collected on an album called “Reunion.”) This was just about the final season for Mulligan’s famed pianoless groups, and the lack of the keyboard makes the telepathic communication between the trumpeter and the saxophonist even more apparent. You hear them playing off each other, complimenting each other, providing contrapuntal commentary.

Even without a conventional chordal instrument, Mulligan, as much an arranger as a player, was always thinking about harmonies. It’s amazing to hear what he does with the chords to “How High the Moon,” which is wrapped up in the melody of Charlie Parker’s “Ornithology.” He digs into them, follows all sorts of mysterious paths, stops to quote a circus lick, and almost transforms the tune into a blues. That, obviously, was the main reason for not using a piano: He could think of more interesting places to go melodically without it.

The box’s 16 tracks with Ms. Ross are also inspired: These were done over two dates, one with Baker, the other with the brilliant Art Farmer replacing him on trumpet, and both within a pianoless quartet. Ms. Ross is every bit as spontaneous as the other front-liners. She doesn’t scat much here, but when she uses wordless singing for coloration or to join the two-horn ensemble, as on the contrapuntal lines to “I Feel Pretty” (the Jule Styne-Stephen Sondheim song from “West Side Story”), it’s tremendously effective.

Throughout, Ms. Ross is less like a star singer accompanied by a famous band than a working member of the group, yet her singing is saturated with the warmth and sensuality that only the female voice can provide. Another contemporary show tune, “I’ve Grown Accustomed to His Face,” starts with Ms. Ross singing the melody warmly and romantically, accompanied by an obligato from Mulligan; in the second chorus, Mulligan and Baker play the tune while Ms. Ross works the lyrics into a vocal obligato.

The recordings with strings, originally compiled on a 45-minute album called “Stringtime” that was never released, feature the Vinnie Burke String Jazz Quartet, a foursome whose instrumentation (cello, violin, guitar, and the leader on bass) was as unusual as its ambition to play jazz. Mulligan’s arrangements for this unprecedented ensemble seamlessly incorporate the four strings into the open ensemble texture of his pianoless sound. All nine tracks here are jazz standards by other player composers of his generation (Horace Silver, Milt Jackson) or pop and show tunes that became jazz standards (like “Body and Soul”).

Why did Mulligan and producer Bock record this delightful album – and even go to the trouble of preparing cover artwork – but never release it? That remains a secret.

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In keeping with the Mulligan theme, it’s worth noting the release of Bill Holman’s first new album in several years, “The Bill Holman Band Live” (Jazzed Media JM1007). At 78, the orchestrator continues to write compositions with heart, swing, and wit, among them “The Bebop Love Song” and “Bary Me Not” featuring the weighty baritone of Bob Efford. Mr. Holman even interjects what seems like a slice of Bartok or Berg into the middle of the Beatles’s “A Day in the Life.” His treatment of Miles Davis’s “Indiana” variation, “Donna Lee,” and a dedicatory piece to Zoot Sims and Al Cohn (further harking back to the original Mulligan songbook) reimagine the early bop era in Mr. Holman’s contemporary palette.

wfriedwald@nysun.com

“Mulligan Stew” with Jazz Band Classic tonight at Symphony Space (2537 Broadway at 95th Street, 212-864-5400).