Charles Mingus was a great composer, but his principle legacy was not a catalog of tunes. Rather, it was the jazz ensemble itself. More than anyone else – even Ornette Coleman or John Coltrane – Mingus determined what the jazz band would sound like in the postmodern era. Yet for this reason you don’t usually hear contemporary jazzmen playing Mingus. His compositions, though often on a par with those by Duke Ellington and Thelonious Monk, can’t be reduced to a basic set of chord changes and a melody that can be readily reinterpreted. To play Mingus, in many ways, you needed to be Mingus.

The man’s bands sounded like the whole history of jazz at once. Taking a cue from Coleman and the avant-garde free jazz movement, he incorporated over-blowing and extended solos. At the same time, he evoked the funky fundamentalism of New Orleans parade bands – he even resurrected the antiquated concept of polyphony to give his modern jazz a decidedly Dixieland feel. I can’t imagine Mingus ever working in a ballroom, but his catchiest riffs, like “Haitian Fight Song,” “Boogie Stop Shuffle,” and “Better Get (H)it in Your Soul” are eminently danceable. Even Mingus’s airiest flights of fancy were grounded in blues and gospel.

Mingus was also one of the most powerful bassists ever, capable of commanding an audience’s attention in the way great trumpeters and saxophonists could. Yet his solos were secondary to the way he used his bass to drive his bands. Mingus would push the band from behind, assisted by his long-standing lieutenant, drummer Dannie Richmond. At the same time, he would be way out in front, leading the other players with bass, daring them to follow.

There are two ways the legacy of great composer-bandleaders is kept alive. One is a band dedicated to playing his music. The other is new and improved releases of classic recordings. Mingus has been well served in both regards.

The melody to “Half-Mast Inhibition” by itself, without the sound of a Mingus band, just wouldn’t mean much, any more than the melody to “Moonlight Serenade” would without the Glenn Miller reed section. The answer, in both cases, was to keep the ensemble alive even after its auteur moved on. Sue Mingus, Charles’s widow and the caretaker of his legacy, actually does Glenn Miller two better: There are now three official ensembles – two appearing regularly in New York – that celebrate the music of her late husband.

Mingus’s music occasionally had a science-fiction aspect to it, and now his posthumous bands have promulgated like “Star Trek” spin-offs. The Mingus Dynasty, which has been around since the composer’s death in 1979, lately has been hitting the festival circuit again. The Mingus Big Band, which over the last 14 years has become a New York institution, now holds forth Tuesday nights at the Iridium. The newest of the three, the Mingus Orchestra, just launched a late night series at Joe’s Pub.

The triumvirate of bands is featured on the first release on Mrs. Mingus’s new label, “I Am Three” (Sue Mingus Music SSC-3029). Unlike Miller or Count Basie, Mingus never had a trademark sound, and these ensembles don’t stringently recreate him. The Mingus Big Band continues to attract the most attention on the disc, especially on the 10-minute opener, “Song With Orange.” For much of its six (out of 10 total) tracks here, the big band sounds like it could be any first-rate big band that plays Mingus’s compositions extremely well.

The new CD is the best way to hear the Mingus Orchestra, unless you’re jazzed to stay up until 11 p.m. or even 1:30 a.m. for their wee-small-hours sets at Joe’s Pub. Mrs. Mingus describes these as “an experiment to prove that people really do want to hear late-night jazz in the city that never sleeps.” The Orchestra concentrates on an underappreciated aspect of Mingus’s legacy. Rather than play up the freewheeling side celebrated by other groups, the mostly woodwind ensemble emphasizes Mingus’s more ambitious compositions, such as the evocative “Tonight at Noon” (arranged for them by Gunther Schuller) and its companion piece, “Noon Night.”

The Orchestra features 10 musicians, but not broken down into traditional big band sections. In the manner of many contemporary “free jazz” orchestras, each player is a section unto himself: one trumpet (Kenny Rampton), one tenor saxophone (Lauren Sevian or Seamus Blake), one trombone (Frank Lacy or Jonathan Arons), all driven by bassist Boris Kozlov (or Andy McKee) and drummer Donald Edwards. There are also some instruments not usually found in jazz groups, such as bass clarinet (which Mingus helped introduce to jazz, courtesy of Eric Dolphy), French horn, and bassoon.

The best recent releases of Mingus recordings are “West Coast 1945-1949” (Uptown 2748), produced in 2000, which includes some of the rarest tracks of the entire Mingus saga; and the new “Great Concert of Charles Mingus” (Verve 000268002). Recorded in Paris in April 1964, this album contains one the most famous live recordings of what is often presented as the composer’s single greatest band. With the addition of roughly a half-hour of previously unissued performances, it now fills two full CDs.

Almost every track (and they’re nearly all 20 minutes or longer) would be enough to teach a course in the entire history of jazz. “Fables of Fabus,” unlovingly dedicated to the segregationist governor of Arkansas, begins with a memorable minor melody that suggests one of Kurt Weill’s tango ballads. Tenor saxophonist Clifford Jordan solos first, in an extended statement that changes tempo and is deep in the fundamentals, referencing but not exactly quoting “Over the Rainbow,” “Summertime,” and “Old Folks at Home.”

Where Jordan is bop and blues, Eric Dolphy, here playing bass clarinet, takes the music considerably further out, with over-blowing and other free jazz techniques. Jaki Byard offers a compact history of the piano, referencing Art Tatum’s chromatic runs and Erroll Garner’s cascading block chords. He ends by saluting the French audience with their national anthem. There’s also a juicy “duel,” of sorts, between the two reeds, behind which Mingus and Richman supply rhythmic patterns that suggest Spanish flamenco music. The leader’s own solo is long and complete enough to stand as a track by itself.

Indeed, though Mingus’s tunes tend to be “covered” less than some of his lesser contemporaries, fate (and Mrs. Mingus) have taken a strong hand so that his music is now performed by more musicians than ever.