Composer/saxophonist Henry Threadgill has a gift for self-renewal that’s shared by just a handful of jazz greats, like Duke Ellington, Coleman Hawkins, Miles Davis, and Anthony Braxton. He can change the shape and sound of his music year after year without losing his individuality. Now, after a five-year recorded silence, he’s back with two releases that recast his music: Everybodys Mouth’s a Book, by a new edition of his Make a Move quintet, and Up Popped the Two Lips, the debut by a new sextet called Zooid, both on the new Pi label.

Threadgill’s knack for putting together quirky ensembles that mess with conventional jazz instrumentation first emerged in his seven-piece "sextett" of the ’80s, with three horns and two drummers deployed around the core of cellist Deidre Murray and bassist Fred Hopkins. The group’s reeds-trumpet-trombone front line echoed both the Jazz Messengers and New Orleans ensembles, but the cello and two drummers skewed it in more modern directions. In the ’90s, he abandoned even this remote resemblance to traditional jazz ensembles with the eccentric Very Very Circus: two guitars, two tubas, drums, French horn (or trombone), and reeds. For Make a Move he inverted these bottom-heavy ensembles, scoring the music around the higher-pitched electric guitar, harmonium, and accordion.

Zooid (pronounced "zoh-oid") takes similarly sly liberties, interweaving several strands in modern jazz into a pattern of references and sonic textures only Threadgill could concoct. Tarik Benbrahim’s oud infuses the "world music" influences that play a large part in so much modern jazz today. But Threadgill blurs the distinction between the familiar and the exotic by scoring Liberty Ellman’s acoustic guitar as if it were an oud. Dana Leong’s cello carries European art-music baggage; Jose Davila’s tuba throws in early jazz. Threadgill has mixed these elements before, but not all in one working band, and he’s rarely given himself as much solo room in music so heavily composed.

On Up Popped the Two Lips’ "Did You See That" and "Do the Needful," shifting meters create a pulse that recalls one of those old funhouse rooms where sections of the floor spin in different directions: just when the footing seems firm, you’re whipped off in a different direction. Mustered into tightly asymmetric formations on "Tickled Pink" and "Look," the line-up is compelling and touching and absurd all at once, with the elephantine huffs of the tuba bumping up against the brittle plinks of the oud and the guitar while the cello weeps and Threadgill’s alto seethes.

Few soloists are as sensitive to the underlying currents in a band as Threadgill; his solos are always calibrated to the mood and tempo of a piece. On "Dark Black," he enters at a wary angle, edging tense stuttering riffs and long, subtly inflected tones into the holes and eddies of the layered rhythms. He’s rarely sounded as good or solo’d at such length as he does here.

Everybodys Mouth’s a Book, the Make a Move quintet’s second release, feels like a more traditional jazz album: the tempos are faster, and the instrumentation is closer to what you expect from a jazz quintet. But after the band’s first album, this one too defies expectation. The first edition of Make a Move slipped in one CD for Columbia before the label dropped Threadgill. Original drummer J.T. Lewis was less resourceful at implying the beat than Dafnis Prieto, and the new music is slipperier and more elusive. Vibraphonist Bryan Carrott replaces Tony Cedras, who played a wheezy and sometimes lugubrious harmonium and accordion in the first edition; Carrott makes the music airier and more supple. Gliding on Prieto’s traps and Stomu Takeishi’s coiled-spring electric bass, "Platinum Inside Straight" and "Biggest Crumb" boast a sexually charged slither over which the vibes hover like ghostly wind chimes or dart and weave within the colliding layers of different time signatures and contrasting textures and colors. Threadgill’s alto is at its most bracing and strident on "Pink Water Pink Airplane"; it alternates between operatic grandeur and gospel shout on "What To Do, What To Do." On "Where Coconuts Fall," guitarist Brandon Ross’s molten tones and elegant phrases drift and roll like lava, and he melds avant-garde dissonance and down-home blues to great effect on "Burnt ’til Recognition."

What both ensembles share is a penchant for music that is simultaneously unnerving and reassuring. The lack of a rhythm center creates instability, but there’s never a lack of structure. And even as Threadgill continues to change his tune year after year, his ability to juggle opposites, to give shape to chaos, remains constant.