In the voiced-over roster of black musicians that Samuel Jackson gives halfway through Spike Lee’s Do The Right Thing, the final, most honored position goes to Mary Lou Williams. Her Zodiac Suite (1945) was itself a catalogue of iconic jazz portraits, famously crisscrossing blues, boogie and bebop to match star with star sign.

Zodiac Suite: Revisited is a bright and earnest undertaking that animates Williams’ canvas and gently stretches it just a bit. Geri Allen leads the Mary Lou Williams Collective in the remake, buoyed by game performances from Billy Hart (drums) and Buster Williams (bass), who is more alive and integral on Revisited than he has been in recent sets around town.

A faithful officer of the Mary Williams Foundation, which backed the venture on its own “Mary Records” label, Allen is nonetheless a 25-year veteran of several major labels in her own right. Her independence shows up from the first bars of “Aries,” a loping ode to Billie Holiday. Where Williams sketched her themes in long solos, Allen improvises against the rest of the band, upping the crazy quotient as if in recognition of the singer’s frenzied career.

Williams composed entire masses after her conversion to Catholicism; the more episodic but comparable scale of Zodiac is reflected in “Taurus,” for Duke Ellington. The bull’s strides are a little heavier in Allen’s piece, but real departures are subtle. By adding Hart’s cymbals, Allen dispels any brittleness from Williams’s initial chords. The choice captures the lyrical wonder of a master arranger whose own long-form works were never very well received in his lifetime.

The most interesting expansion of Williams’s original scheme may be Allen’s take on “Libra,” devoted to Dizzy Gillespie and Thelonius Monk. Under Williams’s fingers, the piece’s initial progressions were a study in clarity, showcasing the narrative potential of a still-emerging harmonic framework. In a fitting and easy gesture to those innovators, Allen distends the experience, breaking down the progressions and softening the atmosphere for each.

Allen’s own “Thank You Madam” is an even purer mood-piece. Though dedicated to Williams, it stretches out lazily over a comfortable roomscape of pleasant yawns and morning scratches suitable for any number of less platonic intentions. Take a cue from Allen’s own Holiday, and feel free to paint your own scene.