Arguably the vibraphone’s greatest innovator, Gary Burton and his four-mallet technique — the “Burton grip” — revolutionized the instrument’s melodic and harmonic possibilities. Even so, the New Gary Burton Quartet is an extension of the vibes’ percussive roots. The band (one of 21st-century jazz’s finest) that took the stage Thursday night at Blues Alley for Burton’s 70th-birthday tour was one comprehensive, well-honed rhythm instrument.

Burton’s unaccompanied intro on the opening “Afro Blue” was a virtual Cliffs Notes of his style. A flooding cascade of melody, mallets gliding over the current of sound, coalesced on a dime into stabbing percussion. It soon became a waltz for the full quartet. Bassist Scott Colley and drummer Antonio Sanchez melded into a confident but careful flow — in the pocket, in jazz parlance. On Phil Woods’s similarly grooved “Waltz for a Lovely Wife,” Burton outdid Sanchez’s formidable command in maintaining the song’s triple beat, without sacrificing the grace or whimsy of the Woods tune.

Sanchez and guitarist Julian Lage took opportunities as well to flex some rhythmic muscles. Lage, baby-faced beneath his five o’clock shadow, was the composer of “Sunday’s Uncle”: an oblong, hyper-syncopated tune with such abrupt shifts that even Burton got lost for a fraction of a second. (He made up for it, following Lage’s long, blues-ridden flight with a hair-curling turn of his own.)

Sanchez took a long, devastating intro on Pat Metheny’s “Elucidation,” crashing through ideas that could have served as a stand-alone drum medley before settling on a dead-serious structure that blended funk and swing. It pulled the band in as if on a tether, instantly going as fast and hard as the drummer — with military precision.

Not everything the band did was in such a cooperative spirit, however. Another Lage composition, a 12-bar blues called “The Lookout,” served as an old-fashioned cutting contest. Each of the musicians took turns topping the previous soloist, Burton followed Lage’s nimble-but-sturdy figures with hard-edged, tuneful phrases and Sanchez capped things off in astonishingly melodic form. Colley, however, put everyone to shame with his beat-heavy, soul-drenched blues licks.

Burton’s innovative complexities did not fail him. His accompaniment of Lage’s “Lookout” solo was a worthy composition, with interweaving lines that created luscious chords on the fly. He one-upped that achievement with a kaleidoscope of colors on the band’s encore, a delightful (and delighted) rendition of “The Night Has a Thousand Eyes.” Even so, the band’s rhythmic chemistry carried the night.

West is a freelance writer.