Having shook up the jazz world with Ornette Coleman’s quartet beginning in 1959, trumpeter Don Cherry soon branched out on his own and became a major figure in his own right among the avant-garde. Complete Communion is the first of three albums he made for Blue Note in the mid-’60s. The quartet, with tenor saxophonist Gato Barbieri, bassist Henry Grimes and drummer Ed Blackwell, has a ragged, loose-limbed energy akin to Coleman’s group, although Cherry plays cornet, not the pocket trumpet he used with Coleman (and would return to soon enough). Cherry and Blackwell were partners in Coleman’s group, and their shared language does much to shape the sound of this set. But Cherry’s rapport with the Argentine Barbieri seems equally effortless — Complete Communion indeed — on these snappy unison themes and folkish melodies over abstract swinging rhythm. Barbieri’s own work in the ’70s veered toward a smoother, more electric Latin-funk sound; here he hits on some Ornette-like phraseology at times but emerges with an earthy, adventurous voice of his own. The entire album is two four-part suites, “Complete Communion” and “Elephantasy,” with transitions between individual movements that are fairly easy to discern. Blackwell’s hand-drum sounds on “Remembrance,” the last section of “Complete Communion,” come as a surprise and provide persistent intrigue, as do Grimes’ meaty bass solos at roughly the 12-minute and 17-minute mark. “Elephantasy” begins in a similar free-spirited medium swing mode, with tightly executed melodic passages and departures. Grimes comes alive here as well, bowing beautifully on the chamber-like, out-of-tempo “Our Feelings” and taking a burning bowed solo as well on the uptempo “Bishmillah.” The bassist was in the midst of a celebrated career resurgence when he succumbed to covid-19 in April 2020 at age 84. Complete Communion is one of his standout performances and a defining part of the Henry Grimes legacy.