There are few spaces as striking as the ICA’s Barbara Lee Family Foundation Theater, and the Either/Orchestra rivaled the setting with Friday’s local premiere of “The Collected Unconscious.”

Saxophonist/composer Russ Gershon, who launched the Either/Orchestra in 1985, has long been enamored of Ethiopian music, first reflected in a three-part suite for the group’s 2000 gem More Beautiful Than Death. They’ve since toured Ethiopia, even playing that country’s standards, and collaborated with its musicians here and abroad.

But Friday could have marked bandleader/composer Gershon’s greatest hour (or closer to an hour and a half) with “The Collected Unconscious,” a 12-part suite commissioned by Chamber Music America under the idea of “Ethiopian scales and rhythms.”

In the end, Gershon’s long-form piece bridged the sounds of Ethiopia with Latin music as well as the diverse jazz and rock elements in the composer’s DNA. His arrangements conjured rich, sublimely wound horn cadences from the 10-piece band (plus tuba guest Josiah Rebstein). “Bati Lydian” injected slow, syncopated handclaps from most of the players, at one point centered by a full-bore drum solo from Pablo Bencid. “No Price for a Ride” shifted into big-band swing with a tinge of Ethiopia. And from veteran Charlie Kohlhase, with his silky undertow on baritone sax, to fiery alto-sax newcomer Hailey Niswanger, who doubled on flute, the musicians hit their marks with precision and finesse.

Best of all, despite its broad stylistic sweep, “The Collected Unconscious” delivered cohesiveness, consistency and engaging energy. The musicians nailed the suite with such intense focus (while the band’s mirror-image reflected in the window walls that framed the theater’s panoramic harbor backdrop) that a second set of six additional pieces seemed anti-climactic.

Perhaps the musicians had been waiting to exhale. In any case, the post-intermission victory lap brought the night beyond two hours of music, mixing fine rearrangements of Ethiopian tunes with Gershon pieces that paid spiritual tribute to Charles Mingus (with faceoff between Kohlhase and lead trumpeter Tom Halter on “Town Hall Meeting”) and New Orleans.

Nineteen years since Gershon earned a Grammy nomination for one of his arrangements, the Either/Orchestra can still be found most frequently in local jazz clubs and older theaters. It was nice to see the Boston institution rise to the occasion in a high-class showcase. Wherever the band plays next, hopefully the “The Collected Unconscious” (or at least parts of it) will resurface.

The Either/Orchestra also recorded the suite for hopeful fall release. In the meantime, here are excerpts from “The Collected Unconscious” from a 2011 concert in New York on NPR’s JazzSet: