The New Groove Dictionary of Jazz credited Barber, who had a key role in arranger Gil Evans' sound experiments with trumpeter Miles Davis, as probably the first tuba player "to take solos in a modern jazz style and to participate in intricate ensemble passages," the Los Angeles Times reported.
After performing with the Kansas City Philharmonic Orchestra and other symphonic groups, Barber returned to jazz, winning a spot playing with the Claude Thornhill band, considered a novelty because the swing band incorporated two French horns and a tuba.
Barber, who died June 18, was featured on Davis' "Birth of the Cool," considered the pinnacle of the era's musical creativity, and on later Davis albums as well. Barber also played on recordings by Gigi Gryce, Dick Hyman, John Coltrane and Gerry Mulligan.
He participated in Mulligan's 1992 Carnegie Hall concert, "Rebirth of the Cool," paying homage to the original "Birth of the Cool" release. The group also toured and released an album.