Hamiet Bluiett, a baritone saxophonist who expanded the possibilities of his instrument while connecting the jazz avant-garde with a broad view of its own history, died on Thursday at his home in Brooklyn, Ill. He was 78.

His granddaughter Anaya Bluiett said that the cause had not yet been determined but that his health had deteriorated in recent years after a series of strokes and seizures.

A central figure in jazz, primarily as a member of the renowned World Saxophone Quartet, Mr. Bluiett (whose name is pronounced HAM-ee-et BLUE-it) married a dazzling physical command of the instrument with a passion for the full scope of the blues tradition. With an astonishing five-octave range, he could leap into registers that had been thought inaccessible on the baritone.

“Most people who play the baritone don’t approach it like the awesome instrument that it is,” Mr. Bluiett said in an interview with jazzweekly.com in 2000. “They approach it as if it is something docile, like a servant-type instrument. I don’t approach it that way. I approach it as if it was a lead voice, and not necessarily here to uphold the altos, tenors and sopranos.”