Geri Allen, an influential pianist and educator whose dense but agile playing reconciled far-flung elements of the jazz tradition, died on Tuesday at a hospital in Philadelphia. She was 60.

Her publicist, Maureen McFadden, said the cause was cancer.

Perhaps more than any other pianist, Ms. Allen’s style — harmonically refracted and rhythmically complex, but also fluid — formed a bridge between jazz’s halcyon midcentury period and its diffuse present.

She accomplished this by holding some things constant: a farsighted approach to the piano, which she used both to guide and to goad her bandmates; an ability to toggle between artistic styles without warping her own sound; and a belief that jazz ought to interact with its kindred art forms across the African-American tradition.

“The music of most African societies integrates all of the arts, particularly dance,” Ms. Allen told Marc Myers of the website JazzWax in 2012. “By doing this, the entire culture is embraced, not just music and musicians. The result is that audiences have a more vivid sense of music’s importance. The cultural embrace of music has been a big part of my reality and my art.”