A child prodigy, Herbie Hancock started playing jazz piano around age 16. He’s now 77. And for nearly all of that time, he has been one of the country’s foremost jazz musicians. He’s also one of the few who can claim the mantle of a genuine celebrity, thanks to a spate of such crossover pop hits as “Watermelon Man” to “Rockit” and his foundational influence on hip-hop (not to mention a surprise album of the year Grammy nearly 10 years ago).

Hancock. (Vincent West/Reuters)

But what, besides hit records, does Hancock’s reputation rest on? It’s hard to encapsulate. He expanded jazz’s harmonic palette and helped redefine the relationship between harmony and rhythm as the pianist for Miles Davis’s great 1960s quintet, in ways that took the rest of the world decades to catch up to; he was one of the architects of jazz fusion, bringing it into contact with mainstream funk and R&B, as well as African and world music; and he continued to experiment with the possibilities of electronic music well after that — hence “Rockit” — all while keeping a foothold in progressive, acoustic jazz. All of which makes it a fool’s errand to predict what he’ll sound like in any given performance, let alone any given tour.

That’s even true when he announces his band in advance, as he has for his Kennedy Center show: Bassist James Genus can go for deep swing or hard funk with equal facility; guitarist Lionel Loueke plays jazz and West African traditional music; drummer Vinnie Colaiuta is a titan of fusion; and keyboardist saxophonist Terrace Martin has a reputation as a producer and songwriter who spits in the face of categorization. Nobody can say what will happen, except that the concert will be extraordinary.

Michael J. West

Show: Tuesday at the Kennedy Center. Show starts at 8 p.m. 202-467-4600. kennedy-center.org. $39-$115.