The name Chick Corea has been associated with great jazz piano composition and improvisation for over five decades. Notable milestones include his years pioneering with Miles Davis in the 1960s, his founding of the legendary Return to Forever band in the mid-1970s and his famous collaborations with vibraphonist Gary Burton, fellow pianist Herbie Hancock and, more recently, banjo virtuoso Bela Fleck.

Beyond his virtuosic touch on the keyboard and his fertile abilities at musical composition, however, Corea sees himself as a storyteller, one who uses all the elements of music at his disposal to write music — and then play with it.

“My favorite thing is to compose music,” said Corea, who over the decades has churned out Grammy Awards like clockwork, winning 22. “I’ve always just regarded my piano playing as just an aid and a realization of what I really love to do, which is compose.”

“I like the world of written music, but not to confine me as a creator. I write compositions down for others to play and for me to play, but as a guide. As a composer I create a story or a game, create a scene. But then as an improviser I take that initial scene, that initial spore, and always approach it newly, add things to it and improvise around it, take journeys off the edge of it, go somewhere completely different and then go back to the story.”

Corea was speaking from Florida, where he was about to leave on a three-day jazz cruise through the Caribbean sponsored by Blue Note, which is bringing him to Waikiki for a four-day gig starting Thursday. The jazz club franchise has had a long and fertile association with Corea, which included a two-week birthday celebration residency at its New York club last year that bought in dozens of fellow jazz masters to perform with him.

For Corea, who has played a key role in the development of jazz fusion and the worldwide promotion of Latin jazz, such opportunities are not merely about making music.

“It does come to sound, but even more basic than that, it comes to human beings and personalities,” he said. “What’s behind the banjo, of course, is Bela Fleck. There could be someone else behind the banjo and it would a totally different story.”

COREA’S OWN story in music is long and illustrious. Born and raised in the town of Chelsea across the Mystic River from Boston — he still speaks with a strong Boston accent — Corea’s first music teacher was his father, a jazz trumpeter. “He taught me to read and write music, which was lucky,” Corea said.

Showing promise and passion at piano, Corea’s parents also got him some lessons in classical music, enough to develop a lifelong interest in it. (Currently, he finds inspiration in the music of Domenico Scarlatti, an 18th-century Italian composer, and Alexander Scriabin, a Russian composer who traveled throughout Europe and the United States in the early 20th century.)

Names of his early collaborators read like a “Who’s Who” list of jazz artists — Mongo Santamaria, Herbie Mann, Sara Vaughn and Stan Getz are on it — but Corea’s first major breakthrough came when he joined Miles Davis in the mid-1960s, during one of Davis’ most experimental periods.

Davis, who didn’t even rehearse the band, famously told the young musician to “play what you hear,” which Corea understood as finding his own voice.

“What Miles meant with ‘play what you hear’ was ‘play from your own imagination,’ which was such a humane and loving thing to say and actually a very deep thing to say,” Corea said.

Now 76, Corea has became a virtual sponge for music, as reflected in his innovations. He was one of the first to develop a distinctive style on electric piano — it’s featured on the famous opening bars of “Spain,” his most popular tune — and synthesizer.

He’s considered one of the seminal figures in jazz fusion, and even now he’s experimenting with the possibilities of computer-generated sounds. He’s working with an “elektric” group that incorporates hip-hop.

“I think one of the things I keep for myself as a guiding principle is that I allow myself the freedom to be interested in whatever I want to be interested in,” he said. “If I see something that I think I can do that I think will inspire musicians and audiences, I’ll pursue it and get into it.”

Corea comes to Blue Note Hawaii with bassist Carlitos del Puerto and drummer Marcus Gilmore, whom he considers “geniuses.”

“These guys, they have their own way of doing ‘my’ music,” he said. “I’ll bring a song to the set and they’ll interpret it their own way, and that’s what I’m looking for. … Rather than me being a soloist and two guys backing me up, the group becomes a real trio, with three totally separate voice points creating the music together.”

Colleagues like that really help when it comes to playing “Spain,” which even he admits got a little old for a while.

“I gave up playing ‘Spain’ for many years, but the audiences kept asking for it,” he said. “So my new game with that song is to always come up with an improvisation for it.”