Dan Kuramoto, founder and leader of the distinctive jazz-fusion group Hiroshima, grew up in California, as did most other members of the group. Last week Kuramoto said the only time they really feel “at home” is when they’re in Hawaii.

“I don’t think folks from Hawaii can ever understand how important our acceptance in Hawaii is to us, as an Asian-Pacific band,” he said during a cordial midday call. “We want to feel like we fit somewhere, naturally, and so Hawaii is our only hope. We don’t fit in Japan, and we’re Los Angeles-based kids who grew up in minority ghettos and there’s no place to belong (in California), so it means so much whenever we get to play in Hawaii.”

Before the month is over, Kuramoto and the other members of the group — his former wife, June Kuramoto (koto), Danny Yamamoto (drums, percussion), Kimo Cornwell (keyboards) and Dean Cortez (bass) — will have almost a week to enjoy Hawaii. Hiroshima opens a six-day engagement at the Blue Note in Waikiki on Tuesday.

“We’re building a book for this run since it’s 12 shows, so that every show will be substantially different,” Kuramoto said. “That way we can let June play a solo. It is not known that she is a great classical kotoist as well, and we don’t know what she’s going to do when she does a step-out solo — when the rest of us leave the stage for three or five minutes. Or Kimo — people don’t know what multikeyboard playing is, but he can play all these multiple keyboard parts, he’s like a freak of nature. The time will come when he will get the recognition he deserves.

“I don’t know what they’re going to do when the rest of us step out, but they’re building things just for Hawaii.”

Hiroshima enjoys playing smallish places where they can meet the fans, Kuramoto added.

“We’re excited to be able to come actually play someplace like the Blue Note, where people can sit in a small room and really kind of talk story with us and really see what June has created.

“Kimo even says, ‘To this day, every time June sits down and plays, I don’t believe what I’m hearing and seeing.’ We all feel that same way — except June. She always says that she needs to get better.”

A few of the most serious fans of June Kuramoto and her koto technique will be able to sit within a few feet of her. Seating at the club within each of the sections is first-come, first-sit, and so people who buy premium table seating, and then are first at the door, can claim the seats directly in front.

“It’s like watching up-close magic,” Dan Kuramoto said. “The range of what she can play and her fearlessness in adapting it to different situations is amazing. She has the ability — because of her amazing ear — to correct the tunings in the middle of a song and still look composed and beautiful and play things that functionally no one else in the world can play yet on the instrument.”

Dan and June Kuramoto and percussionist Yamamoto founded Hiroshima with three other Asian-American musicians in 1974. Soon, June Kuramoto’s skill at playing the koto gave the group an instantly recognizable sound and set them apart from every other jazz fusion and smooth jazz act on the scene.

Hiroshima’s self-titled debut album, released in 1979, was embraced by the mainstream “easy listening” audience as well.

The group became statewide celebrities in Hawaii in the mid-1980s when June Kuramoto was seen playing koto in a Hawaiian Electric Co. commercial. The song — titled “Hawaiian Electric” — was included on their 1987 album, “Go.”

Hiroshima has worked with some of the major names in American jazz since the 1970s — Miles Davis, Stanley Clarke, George Duke and Chick Corea, to name four. Dan Kuramoto says that support from the African-American jazz community was an important part of Hiroshima’s early success and adds that June Kuramoto’s koto was the hook.

“Stanley (Clarke) describes her as the world’s greatest koto player. Not that June has an ego about it, but June has been able to take the instrument and put it into (musical) situations where it cannot work — and she makes it work. There is no other musician in the world like June.”

Looking back, Dan Kuramoto said that although Hiroshima faced obstacles in the early years — ethnic stereotypes and some outright racism — the group broke out at a time when radio station programmers were open to original ideas and new sounds. Things have changed since then, he said. Radio stations are much less open to new music than they used to be.

Hiroshima’s latest new idea is the group’s first-ever all-vocals album, “Songs With Words,” a collection of songs from previous albums newly recorded by vocalists Terry Steele and Yvette Nii. Steele was Hiroshima’s featured voice when they released “Between Black and White” in 1999, and shared the vocal spot with Nii on Hiroshima’s 2009 album, “Legacy.”

Nii, who was born in Hawaii, will sit in with Hiroshima on this stint.

“She has a beautiful voice, and for us it’s really a blessing and an opportunity to really kind of stretch out and share what and why it is that we do all these years,” Kuramoto said.

“As artists we want to keep evolving,” he said. “We’re doing this because it means absolutely the most that anything can mean to you.”