The Count Basie Orchestra is one of those institutions that seems rock steady — except that its music makes one want to move.

The toe-tapping, swinging 4/4 pulse that has been its metier for 80 years has led to more than 50 albums; concert performances in the grandest venues; collaborations with Frank Sinatra, Ella Fitzgerald and all the great artists of the day; and 18 Grammys. The band makes a stop in Hawaii this week for a holiday concert at the Halekulani Hotel’s ballroom and two already sold-out performances commemorating Frank Sinatra at the Halekulani with Jimmy Borges.

Band leader and trumpeter Scotty Barnhart, who took over the band in 2013, attributes its continuing popularity to the practices set down by its founder, William “Count” Basie. Barnhart says he reveres Basie, calling him “a special individual as a man.”

“In order to do what he did, you have to be able to manage personalities, and you have to have the perfect personality as a leader,” Barnhart said. “Basie was the kind of guy who would just let you focus on what your job was and not focus on him.”

Basie, a fine pianist who nonetheless let his band members shine as much as his flashy fingerwork did, formed the band in Kansas City in 1935, took it to prominence in New York during the late ’30s and, after a brief hiatus after the war, brought it back in 1952.

Though Basie died in 1984, the band has played continuously ever since, remaining true to the arrangements written for it over the decades.

Barnhart has been with the orchestra for 22 years and treats it as a sacred trust, comparing it to classical music’s New York Philharmonic.

“Ureli Hill formed the New York Philharmonic in 1842, though it didn’t take on his name, but what he wanted to do was get the best musicians and play the best music. And that’s exactly what Basie wanted to do,” Barnhart said.

The Count Basie Orchestra “is an institution now. It’s still his orchestra,” Barnhart said. “It will never be mine. It wasn’t anybody else’s after him, whether it was Bill Hughes, Grover Mitchell or Thad Jones” (leaders after Basie).

Barnhart, who concertizes on his own and teaches music at Florida State University, has a connection with the band that goes back a long way. His initial attraction to music was inspired by what he heard in church (Martin Luther King Jr.’s Ebeneezer Baptist Church in Atlanta) performed by the choir.

“They were straight-up gospel, and so the organist would be using the foot pedals walking the bass line,” he said. “And so when I heard Basie, I could hear the bass line moving, and I thought, ‘That’s the same thing I hear in church every Sunday.’ And so jazz is an exact extension of the gospel choir. It’s just a more sophisticated version, with the altos and the tenors and the bass that’s like the saxophones and the trombones and the trumpets.”

Barnhart’s connection is personal as well as spiritual. He first saw the orchestra as a child, then again at age 17.

After seeing the Basie Orchestra as a teen, he was standing in front of a hotel, waiting for his parents, when band members walked up.

The teenage Barnhart struck up a conversation with the band’s Sonny Cohn, who played trumpet with the orchestra for some 30 years.

“Next thing I know, he’s saying, ‘Why don’t you come inside and have dinner with me?’ I’m sitting inside having dinner with him — watching him eat, really, because I was so nervous — and my parents were driving up and down the street looking for me!

“I could literally feel all the 30 years he’d been in the orchestra — he’d been around the world 200, 300 times probably — and I could feel all that wisdom and all that experience coming from him. And he was kind enough to talk to me and give me advice as a young trumpeter, what to practice.

“From that meeting I knew I would be in the orchestra.”

After A lifetime of enjoying, studying and now performing the music, Barnhart knows what makes the Count Basie Orchestra’s sound so distinctive.

Although many might appreciate the band’s great solos by brass and saxophones, written by the artists themselves to show their skills and personalities, it’s the rhythm section of the Count Basie Orchestra — drums, bass, guitar, sometimes piano — that holds it all together, Barnhart said. Those instrumentalists know just how and when to add the “slip” notes into a bass line to give it that extra hop.

“That particular facet of it is something that has to be felt. You can’t really teach that,” he said. “You can have the greatest musicians in the world, but if they don’t have the understanding, it just won’t work.”

Basie was also a genius at choosing arrangers who could write for his band. He himself did not compose or even arrange that much on his own, but he had an uncanny talent for disassembling and reassembling others’ arrangements, which he usually did after a single hearing, Barnhart said.

“An arranger might have written all this fancy, hip stuff, thinking it’s going to be great, and Mr. Basie takes half of it out,” Barnhart said. “He just knew what to do. I think underneath it all was making sure that the music was accessible to the average Jean and John Doe and also was danceable for the average Jean and John Doe.

“That’s why every time we play a concert, even if it’s in a concert setting and concert hall and it’s formal and everyone’s scared to move and all this kind of thing, I always tell the audience, ‘If ya’ll feel like dancing, go ahead and do it. We don’t care. That’s what the music is for.’ Everything we play, you can dance to.”

For its performance at the Halekulani Ballroom, the band will feature tunes from its new recording, “A Very Swingin’ Basie Christmas!” (Concord), the band’s first holiday album, with new arrangements of such holiday classics as “Silent Night,” “Sleigh Ride” and “Little Drummer Boy.”

The performance promises to include more holiday music than the single line from “Jingle Bells” that the band has been playing for decades at the end of “April in Paris,” a hit for the orchestra in 1955 — though it will include that, too.

“That sounds like something that Sonny Cohn would have done,” Barnhart said. “It could have been during the holidays one year, and it stuck. We still play it every single night now.”