Jazz is known for that hard-to-define quality we call swing. We use the term broadly. There are “swing bands,” generally large ensembles that play jazz-informed dance music.

But usually the term refers to something intangible within the music itself, something that causes involuntary rhythmic movement, something that makes us smile, something that gets the blood flowing.

Jazz ain’t jazz if it don’t swing.

The Charleston Jazz Orchestra, led by trumpeter Charlton Singleton, proceeds with its Season Five on Saturday, offering its “Atomic Basie” program, a testament to swing. Two sets are planned, at 7 and 10 p.m., at the Charleston Music Hall.

The Count Basie Orchestra, a big band that got its start in Kansas City in 1935 and continued to perform well after Basie’s death in 1984, helped define swing.

Initially called The Barons of Rhythm, the band transferred to New York City in 1937 and acquired Freddie Green on rhythm guitar. Green was a Charleston-born Jenkins Orphanage alumnus, now widely considered one of the most respected core musicians of jazz.

If the Basie Band swung, much credit must go to Green. He was part of what became known as the “All-American Rhythm Section,” with Basie on piano, Jo Jones on drums and Walter Page on bass. He remained with the band for 50 years.

Other South Carolinians enjoyed stints in the Basie Band.

Rufus “Speedy” Jones was a drummer from Charleston. He joined the group for a spell in the mid-1960s.

Eli “Lucky” Thompson, born in Columbia, played tenor and soprano saxophone for a while in the middle part of the past century. Thompson introduced elements of bebop into the big band swing style.

Pete Minger, an Orangeburg native, was the trumpet soloist with Basie in the 1970s and 1980s. Minger died in 2000 at 57.

John Williams, also an Orangeburg native, was one of the last few hired by Basie. Williams still can be heard playing his baritone sax in the Basie Band.

And then there’s trombonist Fred Wesley. Technically, Wesley is from Georgia (where he was born) and Alabama (where he was raised), but we won’t hold that against him. He lives in Manning and is a fixture of the South Carolina jazz scene, playing frequently with the Charleston Jazz Orchestra and its musicians. He joined the Count Basie Orchestra in 1978.

He is also an accomplished funkmeister. He backed James Brown and Parliament-Funkadelic during the 1960s and 1970s and today leads his own funk band.

So if swing is your thing, “Atomic Basie” ought to meet the need.