The ironic thing about bebop is that when this style of jazz was introduced and presented to the general public in the mid-1940s, it was widely regarded by the music industry as the most esoteric thing imaginable, something that would drive listeners out of clubs in droves. Not only could you not dance to bebop, but it was pretty difficult to sing to as well, and there wasn’t much chance of it interacting with the hit parade.

Yet during the course of the last 60 years, bebop (and its closest offspring, hard bop) has become by far the most popular subgenre of jazz, so much so that all other forms, including those more “far out” (the avant-garde) and “far in” (traditional jazz and swing) are left fighting for table scraps. When nearly anyone, from tourists to jazz cognoscenti, go out for an evening of jazz, they expect to hear some variety of bop, and, consequently, that’s what the mainstream clubs present most of the time.

Certainly that’s what the packed crowd, schvitzing from the 90 degrees and 90% humidity outside, were expecting at the late show on Tuesday night at Dizzy’s Club Coca-Cola. By its very name, Dizzy’s has a mandate to present music that has its roots in the bebop revolution of the mid-1940s, and several times a year Dizzy’s mounts either a direct celebration of the music’s key founders — Dizzy Gillespie and Charlie Parker. This music still represents the essential vocabulary of jazz — so much so that even when musicians present it in performance, they don’t need to “re-create” anything. You can just ask virtually any current working musician to play what he knows.

For its presentation of basic bebop, Dizzy’s has conjoined a quintet of players who excel at dishing out that old bebop magic, starting with Charles McPherson, who is as fine a mainstream bopper as currently exists on alto saxophone, in front of a trio of veterans in Ronnie Matthews (piano), Ray Drummond (bass), and Jimmy Cobb (drums).

The other half of the front line is the trumpeter Tom Harrell, whose own bands generally play a highly advanced and idiosyncratic take on the bebop legacy, but who is supremely capable of essaying the style at its most fundamental. Throughout the evening [what evening? What event? You need to set up the peg to this article, and you should do it higher up so people know what they’re reading about], Mr. Harrell played mostly flügelhorn, an instrument that most jazz trumpeters use when they want to get mellow, but with the force and intensity of a trumpet.

One thing that makes bebop easy to enjoy is the exhilaration of sheerspeed; in the1920s and ’30s, the basic level of jazz virtuosity so increased that by the time bebop burst on the scene, it was a foregone conclusion that it would be played unbelievably fast. In fact, during the late set on Tuesday night, the quintet demonstrated three bebop approaches to familiar songs: Mr. McPherson’s opener, “Groovin’ High,” showed how Gillespie and the other early bebop composers mastered the art of taking standard chord progressions and working them into new melodies.

On “But Beautiful,” on the other hand, Mr. McPherson more or less dispensed with the melody altogether, dropping only occasional references to it in the midst of an extended improvisation. On “What Is This Thing Called Love,” he played the specific notes and intervals as dictated by Cole Porter, but played them so blisteringly fast that no other stylization or interpretation was necessary — he made a show tune into a bebop number by sheer speed alone.

Mr. Harrell was the only one who played a ballad melody with a ballad tempo, in a feeling-full rendition of “Darn That Dream.” Mr. McPherson offered an original, “A Tear and a Smile,” in which a rubato intro led into that great rarity of the bebop era, a tune in 3/4 time. (After Coltrane, there were no shortage of modal waltzes in the 1960s, but they are fairly rare in the strict Gillespie-Parker idiom.) Messrs. Matthews, Drummond, and Cobb, who often work as a unit, claimed Johnny Mandel’s “Theme From M*A*S*H” as a funky, blues-driven trio feature.

After the group’s riotous rendition of Parker’s fundamental blues in F, “Billie’s Bounce,” the crowd gathered at Dizzy’s assumed the quintet had said all it wanted to say. But the fivesome had two more pieces to offer, stretching the set out to a concert-length 100 minutes and winding up with one of the Ur-bebop classics, “Night in Tunisia.”

In his later years, Gillespie increasingly Latinized this most famous of his tunes, but Messrs. McPherson and Harrell brought it back to its mid-‘40s origins — basic bebop, plain and simple, except that there was nothing remotely plain or simple about it.

* * *

Dragging me, or any other rhythmically challenged individual, to a dance is like taking a married man to a singles bar: Not only is it not my scene, it would be a sin for me to participate. But sometimes I can’t resist showing up at Midsummer Night Swing at Lincoln Center Out of Doors, because the programmers astutely import interesting big bands from beyond the roster of usual suspects.

On Tuesday, the featured group in Josie Robertson Plaza was the Billy Strayhorn Orchestra, which hasn’t played anywhere in four years. Led by Michael Hashim, an unbeatable swing-style alto saxist, the group plays the original orchestrations of Strayhorn, who was Duke Ellington’s essential musical partner and one of jazz’s most celebrated composers. Strayhorn has been most remembered as a balladeer, but Tuesday’s performance reminded me that back in the day, Strayhorn wrote a trove of music that was hard-swinging and for the express purpose of pushing couples around the floor.

Mr. Hashim’s emphasis was on driving works like “Midriff” and “Upper Manhattan Medical Group.” He also worked in a few rarities, like the barely heard ballad “Lament for an Orchid,” and an unusual later take on Strayhorn’s famous “Take the A-Train.” The temperature was well over 90 degrees when Mr. Hashim started playing, but the heat the orchestra generated could not be measured on a thermometer.

wfriedwald@nysun.com