Many people think of “big-band jazz” as if it were a style unto itself, like Dixieland or bebop. The truth is that the term “big band” connotes an instrumental format, employed in a wide variety of styles. Even though big bands are associated most with the swing era, they can be as different from one another as Earl Hines is from Cecil Taylor, to name two piano-centric institutions.

Summer is traditionally a good time for big bands in New York; they tend to be presented outdoors in the festivals and dances at Lincoln Center and elsewhere, and they also are featured more in the regular clubs since many of the usual headliners are in Europe.

This summer promises to be a particularly rewarding one: The Vanguard Jazz Orchestra has an ambitious new double CD and will give a rare full-scale concert later this month at the 92nd Street Y, while the Blue Note is mounting an ongoing band festival that includes the Duke Ellington Orchestra (through Sunday) and Charles Tolliver’s very loud and very exciting large-format band (next week). But of all the clubs, ground zero remains Birdland, where no fewer than four big bands hold down regular spots every week (two on Sunday alone), including Chico O’Farrill’s Afro-Cuban Jazz Orchestra (Sunday nights), David Berger’s Sultans of Swing (Tuesdays), and Tommy Igoe’s Birdland Big Band (Friday evenings). There’s also David Ostwald’s fine Louis Armstrong Centennial Band on Wednesday evenings — not quite a big band but certainly applicable.

Recently, two veteran bandleaders launched regular runs. The arranger-composer-saxophonist Andy Farber joined the roster at Birdland on Sunday evenings, and the bass virtuoso and virtual one-man-band Vince Giordano has taken up residence at Sofia’s. Both players are historically oriented, rather than “contemporary” (in the sense of Maria Schneider or William Parker), but each takes a distinct approach to bringing classic jazz to life.

Mr. Farber’s band primarily plays his own hard-swinging arrangements, mostly of standards, such as his up reading of “The Man I Love.” The leader remains faithful to the swing idiom even when playing in 3/4 (which the great big bands rarely did back in the day) on two evergreen Richard Rodgers waltzes, “Oh, What a Beautiful Morning” and “Falling in Love With Love.”

Mr. Farber’s North Star is the Count Basie New Testament band of the 1960s. He retools Al Cohn’s famous “I Got Rhythm” variation, “The Goof and I,” with more of a Basie beat, and the two most Basie-esque numbers in the show are his two originals, “One for Ernie” (a dedication to the Count’s stalwart arranger, Ernie Wilkins) and “Squad Room Shuffle.” The latter is a recent commission for a proposed police show in the vein of Basie’s “M-Squad Theme.”

The second half of Mr. Farber’s Sunday evening set is devoted to Hilary Kole, a charismatic, outgoing vocalist who never sounds better than when she’s in front of a 15-piece big band. The Basie touch serves her well, too. She is sassy and agreeably impudent on “Deed I Do,” over a “Splanky”-like orchestral template, while her winningly up-tempo “I Only Have Eyes for You” utilizes figures reminiscent of “April in Paris.” The only thing lacking in this show is the blues, which is essential for any vocalist wanting to work in a Basie context — be it fast or slow, pure 12-bar blues or some kind of hybrid.

The combination’s “Lullaby of Birdland,” however, is an improvement over the original. In the 1950s, the New Testament orchestra played Birdland on Broadway so often that the club should have been renamed “Basieland.” But Basie’s own version of George Shearing’s “Lullaby” was only an afterthought and far from a Countish classic. The Farber-Kole treatment is more substantial, showcasing the singer and the band at their best, “Flying high in Birdland,” as the lyric goes.

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During the past five years, Vince Giordano has enjoyed long runs in at least five different Manhattan clubs, the latest (and, with any luck, longest-running) of which is Sofia’s, under the Hotel Edison, which itself was a dancing spot for big bands in the 1930s and ’40s. Mr. Giordano’s general approach is twofold: to play the classic “hot” big-band charts of the 1920s and ’30s as authentically as possible, by means of exhuming the original orchestrations whenever possible, and to play them with as much energy and pure speed as his highly trained musicians can manage.

In the past, Mr. Giordano has tried to outrace the beboppers for sheer hell-for-leather velocity. But the current edition appears to be playing with more of a relaxed bounce than usual: The leader looks to be enjoying the horn men (especially saxophonists Dan Levinson, Dan Block, and Mark Lopeman, the latter two of whom are also in Mr. Farber’s reed section) more, and inspiring the band to swing out more organically. I can’t imagine that Mr. Giordano has mellowed in middle age; more likely he is approaching his career-long goal of nailing the idiomatic rhythmic feel of the Jazz Age in a way that meets his demanding standards.

On Monday at Sofia’s, the centerpiece was the Fletcher Henderson classic “St. Louis Shuffle,” a fast and furious arrangement by Don Redman that is not only a model of call-and-response (the saxophones answering the trumpets), but a showpiece in which the instrumental texture seems to change completely every four bars or so. As played by Mr. Giordano’s band, the Nighthawks, it’s always been a highly pyrotechnic display, yet jazzy and bluesy at the same time. Now it has more of a danceable groove, which has to be due at least in part to the presence at Sofia’s of a dance floor. The Nighthawks are the undisputed masters of syncopated sounds from the pre-swing era, a period when even the much-disparaged “sweet bands” were incredibly innovative.

In three sets on Monday evening, the band also played everything from milestones (“I’m Comin’ Virginia” by Bix Beiderbecke, spotlighting Randy Sandke) to curios (“Treat Me Like a Baby,” from Sunny Clapp and His Band O’ Sunshine), and everything between (including Ellington’s early “Tiger Rag” variant “The Creeper” and King Oliver’s more derogatory “Mule Face Blues”).

In their own very different ways, Messrs. Giordano and Farber are exemplary representatives of the contemporary big-band scene, offering a kind of history that you can dance to — even if, like me, you can’t dance.

wfriedwald@nysun.com