Chris Whitehead Rabbi Greg Wall, one of the founders of the Ayn Sof Arkestra and Bigger Band.

The saxophone of a Carnegie Hall veteran and trumpet of a Grammy winner nimbly croon and sway to the drum-brush beat, punctuated by sharp brass notes and bass thumps so close that the front row sees players’ tendons twitch.

That might sound like $150 seats at Lincoln Center, but catching this performance actually requires a padded pew at Sixth Street Synagogue, between First and Second Avenues, home of the Ayn Sof Arkestra and Bigger Band, a Jewish ensemble founded by Greg Wall, the well-known sax-playing rabbi there, and Frank London, his friend and an accomplished trumpeter.

Believed to be one of only a handful of Jewish big bands in the country, the 15-piece group rehearses and plays shows in the Modern Orthodox shul. Lately, its music has added the Talmudic verse of Jake Marmer, poetry columnist for The Forward, the weekly Jewish newspaper.

At a recent rehearsal, Mr. London alternated between bellows into his mouthpiece and animated directions to his bandmates, several in yarmulkes, while Mr. Marmer read lines from his “Perek of Vacuum” into the mike: “If Rabbi Nachman was born today, he’d work for Disney, maybe even Deloitte. Come home and read, read, alone, all night.”

If jazz in the temple sounds remarkable — especially on Sixth Street’s historic stage — that, Rabbi Wall said, is because “extending the canon of Jewish art” was part of his charge when he was installed last September at the red brick pre–Civil War building.

Ayn Sof brainstorming sessions with Mr. London began soon after. He and Rabbi Wall, East Village jazz icons and vanguards in the Radical Jewish Culture tradition, met decades ago at the New England Conservatory and have used their clout to train eyes on Jewish jazz voices. “We want to blaze new trails,” Rabbi Wall put their mission plainly. A kabbalist term, ayn sof means — fittingly — “without end” in Hebrew.

Mr. London, who won a Grammy in 2006 with The Klezmatics for “Wonder Wheel,” said that although the aim was innovation in the jazz and Jewish scenes, the Ayn Sof Arkestra is also a throwback to tradition.

“One of New York’s biggest jazz traditions, is the Monday night big band,” he said seated beneath Sixth Street’s ark, a reminder of the other (the Jewish) tradition. “It came about because the Broadway shows are all dark on Monday, and all the musicians wanted to have someplace fun to play.”

Chris Whitehead The 15-piece group is believed to be one of only a handful of Jewish big bands in the country.

Sold on what one bandmate, Paul Shapiro, called “this wild and woolly and wonderful idea,” talent from all over the Tri-State Region showed up for the first rehearsal in February and then the first monthly concert in March. “I contacted musicians with John Zorn’s label Tzadik,” Rabbi Wall said. “That’s the most important label for artists who are combining cutting-edge music with Jewish sources. We know everyone there.”

They added Mr. Shapiro on the sax, a collaborator with Jay-Z and Hollywood composer; Pam Fleming, a trumpeter who leads Fearless Dreamer and has soloed with Sarah McLachlan; David Chevan, who studied under a New York Philharmonic bassist; and Marty Fogel, who played tenor sax with Don Cherry and Gerry Mulligan.

Not everything is ideal; Ayn Sof is time consuming, but not terribly lucrative. However, new gigs, like one with Mr. Marmer at the Cell Theatre in Chelsea on Sept. 27, do drum up demand, and a grant last year from the Dorot Foundation hasn’t hurt, either. And Rabbi Wall said he wants the group to begin recording its first album this winter, most likely through Mr. Zorn’s Tzadik label.

Still, few bandmates trek to Sixth Street for Shabbat. They come for Ayn Sof’s creative, improvisational timbre. Members write their own charts if they want—a rarity in the biz. Besides, where else would the ensemble’s playing partners include Itzhak Perlman, Rex Cadwallader, Jon Deak and Mr. Zorn.

“Let’s put it this way,” said Uri Sharlin, the band’s keyboardist, when asked why he committed to a side project like Ayn Sof. “If you’re a jazz musician in New York, these are the guys you want to play with.”

This post has been updated to correct an error. Mr. Sharlin’s surname was misspelled in an earlier version.

Rabbi Wall Jazzes It Up

Rabbi Greg Wall, of the Sixth Street Community Synagogue, juggles a life of jazz and modern Orthodox Judaism. He spoke with NYU Journalism’s James Matthews and Matylda Czarnecka about his two greatest passions in life.