As Jon Madof worked at his computer one Friday in 2011, doing the graphic-design job that supported his life as a guitarist, he listened to the Afrobeat music of Fela Anikulapo-Kuti. Then, with the Sabbath sundown nearing, he shut down his home office and began humming one of the Jewish religious songs made famous by Rabbi Shlomo Carlebach.

The mental mash-up of Fela and Carlebach continued through the next day, as Mr. Madof found himself weirdly hearing the rabbi’s version of “Ein Keloheinu” with the Nigerian musician’s polyrhythmic beats. When the Sabbath ended and Mr. Madof, an Orthodox Jew, could use electricity again, he went online with one question about the unlikely hybrid: “Did anyone ever do this before?”

Satisfied that nobody had, Mr. Madof set about filling a musical vacuum only he seemed to recognize. Now, two years later, his 13-piece band, Zion80, named in homage to Fela’s ensembles Afrika 70 and Egypt 80, has released its first, eponymous CD and will be performing on Thursday at Joe’s Pub before doing summer shows in Poland and Austria.

These events come after a year of gigs at the Stone, City Winery and Le Poisson Rouge, with the band drawing curious though admiring coverage on public radio and in the Jewish media.