January sees the eclectic jazz crossover guitarist Joel Harrison campaigning in a variety of venues around the city, giving contemporary music fans ample opportunity to get current with one of NYC’s more inventive musical residents. Joel Harrison’s End Time Quintet debut new music Jan. 10 from his April 2007 release as part of the Winter Jazzfest.

Then on Jan. 12 Joel’s doing the dirty deed to his fellow Harrison, George, as part of the Rubin Museum’s ultra-hip “Harlem in the Himalayas” series. The following day he’s back in action with his alt-music group, Starfish Parade.

The “Harrison on Harrison” project is an especially engaging milestone in the current effort by forward-looking jazzmen to integrate the pop-rock cannon into the always-evolving jazz repertory, and George is arguably the Beatle whose songbook most invites such assimilation. With their Indian modalities and harmonic complexities, numbers like “While My Guitar Gently Weeps” and “Within You and Without You” call out for the kind of sophisticated re-invention that’s at the heart of any great jazz cover (never, incidentally, has a musician made a Western guitar sound more sitar-like than when Joel covers George). And Harrison’s joyous take on “Here Comes the Sun”—beautifully captured on the Harrison on Harrison album—is pure fusion gold.

Harrison’s Starfish Parade holds forth at Toad Hall every Sunday (since there’s no cover for these shows this has got to be one of the best performance deals you’re going to find in the coming weeks.) The Starfish Parade gigs should be more unpredictable and perhaps even more serendipitous, partly because of Harrison’s startling and joyous improvisational skills—and partly because of the audacious variety of material he’s been willing to explore over the years. One can expect to hear some of the layered but listenable works recently commissioned by Chamber Music of America, and also some of the Appalachian and country music covers that have become one of the guitarist’s signatures. But Harrison is amply capable of playing jazz that is as straight-ahead and grounded in the familiar bop vernacular as anything you’re likely to hear at Lincoln Center.

An authentic experimentalist, he plays without taboos or preconceptions, but also without a need to smash conventions simply to prove he can. It’s fascinating to listen as Harrison and his sidemen take an armor-plated warhorse of a song like “Folsom Prison Blues” and produce something that is at once an instantly recognizable homage and a genuinely new and idiosyncratic work of art.

Harrison has written of his desire “to combine simple, direct song forms with more mysterious and abstract improvisational language,” and it’s just that willingness to keep the outer reaches of new music connected to the irresistible heart of popular song that makes Harrison’s work so appealing and infectious.

Joel Harrison’s End Time: Jan. 10, Knitting Factory (Tap Room), 74 Leonard St. (betw. B’way & Church St.), 212-219-3132; 8:20, $25.

Harrison On Harrison Ensemble featuring David Binney: Jan. 12, Rubin Museum of Art,150 W. 17th St. (at 7th Ave.), 212-620-5000, ext. 344; 7-8:30, $15.

Joel Harrison’s Starfish Parade: Ongoing, Toad Hall, 57 Grand St. (at W. Broadway), 212-431-8145; Sundays 8-11 p.m., free.