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The articulate melodic eloquence of Bill Frisell

"And lots of Donna Summer hits, too," the guitarist recently recalled during a chat in New York's Washington Square Park. "It was right when disco was starting. I remember on the second or third gig, Vinnie was bashing — he was really into Tony Williams at the time — and I started to mess around with different ideas. We were supposed to be playing it straight, but I was going all over the place. The bandleader gave me a big lecture — I almost lost the gig. I learned something there, though. I've always had some kind of itch to change things around."

That impulse has worked out well for Frisell, who brings his Beautiful Dreamers trio to the Narrows Center for the Arts on Saturday (and the Regattabar in Cambridge on Friday). Throughout the past three decades, the 60-year-old has fashioned the persona of a transfiguration man, a guy able to turn jazz, pop, and country chestnuts on their heads while sustaining — and often enhancing — their original beauty. From a luminous spin on Dylan's "A Hard Rain's a-Gonna Fall" to a cello-flecked bounce through Monk's "Hackensack," he has made his mark on many a nugget.

You could hear it in the way he bent "Cluck Old Hen" and "Honeysuckle Rose" at a late spring performance at the Village Vanguard. Frisell is one of the few artists who is given the green light to book two consecutive weeks at the historic NYC jazz club, and Beautiful Dreamers, featuring violist Eyvand Kang and drummer Rudy Royston, proved to the audience just how pliable his approach truly is. A demure pluck here, a scalding shriek there — the guitarist often plots his solos using shards of ideas that are eventually meshed into a fluid statement.

On last year's Beautiful Dreamer (Savoy), the band shows how effective the process is by turning Little Anthony & the Imperials' "Goin' Out of My Head" into a fractured minuet that steadily picks up steam until it becomes the hippest piece of muzak ever — a blend of wit and sentiment. Something similar happened when Frisell appeared with saxophonist Lee Konitz's quartet at the start of June at New York's Blue Note club, breaking the melodic elements of "All the Things You Are" into kaleidoscopic fragments and then piecing them back together. It's an engaging way to work because it makes a tacit demand of the audience: Follow along for a bit and see where this leads.