Whoopi Goldberg and Peter Schickele may seem like strange bedfellows. She’s an African-American comedian with dreadlocks and a trash mouth (not to mention an Oscar, Emmy, Grammy and Tony). He’s a white guy from Iowa with a mountaineer’s beard and a cornball, albeit academic, sense of humor based on inside jokes for music geeks. While those distinctions didn’t exactly disappear over the weekend when each performed at the Maine Center for the Arts, it’s clear they have more in common than simply being radio personalities. (Naturally, Whoopi is on Clear Channel Radio, and Schickele is on National Public Radio.)

First an industry disclaimer: Typically, reporters refer to subjects by their last names after a first reference. That won’t happen here. It feels inaccurate referring to Whoopi Goldberg as “Goldberg.” She’s Whoopi. That’s how we know her, and it’s a testament to her professional intimacy, rather than some kind of girlfriend familiarity, that I am sticking to her first name. So Whoopi it is.

And Whoopi it was on Saturday when she returned to her stand-up roots and spent one hour riffing on politics, parenting, menopause, gay marriage, high-fructose corn syrup and the trials of living in the speed zone of a technological world.

But first, she gave the typical newcomer celebrity chatter about Maine: “Who knew you guys were up here?” and “I love Stephen King.” She also warned the audience about her propensity for foul language and promoted her habit by explaining that the f-word is one you can say with a smile. She lamented that it is banned from the airwaves but a far more offensive word – “stupid” – is perfectly acceptable.

In one of her funniest bits, Whoopi demanded accountability from the current White House administration, beginning with U.S. Attorney General Alberto Gonzales. “Where has he gone?” she asked. “He’s like the guy Cheney shot. He was there. Then he’s gone.” (On Sunday, the Washington Post ran an op-ed by Gonzales, which catapulted him back into the media spotlight – and presumably into a new routine for all comedians. The Gonzales piece also runs today on the BDN OpEd page.)

And more on politics: “It’s exciting that people really want to take over the running of our country, and it will only take you a hundred mill. Who could run? I can’t. Oprah could.”

Hard to believe Whoopi is old enough (52 this year, she said) to do a segment that might be called “Kids These Days,” but she’s shopping it, and her audience, which has aged with her, was buying. Toward the end of the night, Whoopi seemed to lose her train of thought several times, resorting to the old line: “Maybe it’s just me.” True: She can just be Whoopi if she wants and audiences will still applaud, even if she’s defending smoker rights. But she’s at her best when she’s being smart and irreverent and setting up her “can you believe this?” insights.

On Sunday, Peter Schickele premiered his new show, “P.D.Q. Bach: The ‘What’s Your Sign?’ Tour,” to an equally admiring audience – including a handful of very young audience members whose giggles underscored his cross-generational appeal. Schickele appeared under the pretense of receiving the highest award from the American Musicological Junta – humming “Pomp and Circumstance” as he crossed the stage toward a podium. “I’m Professor Schickele,” he began, “and I just had a very good lunch. I’m a full professor.”

Ba-dum-dum, one might say, except that Schickele says it for you. The set-up could be annoying, but Schickele’s style is utterly inoffensive. Even his outfit – misshapen tuxedo, untucked shirt, red suspenders, workman boots – somehow works. And when he adds not only his own voice but those of soprano Michele Eaton and tenor David Dusing, he pretty much updates “The Carol Burnett Show,” but with a fusion of classical erudition and old-rocker passion.

The program kicked off with Allegretto Gabinetto, for plumber and itinerant keyboarder, during which Schickele blew into PVC pipe and other plumbing materials, while Lloyd Peterson accompanied him on a roll-up LED piano laid out on an ironing board. Most musicologists argue that P.D.Q. Bach, the least well-known of J.S. Bach’s children, never existed. Schickele, of course, has built a career on exhuming P.D.Q.’s music, and it’s because of pieces such as the Gabinetto (which means “bathroom” in Italian) that most of us are believers.

Otherwise, we might not give Schickele two hours in which to perform a lineup of personal songs written for co-workers, family members or a woman named Cindy who works in a store near where Shickele lives in New York. (The song helped him remember her name.) Or we might grow impatient with a series of “Heavenly Songs” with fablelike lyrics based on zodiac signs.

But Schickele, who is as much a literary writer as composer, satirist and musician, has trained a generation of fans to expect such conceits as musical adaptations of Shakespeare’s soliloquies and musical rounds called “The Art of the Ground Round.” Even “Happy Birthday, Beth,” a two-part chorus written for his mother’s 80th birthday, showed his gift for breaking the rules while employing vocal principles.

In addition to writing music that fills a sketch comedy bill, Schickele has also written works performed by Yo-Yo Ma, Emanuel Ax and the National Symphony Orchestra under the baton of Leonard Slatkin. That he also has arranged music for Joan Baez, “Sesame Street,” Buffy Sainte-Marie and was one of the composer-lyricists for the musical “Oh, Calcutta” adds a populist component that has made him a crossover artist of unusual range.

Comedy of this caliber – Whoopi and Schickele – doesn’t show up that often in this part of the state. To have two masters of humor in two days may well be one of the great comic pairings of the year, if not the decade.