“It’s a grueling process,” Sleep says. The rapper is referring to the differences between him and Josh Martinez — the other half of the Portland-based hip-hop duo the Chicharones (their name, essentially, means “pork rinds”).

Sleep is a dark and powerful lyricist in his own right, having long maintained a robust solo career. He is a founding member of the distinguished Seattle crew Oldiminion, a sprawling 28-person collective that includes such Northwest rap luminaries as Smoke, Syndel and Onry Ozzborn.

Martinez, originally from Canada, runs the independent label, Camobear Records, and has consistently broken away from the tenets of underground hip-hop with projects like the Pissed Off Wild — a band that has drawn comparisons to Beck and the Black Keys.

“As solo artists, we’re completely different,” Sleep goes on, having just phoned from Portland, where he is minutes away from taking the stage at the Mount Tabor Theater. “We try to meet in the middle, to find some common ground … to meld the texture of our voices in a [complementary] way. It’s hard, but it works. I mean, we’ve been best friends for 10 years.”

That closeness is evident in the results of their creative struggle. Harmonizing fluidly in their choruses and then trading verses, Martinez’s melodic flow bounces off Sleep’s rough voice and rapid-fire delivery with ease.

Both Sleep, who was born in New Mexico (where he began rapping at the age of 9), and Martinez now call Portland home. While they also devote time to other, individual projects, the Chicharones have become a focal point for the pair’s creative energies — and for good reason. It’s a captivating sound that the two artists generate, at once silly and intense, boisterous and melancholy.

The Chicharones could be described as surf rap, folk hip-hop, or any number of other labels — but none accurately describe tracks like “Little By Little,” on which Sleep’s words dance over a fluttering piano riff, or “The Put Out” — a song that evokes the Beach Boys, if Brian Wilson had peppered his harmonies with harsh rhymes about knife fights.

They perform with an electrifying live band as well as DJ Zone, who once attended a school for magicians, as did — coincidentally — Sleep. Illusion and levitation are woven into the group’s stage show, as are immense pig masks and the comedic interplay between Sleep and Martinez. It’s inarguably a singular act, not unlike Gnarls Barkley or Gorillaz in terms of sheer flavorful peculiarity.

With two warmly received, independently released full-lengths (2003’s Boss Hogs and 2006’s When Pigs Fly) under their belt, the duo is attempting to parlay the modest success of their porcine rap mythology into a wider market. They are finishing up Swine Flew Over the Cuckoo’s Nest, their third LP, which they plan on shopping around to a few labels. While they have thrived on a smaller scale through touring and independent work, the two haven’t caused much of a ripple in the industry so far.

The resonance of their sound nevertheless seems designed to gnaw through the barriers of musical taste, though, as a hog chews through tendon. Unconstrained by the expectations of underground hip-hop, the Chicharones are a cartoon pop anomaly.

Or, as Sleep puts it: “We’re just good vibes.”

The Chicharones play at Mama’s Thaiway Lounge (5908 E. Broadway Ave.) on Tuesday, April 20, at 8 pm. Tickets: $10. Call 534-3040.