Right side set? Left side set? OK let’s go.

Clad from head to toe in white and black — in fact, divided directly down the middle between the two — Thomas Duffy, Yale director of bands and professor in the School of Music, will take the stage Saturday to conduct the Yale Symphony Orchestra in the orchestral premier of his composition “Corpus Callosum.”

He’s expecting a lot of laughs.

“It has always been the same reaction — I walk out and people laugh,” he said. “And then they’re like, ‘HUH?’”

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Maybe that’s because the composition is anything but typical.

Commissioned to write the piece for the United States Army Field Band in 1999, Duffy recalled telling the colonel he could write him some “contemporary crap” or something else entirely.

Something else won and, in 30 minutes one fateful day, “Corpus Callosum” was born.

It was like writing a good paper, Duffy explained — the best projects are the ones you think about forever before sitting down to write.

“It’s all military stuff jumbled up with patriotic music,” Duffy said.

The name of the piece refers to the bundle of neural fibers in the brain that connect the left and right cerebral hemispheres. The score pits various meters against each other: sometimes five against four, sometimes four against three. Some parts are in 15/8 time. When it’s performed, it requires the conductor to essentially split himself in two — each hand directing a different rhythm.

Michael Solotke ’13, the co-principal trombonist of the YSO, said the piece is complex and has taken the orchestra a while to learn. Solotke said he follows a different one of Duffy’s hands at various points in the piece. Everyone is jumbled up, Duffy said. Your neighbor could be watching the left hand while you watch the right — and it might switch seconds later.

“I think his piece is a really cool idea,” Solotke said. “It’s really impressive that he can do two different beat patterns at the same time and his hands are completely independent.”

Duffy, 55, said his goal in writing “Corpus Callosum” was a simple one: He wanted to “out-Ives” Charles Ives 1988, the internationally renowned American modernist composer known for his experimental music. Ives dabbled in rhythmic subdivisions, especially in his “Three Places in New England,” Duffy said. But the Yale professor insisted he could do better.

“It’s the 15/8 [time signature] that allows me to subdivide a lot more than Charles Ives could,” he said enthusiastically.

The unconventional time signature also means Duffy is one of the few people — if not the only person — who can conduct “Corpus Callosum.” When he performs it — indeed, it is a performance — Duffy dons a half-white, half-black suit custom made at Greg’s Tailor Shop in New Haven, paints his face and dyes his hair accordingly. He steps out, he said, and tells the audience to “please welcome Thomas C. Duffy and Thomas C. Duffy.”

Duffy says he’ll pay someone $100 to perform the task as well as he can. After the piece premiers with YSO, he hopes to send it around to other orchestras and have a career as a guest conductor. (Duffy said his unique ability to conduct the piece was not a factor in its composition.)

And where did he get that skill anyway? Duffy believes it developed during his six-year career as a lifeguard through the start of graduate school. The job was a great opportunity for thought, he said.

“What do you do with your brain while you’re sitting watching people swim?” he asked. “NOTHING.”

Visit the Yale Bands website and there’s a long list detailing Duffy’s accomplishments. He’s served as president of the College Band Directors National Association, president of the New England College Band Association and filled a bunch of other positions with those long, impressive-sounding titles. He’s conducted orchestras and bands in the United States, Japan, Ireland, France, Italy and England.

Duffy joined Yale’s faculty in 1982, and said he thinks of himself as a teacher first and a composer second. University President Richard Levin named Duffy acting dean of the School of Music for the 2005-’06 academic year.

His post at Yale finally offered him the chance to make ideas such as “Corpus Callosum” realities, he said.

“It was when I got to Yale that I realized this party trick of mine was the mechanism by which I could increase the polyrhythmic complexities that Charles Ives produced,” Duffy said thoughtfully.

He paused.

“Wow,” he said, “that sounds good. I sure wish I could have written that down.”