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In many ways, his remixed Chaucer is a return to his roots. After getting his master’s, Mr. Brinkman toured with a version of “The Canterbury Tales,” which by then included “The Miller’s Tale” and “The Wife of Bath’s Tale.” For the new show, he’s rewritten everything and collaborated with Mr. Simmonds on original music.

Deciding to rap about “The Canterbury Tales” makes a perverse sense. Mr. Brinkman explains that Chaucer wrote a rich and elaborate tapestry of medieval social life, combining snapshots of all classes, from nobles to workers, from priests and nuns to drunkards and thieves.

There was another reason, too: “He’s dirty,” said Mr. Brinkman, laughing.

“He’s the Slick Rick of that era,” Mr. Simmonds added.

” ‘The Canterbury Tales’ are so unashamed and a totally piercing portrait of human nature and human foibles. And I think rap is that as well. It doesn’t blush when it looks at human behavior,” Mr. Brinkman said. “It’s all on display in rap - warts and all. And that’s what ‘The Canterbury Tales’ is, too.”

In the show, Mr. Brinkman’s lyrics - performed over Mr. Simmonds‘ moody, orchestral score - explain the work through a cheeky modern lens. In “The Pardoner’s Tale,” Mr. Brinkman raps that the title character is “a medieval televangelist. He’s Creflo Dollar, he’s Ted Haggard, he’s got mad swagger like Jimmy Swaggart.”

In the same tale, Mr. Brinkman offers a way to understand the three drunken men who seek to kill Death: “Think Boyz in the Hood; think Menace to Society/Just from the Middle Ages, of the Flemish variety.”

His work on Chaucer led to “The Rap Guide to Evolution,” “The Rap Guide to Human Nature” and “The Rap Guide to Business,” which he was commissioned to write to welcome a new class at New York University’s Stern School of Business.

“Human capital, it’s tough to quantify,” he rapped in one song. “But without it your business will not survive/Human capital, it’s tough to quantify/You got to offer people more than just a nine to five.”

Mr. Brinkman and Mr. Simmonds both have moved to New York and are preparing to take full advantage of their three-year work visas. Their evolution rap will tour in the spring and the Chaucer work is now enjoying a run until early January, and may tour as well.

The two are plotting a new rap guide, perhaps on religion or maybe on climate change. Whatever it is, it won’t be fluffy. “I’m not exactly drawn to small talk,” Mr. Brinkman said. “As an MC, I want to tackle the most controversial, interesting things in the world.”