A nice boy from Westchester might not be the typical hip-hop star, but that didn’t stop 24-year-old Matt Sax from creating “Clay,” a one-man all-rap musical now open at New York’s Duke Theater.

A coming-of-age story based in part on Shakespeare’s “Henry IV” and “Hamlet” as well as Greek tragedies, it’s a show that Sax first put together after applying to the Edinburgh International Festival on a whim. “I had never studied or written music before,” remembers the actor, who used to rap for fun about his high school teachers back in Mamaroneck, N.Y. No matter, because the show got raves and traveled to Chicago and Los Angeles before coming to New York as the inaugural play in Lincoln Center’s new LCT3 program for emerging artists. It’s also landed Sax an encore gig at L.A.’s prestigious Mark Taper Forum, for which he’s creating a futuristic 17-person hip-hop musical loosely based on “Othello.”

Herewith, Sax talks beat-boxing, cultural stereotypes and the Notorious B.I.G.

HUMBLE BEGINNINGS: “At Northwestern, I auditioned for a production of ‘The Seagull’ that I didn’t get. I needed to do something extreme, so I decided to write my own piece. Basically I drank a ton of Mountain Dew and I applied to the Edinburgh festival without having written anything….We got accepted, so I was like, s--t, ‘I have to write something now.’”

RHYTHM NATION: “The first album I ever bought was Biggie’s album ‘Ready to Die.’ At the end of the album he calls Puffy and kills himself. [I realized] the extraordinary theatricality that hip-hop expresses [and wanted to figure out] how I could be a part of it without posing in any way. There’s a segment of the show where I do what I used to do as a kid, which is ‘F--- this b---h,’ and it always felt terrible coming out of my mouth. So I thought, ‘If I can teach myself to beatbox, people may allow me to be part of this culture.’...The form [of hip-hop] itself is really flexible. It can tell your story or the story of someone who’s been living in the streets their whole life. All it really takes is a beat.”

FITTING IN: “Immediately people see that I’m not black — there is no getting around it. But you see the minute I begin to rap that I’m not pretending to be something I’m not. I don’t deny the stories I tell are not those that are being told by a majority of the black artists….The comparisons to other white rappers are inevitable. People aren’t used to it. But the Beastie Boys were Jewish, too.”