It’s looks like 2017 could be the biggest year for Betty Buckley since “1776.”

Buckley, who first lit up Broadway 48 years ago as Martha Jefferson in that star-spangled musical, is flying high as a flag on the Fourth of July these days. She recently appeared in M. Night Shyamalan’s hit thriller “Split,” and she just joined the cast of The CW’s “Supergirl” as the adopted mother of Samantha, aka Reign. (She’s sworn to secrecy about plot details.)

On Saturday, she’ll stop at Tilles Center in Brookville to perform numbers ranging from Rodgers & Hammerstein to Radiohead off her album “Story Songs.” (She also has dates at Joe’s Pub in Manhattan Oct. 12-15.) During a recent phone interview, she talked about the album and some career-defining moments.

How did you choose the songs for the album?

Many of them were suggested by friends. . . . One suggested Radiohead. I love Radiohead. I have their albums, but I had never thought of choosing a song of theirs for my repertoire, but I love ‘High and Dry.’ ”

You include some great stories on the album, especially the one leading into “Both Sides Now” about Howard Da Silva, who played Benjamin Franklin in “1776.” How did working with him affect you?

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In the beginning it was scary and intimidating working with him. Our choreographer told me “He’s not going to throw you off the stage.” She suggested I take him to dinner, and when we had dinner, I was so moved by his story about how he had been blacklisted [in the 1950s] that I became a devotee. He mentored me and taught me a lot about acting and life. Years and years later . . . it was in his will that I sing “Both Sides Now” at his memorial. It was very touching to me.

“Carrie” was a breakout movie for you. What’s your favorite moment about making that film?

We rehearsed for a couple of weeks in an apartment in Hollywood with [director] Brian [De Palma], and we were all very excited and passionate about working for him. One by one, each of us got killed off in the movie. We would all get together for each person’s death scene, and it took days to shoot that whole gym sequence. Then we would all go out to dinner and toast the person who died that day.

You started out studying journalism. What happened?

My dad was very opposed to my being an actress, even though my mother had been a singer-dancer. He fell in love with her because she was known as the Jitterbug Queen of Texas Tech University. He was from a small town in South Dakota. His only exposure to actors in his youth was the dance hall girls in the bar in town. He thought actresses led an immoral life. . . . My mother was delighted when I manifested this love for song and she really mentored me. . . . She was a journalist and a very excellent PR woman, and worked on several newspapers. He though that was legitimate, that you could be a journalist and still be a wife and mother. I went to school on a couple of journalism scholarships but my love of performing was there and I wanted to do that more.

I guess your father must have been happy with how things turned out?

Not really. He came to the opening of “1776.” He thought that was OK because it was about the Declaration of Independence, but he refused to come to the Tonys when I was in “Cats.” He was a tough guy right to the end.

Did you expect to win the Tony for “Cats”?

We were nominated for eight Tonys and we won them all, but I was concerned that I would be the one who wouldn’t win and let down the whole team, and that would be embarrassing. So I was really relieved when they called my name. And I was very honored and very grateful.

Is there a role that you would still love to play?

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I’d like to play Sweeney in a cross-gender production of “Sweeney Todd.” I just love Sweeney’s music so much.