Cliff Eberhardt plays the Blind Balladeer in the Folger Theatre’s updated production of “The Taming of the Shrew.”

When is a play with songs not a musical? When the composer says it isn’t. The Folger Theatre’s new production of “The Taming of the Shrew” has 37 musical cues. But Cliff Eberhardt, the folk musician who sings and plays guitar onstage throughout the show, says it’s no musical.

“I wanted to stay away from the musical thing because of ‘Kiss Me, Kate,’” he says, referring to the famous Cole Porter musical based on Shakespeare’s battle of the sexes. When director Aaron Posner asked him to play the invented role of the Blind Balladeer, Eberhardt made his objections clear. “I said, ‘Aaron, you already have me co-writing with William Shakespeare. I’m not going to go up against Cole Porter.’ At first he wanted people singing, and I told him, ‘It’s gonna be a musical then, and I’m not really interested.’”

Posner has been a fan of Eberhardt’s for years. “I’d be like, ‘Who are you? Why are you at every one of my shows?’” says Eberhardt. Posner asked him to work on a play 20 years ago. And 10 years ago. And four years ago. Finally, the scheduling worked out.

Eberhardt was familiar with the “Shrew” from community theater productions, so he knew its thematic challenges. It’s a problematic play for any modern director, because the original moral — that women will only be happy when entirely subordinate to their husbands — went out of style when the word “feminism” went into the dictionary. Posner’s version changes some dialogue, trying to make it clear that the marriage between the two leads — evil-tempered Katherine and her violent suitor Petruchio, played by real-life married couple Kate Eastwood Norris and Cody Nickell — is a private deal and not some sort of violent domestic affair.

Eberhardt’s songs — which are available on CD at the Folger Gift Shop — act as a sort of concept accompaniment, highlighting themes of love, property and stubbornness rather than delving into the more complex issues of gender relations and domination.

In one of Eberhardt’s favorite touches, he snags a line from “A Midsummer Night’s Dream” — “Lord, what fools these mortals be!” — for one of his compositions.

“I thought that was a perfect line for a song for these people,” he says. “They’re just completely screwing everything up.”

Folger Theatre, 201 East Capitol St. SE; through June 10, $39-$65; 202-544-7077. (Capitol South)