Since bursting onto the Los Angeles scene in 1978, the Go-Go’s have gone through the highs and lows common to rock bands: No. 1 hits and undervalued deep cuts, hard partying and rehab, splits and reunions. No wonder the all-female new wave group’s members have long fielded, and rejected, offers to dramatize their story.

The writer and actor Jeff Whitty’s idea for a Go-Go’s musical was decidedly different. As “Mamma Mia!” did for Abba, “Head Over Heels,” now in previews at Broadway’s Hudson Theater, fits songs pulled from the band’s catalog into a new story. Well, sort of new: Bridging the 1580s and the 1980s, the show’s plot is based on Sir Philip Sidney’s 16th-century prose poem “The Arcadia.”

The premise: An oracle (Peppermint, from “RuPaul’s Drag Race”) sends the royal court into a tizzy with the warning that Arcadia could lose its life-sustaining beat if four prophecies come to pass. Add to the mix a shepherd in drag and princesses pining after unlikely suitors, and all hell joyfully breaks loose.

“The Go-Go’s have a sense of humor, there is an edge and a twist to us that isn’t always apparent, and to me the show captures that,” the band’s bassist, Kathy Valentine, said by telephone.