Two sounds greet you at the start of “The Hills of California,” Jez Butterworth’s relentlessly entertaining new play: the crashing of waves on the beaches of Blackpool and the tinkling of a tinny piano being tuned.

Both are plot points: The story concerns a musical family operating a rundown resort on the west coast of England. “Boogie-Woogie Bugle Boy,” “It Never Entered My Mind,” “When I Fall in Love” and “Dream a Little Dream of Me” are among the marvelous oldies you’ll hear sung during the course of the action.

But the crashing and tuning are thematic points, too. Though frequently funny and, even at nearly three hours, swift, “The Hills of California,” which opened on Sunday at the Broadhurst Theater, drops you deep into the devastations of time and lifts you gently into the consolations of song.

It does so within a familiar stage format — familiar in life, alas, as well: the dying-parent drama. In 1976, the four Webb sisters reunite at the Seaview Luxury Guesthouse (which is neither luxurious nor within sight of the sea) as their mother, Veronica, who ran the place for decades, under several desperate versions of the name, expires upstairs.

Jillian, the youngest, has failed to thrive; she’s a 32-year-old virgin who lives at home, chatters nervously and secretly smokes. The others have run as far from Blackpool as they could: Ruby and Gloria into unhappy marriages hours away; Joan, the oldest, toward a dream of fame in California. Whether she has achieved that dream is an open question; she has not been back home since she left at 15, and only Jillian believes she will return even now.

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