A joyful, bumpy musical version of Shakespeare’s late romance closes the Delacorte Theater before an 18-month renovation.“The isle is full of noises,” sings Caliban, and on Tuesday night it certainly was. Helicopters, radios, sirens and birdsong were competing to be heard in the Manhattan air.Yet all of them melted away, as they usually do, at the Delacorte Theater in Central Park, where the Public Theater’s new musical version of “The Tempest” was giving its opening-night performance. (It runs only through Sunday.) The seventh in the Public’s series of Public Works productions, it will also be the last for the time being; this fall, the Delacorte begins much-needed renovations that will put it out of commission until 2025.“The Tempest” makes for a fitting farewell, having opened the series, in a different adaptation, in 2013. That “Tempest” introduced the innovative Public Works idea: civic theater made for everyone, with members of local community organizations performing alongside professional actors. This new “Tempest,” adapted by Benjamin Velez (whose songs are tuneful and sweet) and Laurie Woolery (whose staging is bumpy but joyous), continues the tradition but emphasizes a new note: the pang of goodbyes.The goodbyes are generally the same ones Shakespeare plotted around 1610. Prospero, a sorcerer living for 12 years in exile on an enchanted island, must forswear the magic that has helped him survive and, with it, his fury over the betrayal that landed him there. He must also release from servitude his chief sprite, Ariel, and his monstrous slave, Caliban. And when his daughter, Miranda, having little experience of men, falls for one who washes up on shore, Prospero, deferring to love, must give her up too.“Am I not the liar/If I deny her?” he sings in the oddly named “Log Man,” a highlight of the nine-song score.Actually, make that “she sings,” because in this production, Prospero, played by Renée Elise Goldsberry in gorgeous voice, is a woman, and not gratuitously so. Her interactions with Miranda are specific to her gender. “Innocence flies like the last gasp of summer/Childhood dies in the arms of a lover/And no one tries to hold on like a mother,” she notes in a later verse of “Log Man,” getting a big laugh on the inevitability of that last word.Renée Elise Goldsberry, as Prospero, knows how to shape a moment for maximum impact, our critic writes.Sara Krulwich/The New York TimesAt least for the first half of the 100-minute show, the Shakespeare is effectively translated to musical theater — perhaps not so surprising given that musical theater is in many ways a translation of Shakespearean templates to begin with. (Songs and monologues often do similar structural work.) Here, Velez’s poppy melodies and gentle slant rhymes usually serve a second function, crystallizing the themes in quickly recognizable and memorable gestures, as the harsh economy of musicals requires.So Prospero’s opening number, “Cast a Spell,” sets up her conflict instantly: She must “finally be free of the tempest in me.” When Miranda (Naomi Pierre) meets Ferdinand (Jordan Best), the Disneyesque “Vibin’ on to You” characterizes their instinctual infatuation in its first funky measure. A merry operetta drinking song (“A Fool Can Be King”) gives Joel Perez, as the soused clown Stephano, a rousing production number, and the song that introduces Sebastian (Tristan André) and Antonio (Anthony Chatmon II) might as well have “comic villain specialty” stamped on it.Of course, those villains aren’t so comic in the Shakespeare, where their threats recall the culture of deceit and violence bred by greed and politics. But that’s one of the trade-offs of Public Works. You do get to see charming nonprofessionals like Pierre (from the Center for Family Life in Sunset Park, Brooklyn) work side-by-side with Broadway talent like Jo Lampert (who makes an acid-queen Ariel) and Theo Stockman (a piteous Caliban). But you’re not likely to see any of them get the chance to dig terribly deep.The production’s rushed second half shows why, as the late-night subway schedule bears down and the plot gets ruthlessly trimmed to beat it. We don’t miss the cut scenes so much as the connective tissue that might hold up what’s left. Also missed: the rich language that creates emotional context for a story that, with its spirits and spells, can otherwise seem almost inhuman.And though there’s a lovely finale called “A Thousand Blessings” — with members of Oyu Oro, an Afro-Cuban experimental dance ensemble, flooding the stage — the songs now come too close together to represent peaks of feeling. A landscape with only peaks is flat.Woolery, who leads Public Works and directed its terrific “As You Like It” in 2017, too often exacerbates that problem. With as many as 88 people moving about, plus five musicians in a tipped-over house remaindered from this summer’s “Hamlet” (the sets are by Alexis Distler), the stage can sometimes look like a busy airport instead of a nearly deserted island. And the clown scenes, so dependent on imaginative physical comedy, exceptional timing and an understanding of pathos, are not reliably funny.But one of the nice things about watching nonprofessionals in the limelight, especially the children, is that they don’t cover their excitement, which is funny (and moving) in itself. And one of the nice things about watching professionals in the limelight is that they know how to shape a moment for maximum impact.This is something Goldsberry does over and over, no more so than near the end, when Prospero must act on her insight that “the rarer action is in virtue than in vengeance.” As she breaks her magic staff in two, several feelings — fear, wonder, resolve — seem to scud across her face. Has she done right in making that choice?Has Public Works done right in making a similar one? Producing work that by traditional measures lacks polish, it has prioritized the virtue of engagement with actual people, and lots of them, over the secret magic known only to a few.As a critic, I feel obliged to ponder the trade-off. But as a citizen I have no doubts. Even in its lesser outings, Public Works makes its own kind of magic: a communitarian charm sorely missed these furious days. We need the series back in the park as soon as possible — albeit with better seats, more accessible bathrooms and raccoonless backstage facilities — to keep making beautiful music for our beleaguered isle of noises.The TempestThrough Sept. 3 at the Delacorte Theater, Manhattan; publictheater.org. Running time: 1 hour 40 minutes. More