— The soaring arboretum assembled in Central Park for the Public Theater’s open-air “Into the Woods” conforms grandly to the specs for a fairy-tale musical’s magical preserve. Would that the portrayals of Stephen Sondheim and James Lapine’s storybook characters — each singing of his or her own labyrinthine neuroses, hopes and needs — were conveyed with half as much bewitchment.

But no, the performances in director Timothy Sheader’s dissonant treatment — conceived as the dreamed product of a troubled boy’s imagination — come across at times as shrill or, even more often, laboriously bedraggled. And most disconcertingly of all is the number of voices that fail to imbue Sondheim’s gorgeous score with the necessary color and light. The widespread undersinging envelops a show about outrageous calamity in the thinner air of the ordinary.

For the 50th anniversary of its free summer productions at the Delacorte Theater, a tradition started by company founder Joseph Papp and emulated in other cities, including Washington, the Public is offering its first Sondheim musical in the park. “Into the Woods,” which had its official opening Thursday night, is an environmentally apt choice for a theatrical romp under the treetops, and Jonathan Tunick’s crystalline orchestrations, given resonant breath by music director Paul Gemignani and an 11-member orchestra, sound fresh and vigorous in the encroaching twilight.

The set by John Lee Beatty and Soutra Gilmour — a series of winding, multi-tiered stairs through the trees — allows Sheader and his cast to run amusingly with the idea of characters from various bedtime stories, such as “Jack and the Beanstalk,” “Cinderella” and “Little Red Riding Hood,” getting lost and bumping into one another in the woods. (Never before with this 1987 show has the scaling of Rapunzel’s tresses been achieved quite so wondrously.) With just as much stage savvy, puppet designer Rachael Canning concocts a lady giant (voiced by none other than Glenn Close) who stares down at us menacingly through cat’s-eye glasses from atop the natural canopy.

These delights in design receive only cursory competition from an ensemble in which there are more examples of mistaken than inspired casting. The brilliantly malleable Denis O’Hare, for example, makes for a stoic and overly internalized Baker, and Amy Adams, an irresistible presence in such films as “Enchanted,” is merely pleasant as the Baker’s Wife, when what’s required is something like the mixture of heart and ironic detachment displayed in the original Broadway production by Tony-winning Joanna Gleason.

The Baker and his Wife are fictions within a fiction, characters invented by Lapine and Sondheim to endow “Into the Woods” with its most accessibly contemporary dilemma: They’re a couple desperate for a child, sent into the woods by a malicious witch (Donna Murphy) to retrieve the items for a spell to make the hideous witch beautiful and free them from her curse. Pursuing their quest, they run into characters from other fairy tales seeking to fulfill their own wishes: among them, Jack (Gideon Glick), Cinderella (Jessie Mueller), Little Red Riding Hood (Sarah Stiles) and a pair of doltish princes (Ivan Hernandez and Paris Remillard) compulsively rescuing every distressed damsel within 100 miles.

In such lovely ballads as “Stay With Me” and “No More,” “Into the Woods” explores touchstone questions of loss and suffering broached only tangentially in children’s stories, and in comic numbers such as “On the Steps of the Palace” and “Agony,” it muses wittily on the consequences of achieving one’s heart’s desire. The glue for the musical’s fractured fairy tales has to come from the authentic qualities and problems we can identify with in the various characters sent scurrying through the forest.

Few of Sheader’s actors, though, make their moments in the woods truly count, musically or otherwise. Only Stiles’s tough-as-wolf’s-nails Red Riding Hood is a fully realized character; Chip Zien, the Baker in the original Broadway production, plays the smallish role of the Mysterious Man, and your wish in the woods is that he would pop up a few times more. Others, such as Murphy, appear to be working too hard: Her witchy embellishments attempt to turn small jokes into huge ones, and so the performance ends up feeling miscalculated.

The musical has been framed for this occasion by the story of a boy (Noah Radcliffe) who himself has run away from home and, wandering in the woods, spins the stories of “Into the Woods” to keep himself company. (In the original, the lines of the Narrator were spoken by the actor playing the Mysterious Man.) The idea isn’t a bad one. But with some of its key ingredients lacking, the production’s special seasonings don’t help to get the basic flavor right.

Into the Woods

book by James Lapine, music and lyrics by Stephen Sondheim. Directed by Timothy Sheader. Co-director, Liam Steel; set, John Lee Beatty and Soutra Gilmour; costumes, Emily Rebholz; lighting, Ben Stanton; sound, Acme Sound Partners. With Tess Soltau, Kristine Zbornik. About 2 hours 50 minutes. Through Aug. 25 at Delacorte Theater, Central Park. Free tickets distributed two per person at theater on day of performance at 1 p.m. Virtual lottery ticketing: www.shakespeareinthepark.org.