When the character called the Baker’s Wife was singing “Moments in the Woods” during Ten Thousand Things’ “Into the Woods” last week, I suddenly realized I smelled cinnamon.

This is unlikely to happen if you see the show — I suspect someone at the youth shelter where I saw the play randomly chose that moment to bake cinnamon rolls — but my lucky little bit of sensory overload felt entirely appropriate to this production, which hits hard at the humanity of its fairy-tale characters.

As a result, this is the most moving “Into the Woods” I’ve seen. It takes a while for the James Lapine/Stephen Sondheim musical to get going because it has so many stories and characters, as Cinderella, Little Red Riding Hood, Rapunzel and Jack (of Beanstalk fame) tell us their dreams before venturing into the woods in search of them. But the musical sets up those stories-within-stories beautifully, which allows the second act of “Into the Woods” to unleash a succession of emotional payoffs.

The highlight is the warm-but-skittish Baker’s (Jim Licht­scheidl) gorgeous “No More,” a father’s heartfelt song of disappointment and resilience. But there’s also Aimee Bryant’s thoughtful “Moments in the Woods” and an urgent “Children Will Listen” from the Witch (Austene Van), whose curse leads all of the show’s characters to meet.

The staging marks a fluid debut for TTT’s new artistic director, Marcela Lorca. She clarifies the story by using color and space intelligently, gradually moving the action from the four corners of the square playing area in which the company always performs toward the center, where the characters are forced to deal with one another.

There is a whole lot of story to tell, but Lorca gets a huge assist from music director Peter Vitale. He’s essentially the 10th member of the cast, providing witty sounds such as the keyboard notes that plink out the main musical motif while the Baker counts five beans.

Actors join to provide a surprisingly rich musical accompaniment — “Hello Little Girl,” for instance, features Lichtscheidl on ukulele, Sheena Janson Kelley (Cinderella) on xylophone and Tyson Forbes (the Narrator) on percussion along with Vitale on keyboards.

Watching “Into the Woods” at a shelter for young people who are vulnerable and at least temporarily without homes, I was especially moved by the idea that the musical’s characters create a new kind of family, guided by the message that “No one is alone.” But wherever you might see it, the production’s handmade quality and up-close presentation make it easy to connect to a tale that may be set in a “far-off kingdom” but feels very much like the here-and-now.