As direct and warmly intended as a letter from a friend, “A Second Chance” is a heartfelt new chamber musical about a middle-aged New York banker who lost the love of his life and slowly found the courage to open himself up to a second.

The stages of the budding relationship of Dan and Jenna (played by married actors Brian and Diane Sutherland) are delicately traced in this evening of 20 songs by Ted Shen, a former New York business executive who’s long been devoted to musical theater. He’s so ardent that his foundation has given Signature Theatre — where “A Second Chance” had an official opening this week — more than $1 million for a program to spawn new musicals, out of which have come Signature’s world premieres of Michael John LaChiusa’s “Giant,” Ricky Ian Gordon’s “Sycamore Trees” and Joseph Thalken, Michael Slade and Mark Campbell’s “And the Curtain Rises.”

“A Second Chance” reveals the depth of Shen’s yearning for a slot of his own on the production calendar. While the autobiographical musical comes across as a credible chronicle of the halting progress in the romance of a taciturn man and a vivacious woman, there is something a little too reserved about the piece, as if its author were conflicted about how much emotional detail he was prepared to set to melody.

As a result, the show, guided with a sensitive hand by director Jonathan Butterell, stakes out fairly non-dramatic turf. For a form that fusses to an excessive degree over young love, it is gratifying to listen to the complaints, worries, joys and epiphanies of a more mature couple. But the slightly precious songbook of “A Second Chance” lacks an essential element of surprise. It mostly deals with the familiar milestones of a new relationship: the promising first meeting; a chance encounter; an awkward run-up to a first date; the tensions that arise as doubts surface after a courtship grows more serious. I’m not sure the show ever satisfactorily justifies what it is about this particular love story that cries out for the full scale staging of musical theater.

The Sutherlands, as you might expect, have a natural chemistry, and so they make sense of the conceit of opposites attracting. We learn in “A Second Chance” that Dan’s beloved first wife has died and that even as his feelings warm toward the saintly Jenna, he can’t purge the survivor guilt. On the all-but-bare stage of Signature’s smaller space, the Ark, the actors in concert with projections designer Rocco DiSanti conjure the Manhattan museums, parks and apartments in which the affair ebbs and flows.

Married actors Diane and Brian Sutherland assist in giving the musical a convivial polish. (Christopher Mueller/Signature Theatre)

If the score lacks a standout number, it does have a jazz-inflected coherence, enhanced by the crisp attentions of sound designer Matt Rowe and a five-musician combo of saxophones, drums, bass and keyboard, conducted by Zak Sandler.

The show’s stabs at lightheartedness, meanwhile, seem overly self-conscious: a song, for instance, in which the banter between Dan and Jenna concerns a secondary character on “Mad Men” is far too contrived.

But the rapport between the actors does assist in giving the evening a convivial polish. Diane Sutherland, so earthily effective as the suburban mom in “Sycamore Trees,” is again an asset, conferring on Jenna a vibrantly benevolent essence. And in the more recessive role of the grieving widower, Brian Sutherland commendably conveys the idea of a man who’s drawn to a more exciting life force but doesn’t know how to emerge fully from his shell.

Their voices blend agreeably for a show that conceptually might be more at home in a cabaret setting, an environment in which this modest production might indeed get a beneficial second chance.

A Second Chance

Book, music and lyrics by Ted Shen. Directed by Jonathan Butterell. Set, Robert Brill; costumes, Susan Hilferty; lighting, Jennifer Schriever; orchestrations, Bruce Coughlin. About 1 hour 40 minutes. Through Dec. 11 at Signature Theatre, 4200 Campbell Ave., Arlington. Visit or call 703-573-7328.