"Do I Hear a Waltz?" is an entirely serious and very dry musical about an American tourist who goes to Venice and doesn't have any fun. What more can I tell you?…

From his earlier play, "The Time of the Cuckoo," and without doing much more than thinning it out, Arthur Laurents has devised a small diary in which the loneliness, and then the stubbornness, and then the rueful awakening of starchy Leona Samish can be recorded for sound. Leona is single, and likely to be. She has come abroad looking for a "wonderful, mystical, magical miracle," but is not finding it.

By the sixth song of the evening, she is still sitting alone over evening coffee singing "Here we are together, me and I." There is a man hovering in the background, to be sure—a shopkeeper, married, rather blunt about these relationships for a girl like Leona…. Eventually, though briefly, she surrenders….

And there we have it, a straight play, played at straight-play pace, virtually unrelieved by either dancing or comedy, soberly acted, economically directed, and depending for its life upon Richard Rodgers' thoughtful songs. I call them thoughtful because they, too, cling close—firmly, with some dignity—to the plainness in Leona's life. "Take the Moment," the store-keeper urges. "Do I Hear a Waltz?" sings Leona wistfully, then a bit more warmly. "Stay," pleads the storekeeper in fine white high notes. "Thank You Very Much" whisper both, as they realize the moment is over.

With lyricist Stephen Sondheim's assistance, Mr. Rodgers has taken pains to step away from the plaintive and into the cozylively on a few—though not too many—occasions….

Mr. Sondheim seems a perfectly agreeable rhyming companion for Mr. Rodgers to be doing his work with, and if the excursions into animation never quite lift the roof off it is no doubt because they, like the narrative, are at heart mild complaints. The most effective music comes, significantly, when the corners of a bright tune are turned down. There is a chorus of "We're Gonna Be All Right" in which … [the two] young-marrieds who have been having a spot of trouble, hush their voices and rein in their spirits to suggest that it may never be all right. The contrast has an edge to it and for a moment the overcast crackles. And a ballad for three women, "Moon in My Window," is rich with the bittersweet of broken promises and unexpectedly assuaged hearts….

But there is—as the play is saying—an emotional drought in Venice, and while musical-comedy asceticism is a rare and perhaps admirable thing it cannot, and does not, do much for the evening's pulse…. In all of her travels, and for all of her wistfulness, Leona Samish hears a waltz only once.