It is tempting to think about “Do I Hear a Waltz?” as a time capsule from 1965. More precisely, however, the fascinatingly miss-matched musical that closes this season’s Encores! series of semi-staged revivals is more like two — one from musical theater’s past and one from its future.

Richard Rodgers was 62, Stephen Sondheim was 34 when they collaborated on their one and only show. The composer, near the end of his glorious career, remained a melodist unafraid of sentimental soaring. His young genius lyricist was on the cusp of creating the tough-minded heartbreaker “Company” (1970) and, despite having created both music and lyrics for “A Funny Thing Happened on the Way to the Forum” and “Anyone Can Whistle,” was not yet above writing the words for someone else’s music — especially when that someone had been half a team with Sondheim’s mentor, the late Oscar Hammerstein.

So though the show, based on Arthur Laurents’ much-adapted “The Time of the Cuckoo,” is filled with relationships on a Venice vacation that come together and pull apart, one feels the real tension between the creators.

It is almost too easy to see the first act, the hopeful one that promises romance to Leona (Melissa Errico), the middle-aged American secretary, as the Rodgers’ show. After intermission, it feels as if Sondheim could no longer contain his sophisticated cynicism and bursts out with “We’re Gonna Be All Right” and “Perfectly Lovely Couple,” brilliantly brittle with the “mildew/will do” emotions that came to define his sensibility.

The characters, of course, are caught in the middle — first loving, then fighting, perhaps settling for an uneasy compromise about middle-class morality.

In the center of the psychological confusion is Leona, played with an admirable grasp of multiple personalities by the terrific Errico. But, really, who is this woman who arrives, lonely and up for adventure on her vacation, who suddenly turns prim, then grasping and, ultimately, so mad at the world that she gives new meaning to Leona’s mad scene?

Karen Ziemba, wonderful as the worldly innkeeper, plays the only woman character who makes sense throughout. The young wife (Sarah Hunt) of a restless fellow (Claybourne Elder) flips from chic to clingy to blasé so quickly we worry about her. And Richard Troxell, a tenor from the opera world, ardently deals with the high notes as Leona’s suitor.

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Director Evan Cabnet’s lovely production breezes through as if everything were not just historically interesting but stylistically sane.