Michael Tyburski’s film is, after a fashion, about noise pollution: in a 1929 archival clip inserted periodically in “The Sound of Silence”—a title that’s bound to make one recall the Simon & Garfunkle song, with its undercurrent of alienation—a group of experts measure the decibel level of traffic in Times Square, commenting somberly about how high it gets.

But the movie, which can best be described as either a comedy with poignantly tragic overtones or a tragedy with dryly comic ones, is also about a noise problem of a homelier sort—virtually inaudible hums in one’s living environment that, the premise of the narrative suggest, can affect one emotionally, causing irritability, sleeplessness or worse.

Enter Peter Lucian (Peter Sarsgaard), a self-styled scientific expert with some background in acoustical engineering who offers himself as a “house tuner,” a person that can detect the offending sounds and eliminate them—a practitioner of a sort of aural feng shui. He sees himself as performing a service, and is nonplussed when smooth-talking but obviously shady entrepreneur Harold Carlyle (Bruce Altman) suggests that his theories could be monetized by his company, an outfit called Sensory Holdings.

But Peter, who lives a quasi-monastic existence in a basement flat where he hones his theories through experimentation on various pieces of audio equipment, has higher ambitions. He travels the city with his tuning forks to hand, measuring what he sees as the key signatures of different neighborhoods. His intention is to map all of New York City and encapsulate the data into a grand theory of urban sound and its impact on people. He has colleagues assisting him on the project—Robert Feinway (Austin Pendleton), a Columbia University professor, and Samuel Diaz (Tony Revolori), a grad student assigned to organize all his findings. But to what extent they can be trusted is questionable.

Lucian has submitted articles on his theories to academic journals like the New American Journal of Sound, but thus far has had no success in getting them published—toward the close of the film he confronts the editor (Tina Benko) after attending a lecture she’s given, his usually super-calm demeanor unraveling as it becomes clear that she thinks him a kook.

While this overarching plot unfolds, Tyburski and his co-writer Ben Nabors insert the possibility of Peter’s developing a connection with one of his clients, a woman named Ellen (Rashida Jones), whose friends (Tracee Chimo and Alex Karpovsky) recommend him to her. Despite his natural hesitancy at personal contact, their relationship seems to be moving forward until his insistence in putting forward his all-encompassing theories causes her to reconsider.

On the one hand “The Sound of Silence” has a sad vibe, since it’s clear that Peter’s solitary obsession is something he clings to in order to survive the discomfort he feels in human contact, and his failure to convince others about his notions hurts him deeply. Sarsgaard makes this narrative thread work; his performance is beautifully controlled, projecting an air of utter calm even as he suggests the neurosis eating away at him.

But the film has another harmonic thread, as it were, a quietly satiric one that meshes with the apparent seriousness of Peter’s story. The entire concept of house-tuning is a fabrication, of course, but the script makes it credible, in these days when absurd ideas are widely embraced, by presenting it with subtly amusing bits of quasi-evidence. When Ellen is persuaded by her with-it pals that Lucian is the real deal, for example, they cite a profile in The New Yorker as a source. (They also encourage her to try acupuncture.) Sensory Holdings is the sort of outfit that you feel could actually exist, and Carlyle the kind of oily glad-hander prevalent on the margins of the business world. And Pendleton’s Feinway is the spitting image of the over-the-hill professor always on the lookout for a faddish idea to glom onto.

The rest of the cast support Sarsgaard well, maintaining a tone that walks the fine line between seriousness and send-up. And the film has an elegant look, marked by Eric Lin’s lustrous cinematography and Nora Mendis’ sharp production design; one also has to give costumer Megan Stark Evans high marks for the appropriately drab, tweedy look she’s contrived for Lucian. Naturally the sound design is an important element here, along with the Matthew C. Hart’s smooth editing, which accentuates the lapidary rhythm Tyburski favors.

The mixture of sharp but understated humor and similarly restrained drama might strike some viewers as too mild to appreciate, and in truth the whole concept—which is in fact an expansion of a short film called “Palimpsest” (2013)—could be thought a mite thin for feature treatment. But thanks in major part to the alternately witty and touching script and Sarsgaard’s exceptional performance, Tyburski’s refined exercise in sight and sound manipulation should find an appreciative audience, though perhaps a small one.