“Over the course of the next year, we felt we were living on eggshells,” she said. “It became almost a mantra, saying to the kids, ‘The neighbors, the neighbors.’ ”

A frosty détente set in when the couple downstairs had their first child two years ago.

“I think you become a more sensitive person when you have a kid  you have to become more tolerant and understanding,” the Upper West Side mother said. “You kind of realize that life is not as tidy as you’d like it to be.”

Indeed, the vast majority of child-noise complaints are said by those called to intervene to be lodged by neighbors with no children or grown children. Trouble also tends to flare when a family replaces an especially quiet resident, when renovations render layouts incongruent (so that a hallway now runs over a bedroom, for example), and when neighbors have different sleeping schedules.

Deborah Orr’s former downstairs neighbor, a lawyer in her 30s with no children, waited six months after moving in to complain about the noise produced by Ms. Orr’s son and daughter, who were 4 and 1 at the time.

“I think she tried a little too hard to tolerate it, then I think basically she kind of snapped,” said Ms. Orr, 40, a music publicist who lived in a Park Slope brownstone co-op. “When she complained, we bought thick rugs and pads, but I think it was just too late.”

Still, Ms. Orr and her husband tried.

“There was a point,” she said, “where every time the kids would go into the hall we would get this kind of twitchy ‘don’t run  walk, walk.’ We probably tried a little too hard to eliminate the noise because we wanted to have good relationships with the neighbors and to have good kids that other people enjoy being around and not like this focus of resentment. They were not doing anything outrageous. They were just doing normal kid things. But small children, especially toddlers, have this clumsy flatfooted walk. It’s impossible to control.”

The Orrs eventually moved, because they wanted more space.

Parents who hope to avoid having angry neighbors are not presented with many good choices in New York unless they can afford a house. Many of the prewar buildings and brownstones that seem especially solid are worse when it comes to noise.