Instead, the society has embarked on a $55 million, three-year renovation of its galleries, entrance and facade that will create a permanent main-floor exhibition hall showcasing some of its treasures, an interactive multimedia orientation program in its auditorium, an 85-seat cafe and a below-ground children’s gallery and library, society officials said.

A wide coalition of opponents had criticized the height of the tower — 280 feet, doubling the 136-foot height of the current structure — and had charged that the tower would deform the skyline of Central Park West and cast a shadow on Central Park. The society’s building has landmark status individually, and as part of the Upper West Side-Central Park West Historic District and a smaller domain, the Central Park West-76th Street Historic District.

“Our members feel relief that there won’t be this thing over them, this great unaesthetic vertical shadow,” said Peter M. Wright, co-chairman of the Park West 77th Street Block Association, who lives in the 92-unit cooperative at 6-16 West 77th Street where the tower would have blocked some views.

But some preservationists were already looking ahead. “We always knew the society’s plan was a stalking-horse that would have opened the door to more tower development on Central Park West,” said Kate Wood, executive director of Landmark West, an Upper West Side group. “So, this is a victory for the community that cares about the historic skyline and the park, but the fight is far from over.”