Carnegie Hall Tower On Its Way

On a lot just to the east of Carnegie Hall, city officials and representatives from the hall gathered yesterday afternoon to break ground for the construction of a 59-story office tower. The building will provide the concert facility with an additional area of 25,000 square feet in which to create new rehearsal spaces, dressing rooms and an enlarged backstage.

To mark the occasion, there was a brass quintet and bright balloons. In a ceremonial gesture appropriate to the circumstances, Mayor Koch, Isaac Stern, Carnegie's president, James D. Wolfensohn, the hall's chairman, and Henry Elghanayan, president of the Rockrose Develoment Corporation, which is building the tower, assembled as the ''jackhammer quartet'' breaking ground in unison on a small patch of dirt in the middle of the lot.

They were joined by other city representatives, including Manhattan Borough President David Dinkins and New York City Comptroller Harrison Goldin, both of whom spoke about the benefits the building promises for Carnegie Hall. Mr. Dinkins, whom the Mayor praised in his speech for working diligently in behalf of the hall, described the office building as ''much more than a new tower.'' ''For Carnegie it means two things: money and space,'' said Mr. Goldin. Project's Final Step

The project marks the final step in a renovation of Carnegie Hall that began in 1982. The new building, designed by the architect Cesar Pelli, is estimated to bring both the hall and the city roughly $75 million each over the next quarter century in payments from the developer. Carnegie's share will go toward replacing income that the hall lost during its renovation process, which eliminated stores and restaurants in the old building that had provided Carnegie with rent.

The masonry tower, adorned with decorative neo-Italian Renaissance elements, will cost over $100 million to construct and take more than three years to complete, according to hall officials. It becomes the third large building in the immediate vicinity to be erected recently. The Metropolitan Tower is several feet to the east and City Spire is near completion on a site across 56th Street.

Mr. Stern, in praising Mr. Pelli's design, apparently referred to these other buildings during his brief speech when he mentioned ''evidence of things on all sides that do have the artistic input he brings to us.''

The expanded facilities for Carnegie Hall will be situated on the first seven floors of the new tower and will also include additional restrooms, elevators and an expanded lobby for Weill Recital Hall, the small auditorium adjacent to Carnegie's main performing space.