As splendid and theatrical as the museum is, however, it has suffered over the years. Immediately after Gardner’s death the main entry was shifted so that it now lines up with a vaulted side gallery, which meant that visitors lost the impact of stepping from the dark, brick entry corridor directly into the light-filled courtyard. A small bookstore and cafe were stuffed into the back of the first floor in the 1970s. Conservation offices and a temporary gallery are in a small 1930s addition plugged into the back of the museum, an area staff members refer to (not, it seems, with affection) as the doghouse. Meanwhile the number of visitors has grown from a few thousand a year to nearly 200,000.

The addition will clear up some of that mess. The bookstore and cafe will be moved to addition’s ground floor, and the space at the back of the old museum will eventually return to its original function as a meditative space with Buddhas and Chinese screens. The new music hall means that the second-floor Tapestry Room, which is often used for recitals, can now be returned to its original state. The collections will be freer to breathe.

But Mr. Piano has done more, striking an ideal balance between new and old without compromising the identity of either. The addition, whose copper cladding will give it a muscular feel, is set discreetly behind the existing building. A narrow garden, 50 feet wide, separates the two, creating a palpable tension, as between two magnets held slightly apart.

That sense of tension is also apparent in the addition, in a constant play between darkness and light, gravity and weightlessness. The ground-floor lobby and commercial spaces will be wrapped entirely in glass, with the copper-clad gallery, music hall and offices resting above. These three spaces will be divided by vertical bands of glass, so that from certain angles they will seem to be breaking apart. (The gorgeousness of these forms may very well be diminished by the treatment of the copper surface; Mr. Piano plans to treat the copper with acid, which will give it a uniformly green finish, rather than letting it age naturally, which would convey a passing of time.)

Image The addition keeps its distance from the museum’s Venetian palazzo. Credit... Renzo Piano Building Workshop

The sense of discrete spaces is enhanced by the treatment of the individual interiors, which feel less uniform in character than those in some of Mr. Piano’s earlier museums.