Visitors new to the National Gallery of Art’s East Building might not detect any sign that it has undergone a major renovation. The galleries of the I.M. Pei-designed modernist addition to the National Gallery have been closed for refurbishment since 2013. On Sept. 30, they will reopen with 12,250 square feet of new exhibition space, two new stairwells creating improved public flow through the galleries, some 500 permanent collection works on display (up from 350 before the redesign), two new sky-lit tower galleries devoted to giants of 20th-century art, and a new open-air sculpture terrace along Pennsylvania Avenue.

And yet for all of these changes, nothing about the new spaces suggests they haven’t been there from the beginning, when Pei wrapped narrow bands of an art museum around an enormous glass-roofed atrium, creating what was then one of the most challenging buildings on the Mall.

Even the word “renovation” doesn’t seem quite right for this $69 million project (with $30 million from private sources). It suggests relatively superficial change, updates to surfaces and improvement to the amenities. Both of those are part of the new East Building. Old, dark charcoal carpeting has been replaced by smoky-grained oak flooring; the terrace cafe on the upper level of the atrium, which has been closed for years, will reopen, providing much-needed relief from the shopping-mall ambience of the gallery’s subterranean cafeteria; and a new elevator has been added, along with the stairwells, to better connect spaces.

A view of the new diagonal staircase in the National Gallery of Art’s East Building. (Bill O'Leary/The Washington Post)

The changes involve as much archaeology as they do renovation.The designers, who include former Pei associate Perry Chin as concept architect and adviser (and Hartman-Cox as architects of record), have dug deep into the structure of the building to find its hidden recesses and have used those to create a more fluid and open plan that still respects the geometrical structures of Pei’s original design.

Almost 50 years ago, Pei started sketching ideas for the building, which emerged as two connected forms, one an isosceles triangle with its equal sides in a 3:2 relation to its base, the other a right-angle triangle containing the museum’s offices, library and study center. Pei loved triangles (they abound in and around his glass pyramid at the Louvre and in his Bank of Hong Kong project from 1982), and the triangle became much more than just a floor plan. It was an organizing principle, readily apparent in the support structure of the glass roof, in the rhomboid shape (made of two triangles) of its towers and even in the design of its Tennessee pink marble flooring.

It was a classic modernist gesture, a gridlike underpinning that gives intellectual order to what was otherwise a sui generis structure. Unlike the basic ideas of symmetry, balance and proportion that governed the neo-classical West Building built in the late 1930s, the triangle fetish was a stern mistress over myriad details of the new structure; and it has proved no less relenting in its governance of the renovation. The added stairwells, which improve fire safety, have been fitted into hezagonal spaces (formed by six triangles) in the towers, hugging the walls closely enough that rhomboid-shaped light wells provide dizzying views from the bottom to the top of the building. The tower galleries also echo the angles formed by the triangular “grid” plan, creating odd but appealing spaces. Flooring follows the old three-pointed pattern.

The Alexander Calder mobile moves gently on its axis in the East Builidng’s main atrium. (Bill O'Leary/The Washington Post)

If you’re not aware of Pei’s obsession, no matter. Nothing in the new design is likely to make it any more or less apparent. And that’s a great part of the success of the design: It is faithful to both fundamentals and details, without being slavish or pedantic.

But it also introduces new options, the most seductive of which is the tower-level sculpture terrace. This required structural reinforcement to the ceiling-level of the floor below, but it was worth the trouble. From this terrace, over which a large, saturated-blue rooster sculpture by Katharina Fritsch stands sentinel, there are views of the city that are likely be new to almost everyone, into John Marshall Park, northeast toward the Robert A. Taft Carillon and generally in the direction of some of the District’s most rapidly evolving neighborhoods, including NOMA and the Capitol Crossing development (although not all of this is in view).

Katharina Fritsch's saturated-blue rooster sculpture, "Hahn/Cock" is on view in the building’s new sculpture terrace. (Bill O'Leary/The Washington Post)

The terrace allows visitors to escape the interior, to sit on long benches, breathe unprocessed air and generally decompress—without the ambience of food and frolic of the ground-level sculpture garden to the west of the old building. It’s hard to estimate the impact of this new space on the experience of an extended visit to the gallery, but it is certainly destined to be a favorite spot not just in the gallery, but in the city.

Museums often take the opportunity of a building or renovation project to “rebrand” themselves, an ugly and disreputable concept much in fashion in the culture industry. Not so the National Gallery, although subtle changes in its basic ethos have crept through the door. The permanent collection has been gathered into a more orderly presentation, now located in what were the former special exhibition galleries on the second and third levels (with contemporary art temporarily occupying space in the concourse-level galleries). The display is mainly chronological, beginning with rooms devoted to Picasso, the Fauves, cubism and German expressionism on the mezzanine, followed by early abstraction, Dada, surrealism, and postwar styles one floor up and spread through the “bridge” galleries along Pennsylvania Avenue on the upper level.

Pablo Picasso's "Head of a Woman." (Bill O'Leary/The Washington Post)

“In the East Building, it wasn’t easy telling a chronological story,” says Harry Cooper, Curator of Modern Art, of the old, more disconnected gallery spaces. Chronology, which governs the story of art through about the 1970s, isn’t the only change. The new galleries also incorporate more wall text, or “didactics,” to explain the groupings, and that too is another welcome nugget of innovation squeezed out by the glacial forces of change at the gallery. Works on paper, often segregated to their own galleries, have been interspersed with paintings and sculpture. More striking is the inclusion of women artists in the thematically organized concourse level rooms devoted to contemporary work. Highlights of the collection from the old and much lamented Corcoran, absorbed into the National Gallery, have been incorporated throughout the display, with a powerful impact on the whole.

One is always hesitant to celebrate change at the National Gallery. It has, in its 75 years of existence, committed all the usual sins of cultural exclusion and institutional intransigence, but today, when so many museums are turning to commercialism and entertainment for audiences, its conservativism is in many ways a breath of fresh air. The changes the gallery has made so far in its renovation campaign — future plans call for refurbishment of the atrium’s glass ceiling and eventually the offices and library wing on the southeast side — have been careful, well-considered improvements.

There is a moral in all of this: Public buildings should be distinct from private or commercial spaces,not just by their openness and accessibility, but in the integrity of their details, the dignity of their material form, the finesse of their design and the care with which they are preserved. When they indulge luxury, it isn’t for ostentation, but to reflect back at visitors the seriousness of their cultural investment. You don’t cut corners, skimp on materials, or slap some ugly cladding on a box when you’re building in the shadow of the nation’s Capitol.