The Kimbell Art Museum, designed by the legendary architect Louis Kahn, is beloved like few other museums built in the past century. Opened in 1972, it finessed all of the design challenges that still plague museum architects today: how to be monumental but intimate, create a space apart from yet still connected to the world, and make an architectural statement without overwhelming the art. Its parallel arrangement of 16 cycloid concrete vaults, like some Iron Age mausoleum complex dug up on a Mediterranean isle, has elicited effusive praise: One prominent critic declared it the best American building of the second half of the 20th century, and many consider it Kahn’s masterpiece.

Now the Kahn building has a near neighbor, designed by Renzo Piano, who has amassed an astonishing number of museum design and expansion projects. He is deeply trusted by museum professionals, and one of the few living architects who would ever be invited to join a duet with something as revered as Kahn’s Kimbell. The result is a $135 million pavilion of glass and concrete, partially submerged in a low, earthen berm, yet presenting a robust face to the original Kimbell, with solid concrete pillars and a massive wooden beam running parallel to the original structure.

Like other museum additions in recent years, this expansion will please some as modest and unobtrusive and displease others for the same reasons. But it is clear that Piano has thought deeply about the work of Kahn and created a building that echoes the earlier one rather like an old Gregorian chant line woven into a newly composed Renaissance Mass: You have to look to find the subterranean connections, and in the process of looking, there is a deep and satisfying pleasure. And as you explore the tendrils of connection, you realize how much Piano has accomplished while subtly deflecting the biggest problem of all, that the modern museum is unsure of what it wants to be and why it exists.

Plans to expand the Kimbell have been controversial even as the collection grew and the museum sought space for ancillary activities (education and auditorium spaces) that have become an essential part of the contemporary museum’s basic duties. A 1989 proposal to add two wings brought howls of protest from Kahn’s widow and in a letter signed by some of this country’s most prominent architects. The plan was scuttled, but the desire for growth didn’t go away.

“The need to expand was absolutely dire,” says Kimbell Director Eric Lee. Much of the collection was often in storage, and delicate art was frequently moved to create space for the museum’s program of special exhibitions. By 2006, the Kimbell was again ready to brave the idea of an addition and turned to Piano, an Italian architect (whose projects in the United States include expansions to the Isabella Stewart Gardner Museum in Boston, the Art Institute of Chicago, the Harvard Art Museums and a building under construction for the Whitney Museum of American Art in New York). The solution was to build a separate addition, 65 yards from the earlier building but close enough to be linked by a congenial park filled with elms and a grid of orderly yaupon holly trees. Dubbed the Renzo Piano Pavilion, the new space opens to the public Wednesday.

From those devoted to Kahn’s original, there should be sighs of relief. Piano, who as a young professional had worked with Kahn, says he tried to put his pavilion “in dialogue” with the master’s work, a conversation in which the participants are close enough to be heard but not so close as to be aggressively in each other’s space. The new pavilion is well-mannered, immaculately detailed and echoes in discreet ways the long parallel forms of Kahn’s design.

And yet, just as fast as those sighs of relief are registered, there will be grumbling. Does Piano’s building say enough to merit being an interlocutor with Kahn’s? Is this yet another example of the too-retiring addition, a tacit admission that when faced with complementing a work of genius, even smart architects will lapse into decorous platitudes?

When the Saint Louis Art Museum opened an extension by British architect David Chipperfield in June, the same old argument broke out: Is being “quiet and reserved,” as the director there described it, just a lack of design confidence and institutional courage?

There is no winning this argument, and often it seems architects turn inward to avoid the problem — and to please museum executives who are increasingly concerned with the visitor “experience” and less confident about the message their buildings should send on the outside. And so the external form of the building often reverts to something basic, inoffensive and generally blank or transparent, the architectural equivalent of the black cocktail dress. Inside, however, nothing is spared to create the most perfect sense of quiet minimalism, space that is neutral, demur and luxurious in its pure emptiness. Add a few well-orchestrated views to the outside world, framed like paintings, and the job is done.

On one level, this seems to be a perfect description of Piano’s addition to the Kimbell. The inside is exquisite: The concrete is satiny smooth, with a bluish tint, the floors are made of white oak, and movable white wall panels are hung with art without obstructing sight lines that help the visitor keep his bearings. The basic form of the building includes two long, parallel wings, one of them sunk beneath a green roof. The pavilion is low-slung and echoes the basic proportions of the Kahn building.

But there’s more going on, and the more you explore the building, the more impressive Piano’s achievement becomes. The word “dialogue” isn’t used idly, and the conversation isn’t one-sided. Piano’s pavilion reaches out toward the Kahn building with robust concrete pillars supporting a massive wooden beam that, in turn, holds a glass roof that stretches out into the garden between the two structures. Gently, but firmly, the new building makes its approach to its storied predecessor.

And there are other echoes: Two stairwells lead down to a new garage (an amenity that was high on the Kimbell’s wish list). The proportions, the concrete and the play of light in the stairs suggest something archaic, an echo of the monumental yet primitive undercurrents that flowed through some of Kahn’s most ambitious architecture. Canted interior walls give a similar sense of a solidity that transcends any ordinary sense of modern, utilitarian building techniques. And the light inside — some of it coming from overhead, some of it artificial, some filtering in through windows — reminds one of Kahn’s most cherished accomplishment: the stunning play of light reflected through an ingenious window and mirror system at the top of his concrete vaults.

Most striking of all, however, is the back wall of the Piano Pavilion, which is also made of canted concrete, allowing light to pour into a glass-walled auditorium. It was inspired, in part, by a similar wall and light well in Kahn’s building, and although it hugs the property line, it gives the illusion of more space. But it is a strong, resolute gesture, visible from the front entrance of the building, as if Piano is deliberately forcing a confrontation with something massive and final. It internalizes the monumentality that was once displayed on the outside of temple-facaded museums, as if the ponderousness and sobriety of the old museum front is now an object or relic to be considered in the museum. Some may find this a wry gesture, others may find a note of sadness in it, as if Piano is deliberately referring to the end of museums as imposing civic structures.

Walk back through the garden and revisit the Kahn building, and it suddenly feels different, less massive, less archaic, more like a generously proportioned domestic sanctuary for art. That was Kahn’s intention, and it’s wonderful that Piano’s addition brings us back to the animating idea of the Kahn design, making it feel new and disencumbered of its accumulated mystique. Piano is perhaps not quite right when he says the two buildings are in dialogue. Rather, the relation is dialectical — a dialogue of logic and confrontation that moves things to a new level.