In reconceiving the Morgan Library from the ground up, Renzo Piano has faced a problem similar to the one that plagued Yoshio Taniguchi in his recent redesign of the Museum of Modern Art. Unable to start from scratch, he was compelled to forge a sense of coherence and wholeness out of a number of pre-existent and highly discordant parts.

If anything, though, Mr. Piano’s task was more demanding. Mr. Taniguchi sought this unity among various rectilinear artifacts of the International style that he merged into a larger context that itself bespoke the International style. Mr. Piano, by contrast, had to apply the modernist simplicity of his machine aesthetic to two pre-existing Venetian villas on 36th Street that clashed among themselves and that wanted nothing to do with the Beaux Arts Victorian brownstone on 37th Street.

Under the circumstances, the result is about as good as could be hoped for, and possibly even a little better. From the outset, the pitfalls of this thankless task were manifold. Mr. Piano’s brief was to create a signature monument whose modernist core would neither play dead in the presence of its more traditional siblings nor appear to overpower them. Somehow, he has contrived this precarious equilibrium, and it works.

True, the severe right angles of his modernist idiom do not harmonize perfectly with the classicism of the two pavilions on 36th Street. And it is hard to imagine how they ever could. But the pale, pinkish fields of metal in his new additions are clearly meant to recall the august planarity of those two pavilions. That is achieved both in the new main entrance on Madison Avenue between 36th and 37th Streets and in the two wings, one set between the pavilions on 36th Street, the other just east of the Beaux Arts brownstone.

Consisting of what looks like serried ranks of elongated modules – five on Madison Avenue and four on each of the side streets – these structures achieve, in modernist terms, something of the classical regularity that Charles McKim was clearly seeking in the original 1906 library, and that Benjamin Wistar Morris imitated in his 1928 annex. Admittedly, it is starkly different from the brownstone, but that very collision of styles works better than any facile attempt at contextualism.

In Mr. Piano’s grand main pavilion, we can appreciate for the first time the Morgan’s place within the fabric of Manhattan. His three-story atrium, an expansive glass box flooded with light, affords eccentric views of the top of the Empire State Building and the back of the humble brick apartment building just to the east. This glass-and-steel chamber, with its few well-chosen trees, its cantilevered balconies, and its spare columns, is home to a cafe that will doubtless become one of Gotham’s clamorous new scenes.

By orientating itself toward Madison Avenue rather than toward a side street, as before, the new Morgan invigorates this somewhat characterless stretch of Midtown. Though it has always been a jewel in the crown of New York’s cultural supremacy, it has never felt like that in architectural terms, because of the chaotic manner in which it was assembled. Soon it will extend its influence several blocks in either direction along Madison Avenue, and it is hard to see how that will not have some beneficial effect on this part of Manhattan.

The overwhelming sense of the new Morgan, as of the new MoMA, is that no expense has been spared to create the best architectural product possible. There was a sense of cheapness, of slipshod adequacy to the work that Voorsanger Associates did at the Morgan 15 years ago in a first attempt to consolidate all the parts of the museum. In its place you now find an opulence of sheer glass and burnished cherry wood whose well-oiled parts fit seamlessly together.

True, the three main components of the museum continue to feel semiautonomous. That was unavoidable without tearing down some of the walls – which was never even considered. Instead Mr. Piano has been content to create order out of an unruly clash of buildings, and he has done so in a manner whose skill and efficiency recall Norman Foster’s triumphant work at the British Museum in 2000. Like Mr. Foster’s British Museum, the new Morgan attains to the supreme virtue of any architectural act – namely that, one way or another, it inspires a sense of happiness and well-being in all who enter.

jgardner@nysun.com