Architecture may or may not be frozen music, as Goethe may or may not have said. And Amphion of old may or may not have raised the walls of Thebes through the beguilements of his harping. But I saw no such music, frozen or otherwise, at Lincoln Center’s new Frederick P. Rose Hall, housed in the Time Warner Center.

The idea behind the architecture, I assume, was to provide some visual approximation of the rhythms and moods of jazz. Occasionally, there is a half-hearted attempt at this that doesn’t get very far. More often than not, one scarcely senses any attempt at all.

As it happens, the visual approximation of jazz is something architecture has pulled off rather effectively in recent years. If Frank Gehry has achieved nothing else, he has put the swing and syncopated sass of jazz into the stasis of glass and steel. Even as regards Skidmore, Owings & Merrill, that most buttoned-down of firms, you may imagine a certain dark Mahlerian lurch to the Time Warner Center, as it throws its saturnine weight around Columbus Circle.

Though jazz has existed at Lincoln Center for about two decades at this point, until now it has never had a permanent home. Yet at the risk of appearing to pick a nit, I find it hard to see much of Lincoln Center in this new project, which is several blocks away from the main campus and entirely different in feeling. Architectural cohesion, unfortunately, consists of more than a marquee and a letterhead.

Without question – it is a good thing to have this jazz center and to have it in its new location. But housing its 100,000 square feet in a skyscraper that also contains a mall required that the center be five floors up – pretty much precluding any important architectural statement at ground level. When you rise in the dedicated elevators to the fourth floor, you are met by a cavernous, shapeless, poorly articulated space in several dull colors. It is a bad sign when – as in other portions of Time Warner Center – the most compelling architectural feature is the view out the window, in this case the lordly prospect looking north and east over Central Park.

Jazz at Lincoln Center consists of four main architectural events, all but one of which were designed by Rafael Vinoly. The principle space is the Rose Theater, which seats 1,200 spectators and can be adapted for everything from a jazz quintet to a symphony orchestra or an opera. I cannot comment on the acoustics of the place, but visually it is pleasant enough, even if curiously “square” – as they once said in jazz dives, and not by way of a compliment.

The rows of pumpkin-colored seating in the three-tiered theater all stay politely in their serried ranks, and aside from the lozenge-shaped lamps at the top, which apparently will blink in all sorts of colors, there is little jazz here. The exposure of bristling metallic stage gear in the fly-space overhead is hardly as innovative as Vinoly seems to believe.

The Allen Room holds a little more promise. Like the Rose Theater, this is a highly adaptable space consisting of a lofty, crescent-shaped auditorium on several levels that can accommodate tables and chairs. The main attraction here is the towering curtain wall at the front, with its incomparable view of Central Park. Perhaps more importantly, it will present some stunning views into the building from the outside whenever a concert is being held.

Dizzy’s Club Coca-Cola certainly has more rhythm and oomph to it than the two larger venues. It is a quivering, undulating mass of woodwork, with tables set into what I believe is the dance space. Like the Allen Room, it is also a restaurant. Darker and on a more intimate scale than the other two venues, it has the virtue of recalling those jazz clubs that seem to appear in every black-and-white film shot between 1935 and 1950 – the kind that abounded in flatfoots, jellybeans, floozies, and cigarette girls.

Finally there is the Ertegun Jazz Hall of Fame, the smallest part of the complex, designed by the ever-fashionable David Rockwell. I must say, I have never been in a space by this designer that actually clicked in any effortless and definite way. In the present instance, we find ourselves in a room that seems too small to call itself a hall. Here again, jazziness is suggested by a ceiling consisting of irregular rust-colored undulations. The syncopation continues in the carpet underfoot, as well as in the spacing of a series of pillars, which are illuminated with images of such greats as Billie Holiday, Louis Armstrong, and Bix Beiderbecke. Along the walls of this darkened space are moving pictures of the worthies of jazz.

In defense of Jazz at Lincoln Center, allow me to say that, whatever the spaces look like now, they will almost surely look better and feel more successful when they are awash in people. An empty jazz club is a sad thing. But if jazz by its nature embraces extremes, the architectural essence of this new center is its essential unwillingness to take risks.

In this sense, perhaps, it captures the ethos of the institution to which it is a home. There is something very grown-up about these four spaces, in the sense of being primly responsible. You almost feel as though, despite the nocturnal aspirations of the planners, the whole place will close by 10:30 p.m. and everyone will have gone home.

The opening of the new hall may well represent the moment in the history of jazz when it is most dramatically assimilated to the mainstream and most fully estranged from the anarchic riot of its roots. This design reflects such moderation – in that sense, at least – we are perhaps correct in saying that its architecture is frozen music.