ART + Physics = Beautiful Music    By JAMES GLANZ



Can the sense of acoustic intimacy created by a fine concert hall be measured in how many milliseconds it takes sound waves to ricochet from the walls and balconies and reach a listener in the seats? Can a hall's aural warmth be calculated from how efficiently bass notes rebound from the same surfaces? Can the prized quality called resonance be estimated from the rate at which the entire hall fades to silence after a blast of electronic sound?

More to the point, can an architect rely on studies of these quantities, using computer calculations and measurements in scale models, to ensure that a structurally innovative, visually inspiring design for a new concert hall will be an acoustical triumph rather than a disaster?

For years, the answer to all these questions seemed to be no -- the field of concert hall acoustics has had only spotty success.

But now an unusually intense collaboration between architects and acousticians has put the science of acoustics to the test, with two major new successes in Tokyo.

The halls in question are the 1,632-seat concert hall of the multipurpose complex called Tokyo Opera City, and the 1,810-seat opera house of the adjacent New National Theater.

Both have architecturally daring designs, yet both have been praised by musicians who have performed in them.

"This hall simply has some of the best acoustics in which I have ever had the privilege to play," the cellist Yo-Yo Ma wrote in a commentary on the concert hall that appeared recently in a technical journal. He said its visual and acoustic aspects combined in a rare synthesis -- "a miracle," he called it.

Miracle or no, this is no small feat. "Going to the Moon is much simpler as a physics problem," said William J. Cavanaugh, an acoustician at Cavanaugh Tocci Associates who consults on both the construction and restoration of concert halls. In a Moon shot, he said, "you've got one source, you've got one trajectory that will get you there, and you've got one 'listener,' or destination."

But in a concert hall, the trajectories of the sound waves begin at any number of places on the stage, bounce in complicated ways from every cornice and pillar, and reach their ultimate destinations in hundreds of occupied seats.

The research for the new halls, whose principal architect was Takahiko Yanagisawa, president of TAK Architects in Tokyo, may be the most extensive use yet of acoustical measurements and calculations in efforts to design concert halls that are not simply copies of great halls of the past.

"If you make a copy of the old, great halls, you'll have a great hall," said Dr. Leo L. Beranek, an architectural acoustician in Cambridge, Mass., who was the principal acoustical consultant for the projects in Tokyo. But the Tokyo concert halls, he said, "are different in appearance and they have the sound of great halls."

The research is described in three papers, published earlier this year in The Journal of the Acoustical Society of America, by Dr. Beranek and Dr. Takayuki Hidaka, chief researcher of the Takenaka R & D Institute, which conducted acoustical measurements and built models. The papers describe how, as the designs took shape, scientists analyzed and worked to maintain acoustical variables like reverberation time, spaciousness and intimacy, each with a precise mathematical definition and musical meaning.

Without those studies, "you're gambling" on the acoustics, Dr. Beranek said.

Still, the success of two halls in Tokyo is unlikely to persuade all critics that the science of concert hall acoustics has finally arrived. There are still many acousticians who maintain that a knowledge of the technical issues, while helpful, is less important than experience and a repertoire of acoustically successful designs that one can fall back on in a pinch.

"If you know your craft and you know your art," said Russell Johnson of Artec Consultants, "the math today may not help you very much. And if you believe some math that's wrong, you can get into trouble very quickly."

That cautionary note was echoed by Dr. Cyril M. Harris, a professor emeritus of architecture and electrical engineering at Columbia University. The purely technical approach "works much of the time, but sometimes it doesn't, and you don't know the reason why," he said. "So you get trapped. And you get real disasters."

Yet both Dr. Harris and Mr. Johnson acknowledged that recent advances in acoustics could yield crucial clues to designers.

The history of concert hall acoustics is nothing if not contentious. No single approach, whether based on science, experience, art or pure intuition, has been without its heralded successes and unexplained failures.

In a way, in fact, musical styles and performance venues have engaged in what a biologist might call co-evolution, developing in ways that were inextricably dependent on each other.

It is no coincidence that the unhurried, vowel-rich Gregorian chants sound best in medieval cathedrals, whose "reverberation time" -- the time it takes a burst of sound to fade away -- is 5 to 10 seconds. Later in musical history, the polyphonic, highly articulated Baroque compositions of Bach, Handel and Vivaldi benefited from being played in relatively small rooms with hard, reflecting walls, in which the reverberation times might be less than 1.5 seconds.

Those close walls also added a sense of acoustical intimacy. That is, the delay between the arrival of sound directly from the instruments or voices, and sound reflected off the walls and other surfaces is slight. The smaller the delay, the greater the sense of intimacy.

Later still, as the Classical style of Haydn and Mozart gave way to the Romantics, large concert halls with correspondingly longer reverberation times were built to accommodate both the music and its growing audience.

Beethoven's later symphonies were composed "almost as though he anticipated the large, reverberant halls that would be built in the next half-century," Dr. Beranek wrote in his book "Concert and Opera Halls: How They Sound" (Acoustical Society of America, 1996).

In another biological analogue, poor concert halls often did not survive the wrecker's ball. In a kind of natural selection, the best halls of the 19th century were more likely to survive. The three halls most often cited as models of sonorous pleasure are the Grosser Musikvereinssaal in Vienna (built in 1870); the Concertgebouw in Amsterdam (1888), and Symphony Hall in Boston (1900).

Each of those halls is roughly shoebox shaped, leading to quick reflections from the fairly close side walls and balconies. Each has a reverberation time of about two seconds. And each displays numerous irregularities, like coffered ceilings and rows of buxom statues on its interior walls. The diffusion of sound created by reflections from those objects, acousticians agree, prevents a nasty acoustic "hardness" or "glare" that smooth surfaces can generate. (This diffusion is one characteristic that still awaits a precise mathematical definition, being determined for now by visual inspection of the interior.)

Symphony Hall rates a special status in the field, since the person generally regarded as the first to apply science to architectural acoustics, the Harvard physicist Wallace Clement Sabine, consulted in its design. Sabine had just discovered a crucial formula that relates a hall's reverberation time to a hall's volume and the amount of sound-absorbing material, like people and curtains, inside it.

"He really, literally, put the first numbers to this whole question," Mr. Cavanaugh said. But reverberation time alone could not divide the good halls from the bad ones. "Anybody that was working on it knew there was a lot more to it than one number." Dr. J. Christopher Jaffe of the Norwalk, Conn., firm Jaffe Holden Scarbrough Acoustics, who also directs a program on sonics in architecture at Rensselaer Polytechnic Institute in Troy, N.Y., said that a more complete translation of the warm, rich sound of the great 19th-century halls into scientific terms owed much to the development of fresh acoustical measures, or "metrics," by Dr. Beranek.

"Leo got the Rosetta Stone to get that traditional sound developed into reflecting patterns," Dr. Jaffe said. "That gave the architects some great freedom."

That freedom, he said, is most useful for designs, like those of the new halls in Tokyo, that do not carefully copy the tried-and-true, shoebox-shaped halls.

Like intimacy and reverberation time, the additional metrics have deceptively simple names like spaciousness, bass ratio, acoustical texture and clarity. But each has a precise mathematical meaning that seeks to isolate a specific aspect of acoustical quality in a hall. In the studies leading up to the design of the new Tokyo halls, said Dr. Hidaka of the Takenaka R & D Institute, measurements of those and other metrics were made in 20 opera houses and 25 symphony halls in 14 different countries. (While New York's Carnegie Hall is considered among the world's best, it was not included in the study because there was no opportunity to make acoustic measurements there, Dr. Beranek said.)

The idea, Dr. Hidaka said, was to get a quantitative measure of what made the good halls good and the bad ones bad. For the studies, his team generally produced a burst of sound from a 12-sided speaker on the stage -- actually a dodecahedron with a small speaker on each face. Each burst and its acoustic aftermath was recorded on tiny microphones placed in the ears of dummies, and in some cases the ears of real people, scattered around the seats.

The team worked out the value of the various metrics for each hall by analyzing detailed forms of the sound waves picked up by the microphones. Intimacy, for example, was defined as the time delay between the direct arrival of the sound from the stage and that of the very first reflections, which have presumably bounced off protruding side balconies.

Bass ratio gauges how efficiently low notes, compared with middle notes, carom from the walls and other surfaces; a high bass ratio gives a hall what musicians call warmth. Spaciousness is an estimate of what fraction of all the sound bathing a listener has been reflected laterally, from interior surfaces, as opposed to having arrived straight from the stage.

Dr. Beranek, Dr. Hidaka and their collaborators then compared those measurements with an acoustic ranking of the halls based on a survey of conductors and music critics. They found that the most beloved concert halls had reverberation times near two seconds, intimacy times of not much more than 20 milliseconds and relatively high bass ratios and spaciousness factors. Other metrics also took on fairly consistent values in the best halls.

Because of the need for greater clarity in understanding voices, the optimum reverberation times for opera houses turned out to be shorter, around 1.5 seconds.

Then the acousticians turned to large computers that had been programmed to simulate the acoustics in the basic architectural designs of Mr. Yanagisawa.

The team eventually built a 10-to-1 scale model of the proposed designs and made just the same measurements, using tiny speakers, microphones, and one-inch "heads" of dummy audience members, all scaled down in proportion to the model.

Even the wavelengths of the sound in the model measurements were scaled down.

This work led to numerous adjustments in the original designs, including changes in the height of the ceiling near the stage in the concert hall, giving some of the balcony fronts a rakish, forward slant and adding a special sound-diffusing material to the pyramidal ceiling.

The reflected wave patterns in the finished Tokyo Opera City concert hall, wrote the team in one of its papers, "appear to be closest to those for Boston Symphony Hall." Dr. Hidaka said acoustic data for the opera house resembled those of the famed Vienna Staatsoper.

For all the apparent success of the Tokyo projects, Mr. Yanagisawa emphasized that acoustical studies were far from the whole story. He believes that his general immersion in the music of the great halls of the world played as large a role in his understanding of good acoustics as the results of the technical work did.

"I believe an excellent hall can only be realized by a design that assimilates nuances beyond description by scientific data," Mr. Yanagisawa said. "The final work is a world of sense created therefrom."



As a chapter in the fractious history of architectural acoustics, the success of the new Tokyo concert halls can be seen as a vindication for Dr. Leo L. Beranek, who received years of negative publicity after the 1962 opening of New York's Philharmonic Hall, for which he was principal architectural consultant. The bad reviews garnered by the hall's acoustics cast a shadow over the scientific approach to acoustics that he was then developing.

But in the long run, the message from that failure has been decidedly mixed. The science was far less developed in those days, and the architects did not follow many of Dr. Beranek's suggestions, partly out of financial concerns.

Even after Dr. Cyril M. Harris, now a professor emeritus of architecture and electrical engineering at Columbia University, led a complete reconstruction in the 1970's -- when it became Avery Fisher Hall -- and Russell Johnson, an acoustician at Artec Consultants, made further adjustments to the stage in the 1990's, a kind assessment would say that the hall is still not considered among the world's best acoustically.

"At that point, in a sense, the architects had much more say about things," said Dr. J. Christopher Jaffe, an acoustician. There used to be a feeling, he said, that in acoustics, everybody thinks differently, so none of the recommendations need to be taken seriously. But that attitude has changed, Dr. Jaffe said.


A computer-generated analysis of sound reflecting inside the Tokyo Opera City concert hall, shown at right. Architects and acousticians joined to create an innovative and highly praised hall.