Flutes and their kin, including whistles, ocarinas, recorders and pipe organs, are among music's oldest and most versatile instruments. Yet science has long had trouble understanding all but the most elementary aspects of how they work.
Now, however, researchers are starting to learn some of the secrets. In a way, science is glimpsing the soul of a very old machine.
The tardiness may seem surprising. After all, the scientific revolution has been rolling along for centuries and has made great progress in understanding time, space, matter and life, to name a few basics. The physics of wind instruments would seem to be passe.
But the truth is that the methods of science work exceedingly well in some fields and poorly or not at all in others. There are more mysteries than most people realize.
The new insights center on how jets, eddies and waves of air pressure come together at the heart of such wind instruments to form the complex vibrations heard as agreeable tones. Such turbulence is now being photographed and parts of it modeled mathematically with rigor. Even so, the analyses are still sketchy and limited by gaps and approximations.
"These instruments seem very simple," said Marc-Pierre Verge, a leader of the research. "But from a physical point of view, they're very complicated, much more so than the piano or violin."
The new insights are nonetheless plentiful enough to help music professionals make better reproductions of old wind instruments, such as Baroque recorders, and to invent new ones, scientists say.
The advances also are aiding electronic music, including that of synthesizers, organs, home computers, games and movies. The goal is to make artificial tones more realistic and, in other cases, to create sounds and instruments that have no counterpart in the real world.
For instance, scientists can now make a virtual flute of almost any size and shape, its tube curled or a hundred feet long. Notes can be very low and sometimes very strange.
Electronics giants such as Yamaha, the Japanese maker of musical instruments, are incorporating some of the advances into products. The research is global, with work being done in Japan, Europe and Canada as well as the United States.
Scientists agree that the physics of flutes and similar wind instruments is a challenging final frontier, despite the field's long history and recent strides. Julius O. Smith III, a Stanford University expert on music, called the theoretics of wind instruments "perhaps the most slippery in all of musical acoustics."
Perry R. Cook, a Princeton professor of music and computer science who works on flute simulations, said progress of late had been "really profound," especially because European studies are illuminating what had previously been hidden.
"People have been scratching their heads about this stuff since at least Pythagoras and probably before," Cook said. "Aristotle had a theory. So did lots of acoustics guys."
Flutes, whistles and kindred instruments date to humanity's early days, when they were used in hunting, signaling, magic and ritual. The Maya and Incas made flutes of clay that modern scholars have found to be surprisingly complex in tone and construction.
During the Renaissance and Baroque periods, wood recorders evolved rapidly, with bores becoming tapered and tubes made of two or more interconnecting parts. The more elaborate recorders had a wide range of pitch, volume and color tone, allowing them to come alive in expert hands.
By the dawn of the Industrial Revolution, large organs in cathedrals had many hundreds of pipes and a spectrum of tonal characteristics. They were among the age's most complex machines, rivaled only by clocks.
In general, members of the family work by directing a stream of air against a sharp edge, which causes the jet to pulsate back and forth, creating waves of sound. The family is thus commonly known as jet or edge winds.
With some instruments, such as the flute, pan pipe and soda bottle, the player's lips and skill are central to forming the flow of air, which must be fast but even. With other edge instruments, such as whistles, recorders and the flue pipes of organs, the forming job is done by a smooth duct.
For the family as a whole, experts have long known that the basic pitch is determined by the length of the tube.
Throughout history, great scientists have probed the subtleties of such instruments, especially the origin of the sound and what controls its tonal qualities. But the job is very hard. As Lord Rayleigh, an English physicist, showed in 1896, the flow of one gas or fluid past another (or of air moving through still surroundings) is unstable, producing the kinds of swirls seen in puffs of cigarette smoke.
For string instruments, the job is much easier. A plucked string produces waves of vibrations that are easy to see, study and model mathematically, so much so that beginning students of physics often do such analyses to develop their skills.
"The math models are extremely good" for string instruments, said Smith of Stanford. But for many of the winds, he added, "you're on thin ice."
Despite the edge family's many puzzles, music scientists have made some analytic headway in recent decades.
From the 1960s to the 1980s, researchers did so mainly by simplifying the problem to its bare bones. For instance, a math simulation of a flute would assume that the instrument had only one dimension, length, rather than the usual three. And the analysis would focus on the instrument's overall characteristics, rather than the riddle of how the sounds start and evolve.
Scientists would often make ad hoc adjustments to get things going. Then, by trial and error, and careful listening, they would test how well the math and computer simulations matched the real thing, tweaking the model to improve the sound.
Douglas Keefe, head of music for the Acoustical Society of America, said many of these efforts were toylike and produced relatively crude sounds.
Still, progress was eventually sufficient to attract companies that made electronic instruments. For flutes, their products had often used recorded samples of real sounds. But the companies were eager to tap the greater flexibility of tone, timbre and quality that was possible if they had some insight into the real nature of the sound's generation.
Yamaha in the early 1990s drew heavily on Stanford University flute modelers, including Cook, who later went to Princeton. The results showed up in such devices as the company's VL1 Virtual Acoustic Synthesizer, which used physical modeling to create a variety of instrument sounds.
Flute mimicry evolved rapidly as a European research group found a way to illuminate many details of the hidden action. The work, overseen by Avraham Hirschberg, a physicist at the Eindhoven University of Technology in the Netherlands, was done in concert with IRCAM, the Institute for Research on Acoustics and Music in Paris.
To limit variables, the team zeroed in on recorderlike instruments, which can be excited by compressed gas rather than human blowing.
At the heart of the test apparatus was an 11-inch instrument resembling the flue pipe of an organ, its central parts made of glass to permit viewing. For visualizations, carbon dioxide was found to give the best contrast with surrounding air. The gas was shot through the pipe's duct, and the resulting jets, whorls and eddies were photographed up close.
Eventually, the team was able to take a series of snapshots (and even movies) that laid things bare, in particular how the sounds form and develop.
From 1994 to 1997, the team published a series of influential papers based on analysis of the snapshots. And in 1995, Verge, the team's leader, who had come from Paris to study with Hirschberg in the Netherlands, received his Ph.D. from Eindhoven University.
The work, Verge said in an interview, is deeply rooted in the team's observations.
"It was by looking at the pictures that we noticed many, many things that weren't obvious at first," he recalled.
For example, the team found that much influence was exerted by tiny vortexes -- little whirlwinds shed from the jet-edge interface in rising number and complexity as the sound developed. Such eddies were previously presumed to exist, and some scientists had suggested that they were key to sound amplification.
But the Eindhoven team, which included Benoit Fabre, from the Musical Acoustics Laboratory of the University of Paris, found otherwise.
The vortexes actually cut the strength of the fundamental, the root vibration that makes up the instrument's lowest note. Moreover, the team discovered that the tiny whirls were important in the rise of harmonics, the vibrations more rapid than the fundamental that give an instrument much of its tone and distinctiveness.
Finally, the team found that vortex shedding helped trigger the instrument's first sounds, especially when the note's onset, or attack, as musicians call it, was fast. An initial eddy that curled off the sharp edge into the pipe would start a pressure wave that bounced back and forth in the tube, setting up a feedback loop and the instrument's main vibratory state.
The research so impressed the Acoustical Society of America, a professional group, based in Woodbury, N.Y., that it highlighted it last year in its annual "World of Sound" calendar. Splashed atop November were eight of the Eindhoven team's photographs showing how a note is rooted in subtle whorls and vortexes.
Despite the advances, the calendar noted, just how such wind instruments work "is still not fully understood."
Verge said he and some colleagues are turning their insights into products. In Montreal, they have set up a company, Applied Acoustics Systems Inc. that in a few months is to release music-making software based on physical modeling.
Using this software on a computer, a player will be able to be form flute, string, reed, brass and other kinds of electronic notes.
"It's fun," Verge said. "It's like Lego. You have small blocks and you build what you want. The only limit is your imagination."
Verge added that that he had made virtual flutes more than 30 feet long, some with side tubes branching off in different directions.
"You get some very low tones," he said, as well as odd harmonics.
Such studies and products are increasingly of interest to makers of synthesizers, organs, home computers, games and movies, all of whom are eager for sounds that are new and more realistic.
Surprisingly, Verge said the flute research also had many industrial uses.
The team's models of turbulent noise and note generation, he said, have application to industrial design, where ventilation systems as well as gas and water pipes often develop unwanted sounds.
A last frontier of the field is using the new knowledge to illuminate how wind instruments old and new are put together, revealing strengths and weaknesses.
Over the centuries, Verge said, "craftsmen have learned to exploit subtle acoustical phenomena which make musical instruments very interesting as study objects."
Hirschberg, the research team's overseer and an expert in fluid dynamics at Eindhoven University, said that, despite the increasing pace of advance, many of those mysteries were likely to remain unsolved for years, given the nuances.
"I expect," he said, "that the details of the physical differences between fair and excellent instruments will remain obscure" far into the future.