His objective is to start with Newton's Laws, which describe the motion of objects as varied as planets and pingpong balls, and apply them to the components of the piano, such as the hammers, strings, soundboard, even the air around it. The goal -- construct a mathematical model of the instrument.
"There has never been a model that incorporates all these elements in such a realistic way," Giordano says. "But there's no doubt that Newton's Laws apply, and if we're smart enough, we can use them to really understand how a piano works and ultimately computer generate a synthetic sound that sounds 'right.'"
The pianoforte , now known as the piano, was invented in Italy in the early 18th century, during scientist Sir Isaac Newton's lifetime.
Today, what might be the 21st century's version of the instrument lives in a computer in Giordano's lab. From stereo speakers hooked to the computer come a few bars of Bach's famous "Minuet in G," sounding very much as it would on a real piano, but completely computer generated from mathematical equations.
"There are lots of electric pianos around that sound pretty good," Giordano says. "But that sound is based on a different kind of modeling than ours, one that relies on sampling a note from an actual piano, then massaging it electronically to produce a sound. That's certainly not a trivial task, but I think our work might eventually help synthesizer manufacturers create a better sound."
From theory and experiment, Giordano and his students have developed detailed mathematical models of how piano strings vibrate and how the soundboard of the instrument vibrates. They now are working to combine these and other elements into a more sophisticated model.
Last summer, Giordano published a paper in the Journal of the Acoustical Society of America describing his theoretical model of soundboard vibrations. A second paper to be published in the same journal this spring details experiments that confirm the validity of the model.
Giordano, a piano player himself, got involved in the piano study when he started teaching an undergraduate course in computational physics.
"I was looking for calculations that I could use in class, and waves on a string and musical instruments were natural examples illustrating waves and vibrations," he says. "But I was struck by how crude the existing models were. At the same time, I had a student who wanted to do a research project, and he was a music minor, so we started doing experiments."
The professor, who recently won a national award from the Department of Energy for an undergraduate textbook he wrote on computational physics, began working with then-senior Andrew Korty. Inside the piano, they investigated intricate mechanisms that would delight any mechanical engineer. Complex linkages connect the keys to the hammers, which must strike the strings and bounce back quickly to be ready for the next stroke. Foot pedals control dampers on the strings, which can create effects such as sustaining a chord after the keys have been struck.
Korty has since graduated, and Giordano's new research assistant, freshman James Winans of Fort Wayne, Ind. , works in the lab on an upright piano with its guts exposed, giving access to the strings, bridge and soundboard. These key elements are where the researchers have focused their attention, attaching tiny electrical devices called accelerometers in various places to measure motion and vibration. A detached soundboard, complete with a bridge on the front and supporting ribs on the back, has allowed them to investigate in detail how the ribs and the motion of the bridge affect the vibration of the soundboard.
"We've demonstrated that the ribs on the back of the soundboard make a significant difference in how the soundboard vibrates, which is important to the sound you ultimately hear," Giordano says.
In addition, none of the existing string models takes into account that most of the piano strings actually come in triplets -- the hammer strikes three strings instead of just one to create a middle C, for example.
"It's well known from experiments that all three strings are important in making the piano sound the way it does, but the previous models only included one string," Giordano says.
All three strings are tuned to the same note, Giordano explains, and when the hammer strikes the strings, they start out vibrating together. But eventually, the vibrations get out of sync. It's this interference that affects how the sound of the note decays, and ultimately, gives the note warmth.
To make things more complicated, each string is connected to a peg on the bridge, which in turn is mounted on the soundboard. When a piano string vibrates, it tugs ever so slightly on its peg, moving the bridge and causing the string to vibrate in other directions. Also, when the sustain pedal is used, one set of strings can cause other strings to vibrate, adding to the richness of the sound. It's very difficult for synthesizers to recreate this kind of effect, Giordano says.
"None of the existing models takes any of these effects into account, and we're trying to include them in ours," Giordano says.
While using mathematical equations to generate piano music may be helpful to synthesizer manufacturers, Giordano admits that piano designers may benefit little:
"Imagine going to a master chef and telling him that you can make a better cake because you understand the chemistry of how a cake rises. The master chef has an incredible amount of chemical knowledge, but not as a chemist -- it's intuitive. Piano designers are real craftsmen with a great deal of wisdom. The piano technician who takes care of my piano at home can listen to it and know immediately why it doesn't sound right. That's why she fixes it and not me."
Source: Nicholas Giordano, (765) 494-6418 (lab); e-mail, firstname.lastname@example.org
Writer: Amanda Siegfried, (765) 494-4709; e-mail, email@example.com
Purdue News Service: (765) 494-2096; e-mail, firstname.lastname@example.org
Nicholas Giordano, professor of physics at Purdue, uses sophisticated electronic devices and mathematical equations to determine how the vibrations of the piano strings, bridge and soundboard interact to produce the instrument's characteristic sound. The goal is to use basic laws of physics to develop a model of the piano, and perhaps create a more realistic-sounding piano synthesizer. (Purdue News Service Photo by David Umberger)
Color photo, electronic transmission, and Web and ftp download available. Photo ID: Giordano.Piano
Simple model of a piano soundboard
N. Giordano, Department of Physics, Purdue University
The vibrational properties of a simple finite-element model of a piano soundboard are considered. The main focus is on the behavior of the mechanical impedance in the musically important frequency range ~50 - 104 Hz. The model includes the effects of elastic anisotropy and the ribs. It is argued that the ribs are an essential ingredient for producing the behavior of the impedance which is observed experimentally.
To the Purdue News and Photos Page