There is no question that violin-making is an art form. It requires a musician's ear, a craftsperson's skill, and an historian's appreciation of lessons learned over time. Making a violin also takes trust: Violin makers, or luthiers, often must wait until the instrument is finished before they can hear how all their hard work will sound.
But a new tool developed by MIT engineers could help luthiers play around with a violin's design and tweak its sound even before a single part is carved.
In a study appearing today in the journal npj Acoustics, the MIT team reports on a new "computational violin" - a computer simulation that captures the detailed physics of the instrument and realistically produces the sound of a violin when its strings are plucked.
While there are software programs and plug-ins that enable users to play around with virtual violins, their sounds are typically the result of sampling and averaging over thousands of notes played by actual violins.
In contrast, the new computational violin takes a physics-based approach: It produces sound based on the way the instrument, including its vibrating strings, physically interacts with the surrounding air.
As a demonstration, the researchers applied the computational violin to play two short excerpts: one from "Bach's Fugue in G Minor," and another from "Daisy Bell" - a nod to the first song that was ever produced by a computer-synthesized voice.
The computational violin currently simulates the sound of plucked strings - a type of playing that musicians know as "pizzicato." Violin bowing, the researchers say, is a much more complicated interaction to model. However, the computational violin represents the first physics-based foundation of a strung violin sound that could one day be paired with a model of bowing to produce realistic, bowed violin music.
For now, the team says the new virtual violin could be used in the initial stages of violin design. Luthiers can tweak certain parameters such as a violin's wood type or the thickness of its body, and then listen to the sound that the instrument would make in response.
"These days, people try to improve designs little by little by building a violin, comparing the sound, then making a change to the next instrument," says Yuming Liu, senior research scientist at MIT. "It's very slow and expensive. Now they can make a change virtually and see what the sound would be."
"We're not saying that we can reproduce the artisan's magic," adds Nicholas Makris, professor of mechanical engineering at MIT. "We're just trying to understand the physics of violin sound, and perhaps help luthiers in the design process."
Makris and Liu's MIT co-authors include Arun Krishnadas PhD '23 and former postdoc Bryce Campbell, along with Roman Barnas of the North Bennet Street School.
Sound matrix
The quality of a violin's sound is determined by its dimensions and design. The instrument is made from thoughtfully crafted parts and materials that all work to generate and amplify sound. In recent years, scientists have sought to understand what artisans have intuited for centuries, in terms of what specific parameters shape a violin's sound.
In one early effort in 2006, scientists, as part of the Strad3D project, put a rare Stradivarius violin through a CT scanner. The violin was crafted in 1715 by the master violinmaker Antonio Stradivari, during what is considered the "Golden Age" of violin making. To better understand the violin's anatomy and its relation to sound, the scientists scanned the instrument and produced 600 "slices," or views, of the violin.
The CT scans are available online for people to view and use as data for their own experiments. For their study, Makris and his colleagues first imported the CT scans into a solid modeling software program to generate a detailed three-dimensional model of the violin. They then ran a finite element simulation, essentially dividing the violin into millions of tiny individual cubes, or "elements."
For each cube, they noted its material type, such as if a cube from the violin's back plate is made from maple or spruce, or if a string is made from steel or natural fibers. They then applied physics-based equations of stress and motion to predict how each material element would move in relation to every other element across the instrument.
They also carried out a similar process for the air surrounding the violin, dividing up a roughly cubic-meter volume of air and applying acoustic wave equations to predict how each tiny parcel of air would move and contribute to generating sound.
"The entire thing is a matrix of millions of individual elements," explains Krishnadas. "And ultimately, you see this whole three-dimensional being, which is the violin and the air all connected and interacting with each other."
A plucky model
The team then simulated how the new computational violin would sound when plucked. When a violinist plucks a string, they pull the string sideways and let it go, causing the string to vibrate. These vibrations travel across the instrument and inside it; the air's vibrations are amplified as they travel out of the violin and into the surroundings, where a listener hears the vibrations as sound.
For their purposes, the engineers simulated a simple string pluck by directing one of the virtual violin's strings to stretch out and then rebound. The simulation computed all the resulting motions and vibrations of the millions of elements in the violin, and the sound that the pluck would produce.
For notes that require pressing down on a violin's fingerboard, they simulated the same plucking, and in addition, included a condition in which the string is held fixed in the section of the fingerboard where a violinist's finger would press down.
The researchers carried out this computational process to virtually pluck out the notes in several measures of "Daisy Bell" and "Bach's Fugue in G Minor."
"If there's anything that's sounding mechanical to it, it's because we're using the exact same time function, or standard way of plucking, for each note," says Makris, who is himself a lute player. "A musician will adapt the way they're plucking, to put a little more feeling on certain notes than others. But there could be subtleties which we could incorporate and refine."
As it is, the new computational model is the first to generate realistic sound based on the laws of physics and acoustics. The researchers say that violin makers could use the model to test how a violin might sound when certain dimensions or properties are changed. For instance, when the researchers varied the thickness of the virtual violin's back plate or changed its wood type, they could hear clear differences in the resulting sounds.
"You can tweak the model, to hear the effect on the sound," Makris says. "Since everything obeys the laws of physics, including a violin and the music it makes, this approach can add an appreciation to what makes violin sound. But ultimately, we get most of our inspiration from the artisans."
This work was supported, in part, by an MIT Bose Research Fellowship.
