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A new kind of string theory: The physics of playing guitar

A University of Oxford physicist has derived equations that describe how guitar techniques influence the pitch of a note.

Dustin Gaffke, CC BY 2.0

As anyone who's ever picked up a guitar knows, there's a lot more that goes into it than just plucking or strumming the string with one hand while pressing down with the other. Techniques such as vibrato (vibrating a string on with a finger on the fretboard), string bending (pushing the string sideways on the fretboard while playing a note with the other hand) and tapping (tapping the string instead of plucking it) all produce different tones that enrich the sound and contribute towards creating a distinctive style.

And it turns out that the effect each of these techniques have on the pitch of a note can be mathematically described. Physicist, guitarist, and University of Oxford cancer researcher, Dr David Robert Grimes has devised equations that describe how string bending, vibrato, tapping and whammy-bars each change the sound of a note.

"Very good guitarists will manipulate the strings to make the instrument sing," Dr Grimes said. "On a piano, you've got the 12 chromatic notes in a scale. On a guitar, you can bend the strings to get the notes in between. I wanted to understand what it was about these guitar techniques that allows you to manipulate pitch."

It's not just the action that Dr Grimes had to take into account for his study: the physical properties of the string itself have a big effect on the pitch, in particular how much the string will stretch when force is applied, and how thick the string is; and, of course, the material will make a difference, too, with steel strings reacting differently from nylon.

He modified an old guitar, then experimented.

"I took one of my oldest guitars down to the engineering lab at Dublin City University to one of the people I knew there and explained that I wanted to strip it down to do this experiment," he said. "We had to accurately bend the strings to different extents and measure the frequency produced. He was a musician too and looked at me with abject horror. But we both knew it needed to be done -- We put some nails into my guitar for science."

Although the physics of vibrating strings is already solid, this is the first time that someone has taken the time to examine how distinct techniques affect pitch, or how it depends on the tension of the string, the amount of force applied and the angle at which the string is bent.

"It turns out it's actually reasonably straightforward," Dr Grimes said. "It's an experiment a decent physics undergraduate could do, and a cool way of studying some basic physics principles. It's also potentially useful to string manufacturers and digital instrument modellers."

As for whether it could be applied by a guitarist to produce some sweet licks, that's an experiment for another day -- or maybe another guitar-loving physicist. You can check out Dr Grimes' paper in full for free on the PLOS One website.

And just because there's never a bad time to watch some amazing musicians in action...