String theories: the mathematics of the violin

fpjl2 — Thu, 07 Mar 2013 13:08:17 +0000

It was as a mathematics undergraduate in the early 1970s that Jim Woodhouse came across Cambridge鈥檚 amateur violin making workshop. Always a keen 鈥榤aker鈥� of things, Woodhouse developed a love of crafting string instruments that quickly spilled into his academic life, as he went on to do a PhD at the 探花直播 in noise and vibration theories - focusing on the violin.

These days a Professor in the Department of Engineering, as well as a self-confessed 鈥渂ad cellist鈥�, Woodhouse maintains a keen interest in both instrument-making and the science of acoustics, and will be giving a pre-concert talk for the Science Festival at the West Road Concert Hall on Friday 8 March.

探花直播talk will be followed by a virtuoso violin performance from Magdalena Fitzpatrick, accompanied by the Cambridge Graduate Orchestra.

Woodhouse compares violins to guitars. Both are essentially wooden boxes with strings, although played in different way, but a note on a guitar, even if wrong, still sounds musical.聽鈥淵ou can do bad things aurally with violins that simply aren鈥檛 possible with guitars, a fact painfully obvious to parents of children beginning to learn,鈥� says Woodhouse. 鈥淏ut what is it about 鈥榖owing a string鈥� that makes a musical sound that much harder to produce?鈥�

A violin player controls three things: the speed of the bow, the downward force applied, and position of the bow on the string. According to Woodhouse, once you choose speed and position, it is the force that primarily dictates whether the result approaches a musical note or spits out a wince-inducing 鈥済raunch鈥� noise.

This force-based window of 鈥榤usicality鈥� grows ever-slimmer as the bow moves up to the bridge, an analysis first plotted in graphical form by former Bell Telephone scientist and pioneer of violin acoustic research John Schelleng in the 1960s.聽聽聽聽聽

鈥淩elatively inexperienced players need to try and learn to be comfortable hovering in the middle of this space, staying away from the minimum and maximum, but virtuosos will probe the boundaries for the best tone,鈥� says Woodhouse.

鈥淭hese factors feed into the idea of 鈥榩layability鈥� of specific instruments,鈥� says Woodhouse. Some violins are a great deal more valuable than others, but why is this?

鈥淥ne aspect is 鈥榖eauty of sound鈥�, which is difficult to address in scientific terms as it comes down to peoples鈥� perceptions. But ease of playing is also a major factor. Whether an instrument is more accommodating in terms of the Schelleng model is one facet of that, and one that lends itself more easily to scientific investigation.鈥�

Issues of playability have been the subject of increasingly sophisticated mathematical modelling, enabling computer simulations to show how strings on particular violins will respond to certain bow gestures. These techniques are increasingly used to explore design questions, but also in accurate electronic instruments - the virtual violin.

But for Woodhouse, nothing can replace a finely crafted instrument, and the evening class he took forty-odd years ago has gone from strength to strength - the Cambridge Violin Makers still run one of the country鈥檚 top violin crafting workshops and summer schools.聽

鈥淚 still love to work on musical acoustics from time to time. In fact, I鈥檝e got a current violin PhD student at the moment, and it鈥檚 always popular with undergraduates as well as a great outreach subject.鈥�

探花直播talk and concert take place at West Road Concert Hall on the evening of Friday 8 March. For more information, please visit the Science Festival website.

探花直播screeching produced by children starting out on the violin has curdled the blood of many a parent over the centuries. A pre-concert talk at the Science Festival asks what science can tell us about why the violin is so hard to play.

Virtuosos will probe the boundaries for the best tone

Jim Woodhouse

Jason Hollinger from Flickr

Violin -- closeup

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探花直播 of Cambridge - Jim Woodhouse

String theories: the mathematics of the violin