Fun with Harp Guitar Physics or Will the Real Stephen Bennett Please Stand Up?

A young physics student at Cambridge in the U.K. just sent me his rather intense paper on plucked string physics – specifically, frequency response of guitars and harps.  As the study included a nylon strung Celtic harp and classical guitar, he thought it would be interesting to also include a hollow arm harp guitar that he happened to have access to.  As explained in the paper and credited on YouTube, this was a steel-string Kathy Wingert harp guitar owned by Steve Bennett.

But before my American readers get too excited….it wasn’t “our” Stephen Bennett (who famously plays a Wingert) but the “UK” Steve Bennett, who – honestly, what are the odds?! – commissioned his own Wingert HG.  I’ve never met him, but can easily imagine a devilish glint in his eye when he envisioned the confusion and havoc this would cause!

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Anyway, UKSB (on the left at left, with our physics friend Dan holding Steve’s first HG, a Duane Noble) is another nice guy only too happy to share his priceless instrument.  He loaned it to Physics grad student Dan Duffy, who’s already posted a performance video with it (an impressively difficult Debussy arrangement, image link below).  Dan put it under the test bench that the other instruments were subjected to, curious – as we all are – how it would compare to a 6-string guitar.  It wasn’t an apples-to-apples comparison (like say, using a Wingert 6-string of same general materials and construction); mainly he wanted to observe the effect of the hollow arm and the extreme asymmetry of the top.

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The experiment and results are posted here. (Note that “separate bridges” actually means separate saddles.) If, like me, your eyes glaze over and your brain congeals at the equations, just skip to Chapter 8.  Or, here is the takeaway, as Dan explained it to me (italics added for emphasis):

“I spent last summer doing a research project on the physics of stringed instruments in the Engineering department here in Cambridge, and as part of that I did some experiments with the harp guitar that I believe have previously only been done for standard guitars. The results were quite interesting and slightly surprising from a physics point of view. It’s not a whole lot of research and there’d be room for someone to take it much further, but since it’s new I thought that you might be interested.

“The bulk of it is about other (also interesting but less relevant) plucked string physics, but in particular the last section (8) is about the experiments we did with the HG and what we found out. The description of the experimental methods is in section 4, where it talks about the absurdly expensive laser I got to use and how it all works! We were half expecting that actually almost everything about the instrument from a physics point of view might be pretty indistinguishable from a normal guitar. Pleasingly though, it turns out that although there are lots of similarities, there are also a few differences that are interesting and might help explain the difference in sound between standard and (hollow arm) harp guitars. The frequency response of the body in the low-mid frequency region (up to about 600 Hz or so) has a great many more peaks than a standard guitar, which almost certainly has audible effects. There may be several reasons for the extra peaks, such as the lack of symmetry of the body, or the extra mass from the large shape. More on that in the report.

“One surprising thing was that the lowest frequency peak in the body response (sometimes called the ‘Helmholtz resonance’) was actually pretty much exactly at the same frequency as in a standard steel string guitar, around 100 Hz. The extra air volume in the harp arm lowers the frequency of this mode, but it seems that the effect is pretty much cancelled by the presence of the second sound hole on the arm which acts to raise the frequency. I don’t know whether this has been done much, but it might make an interesting experiment for someone one day to try building a harp guitar with no extra soundhole, which would move that lowest response peak down towards the fundamental frequencies of the sub bass strings. My guess would be a bit more ‘mud’, but more ‘bassy’ sub-bass strings.

physics1“One result of the laser vibrometer experiment was a bunch of videos of the soundboard vibrating in its different (approximate) mode shapes which turned out quite nicely images). The motion is of course exaggerated massively from its true size, but the point is the patterns/shapes that tell you which parts of the structure are moving significantly around each frequency peak in the response. Lots of the shapes are essentially the same as in normal guitars, but there are some interesting new ones, especially those involving the harp arm bulging out quite significantly. We weren’t expecting the arm to move so much at any frequency so that’s quite cool!”

Dan also posed this obvious and interesting question, which I couldn’t answer and haven’t (yet) any opinion on (despite having played every version out there!): “Have you ever tried one with a hollow arm but with no extra soundhole?” (My answer was “Yes, but never in any useful comparative way.”)  He later posed more good questions I couldn’t answer (which vexes me!): “Do you know why the extra soundhole was included historically? Was it just for looks? And has it continued being a common feature out of tradition, or are there more tangible reasons people often include it?”

So there you have it – make of it what you will.  And if any future physicists send me any harp guitar information, please note that I prefer it via illustrated cartoons rather than physics math.

  1. Steve Silva Says:

    Hey Gregg, thanks for posting this. I wish there had been more math! Just kidding.

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