If the strings drive a resonator cone instead of a drum head, the resulting instrument sounds more like a resonator guitar than a banjo, no matter how it's strung or played. Examples include the Gold Tone Dojo, the Rickard Resophonic, and a variety of now-defunct instruments that never caught on. On the other hand, some of the sound features that distinguish the resonator guitar from regular acoustic wood-topped guitars are a bit banjo-like.
I got it in my head to try to figure out how resonator guitars work -- from a physics standpoint. My first pass simply addresses their construction and the features of the sound that might be of interest: https://www.its.caltech.edu/~politzer/resonator-guitar/resonator-guitar.pdf "An Investigation of Resonator Guitar Sound." (That file is 12MB. If fewer bites would work better for you, a version with some of the photos and other graphics in black and white or a lower resolution is available as a 4MB file: https://www.its.caltech.edu/~politzer/resonator-guitar/resonator-guitar-BW.pdf ) There are no equations or even mention of square roots, but spectra and spectrograms are essential content.
At a minimum, I think that most folks would find the following recorded sound comparison of some interest. In order, it features open-back banjo, a resonator cone mounted in a banjo rim, a resonator guitar without the protective grill that usually covers the cone, a full-fledged resonator guitar, and a wood-topped guitar:
(The playback volumes have been adjusted to sound about equal. In person, the instruments differ considerably in loudness.)
To your knowledge, has anyone done Interferometry to see what the modes of motion are for an aluminum resonator cone? I would expect considerably different from a banjo head.
sunburst -- What's called in the acoustics business the admittance is plotted in my Fig.s 6 & 7 and discussed a bit in section VIII. The curves relevant to the cone by itself are yellow and labeled resonator banjo. At that level, the cone behaves an awful lot like a speaker cone. There's a low, very broad resonance around 300 Hz that's clearly associated with a piston-like motion of the entire cone. The next resonances (called "break-up for audio speakers) start round 2000 Hz and must involve some flexing and node lines. Those lines have to be circles and diameters, but the corresponding radii and frequencies are not paper-and-pencil work.
I know drum head theory, have done low-tech Chladni figures, and know some literature on careful banjo interferometry -- all with and without bridge and strings. More recent musical instrument research uses laser Doppler vibrometers. It's been done extensively on violins and some on guitars. I couldn't find measurements or calculations for cones. (I've looked.) For audio speakers, it's just the spectrum that's relevant.
There is a fair amount of literature on guitars with holography, and the modes are pretty well understood. My friend Dave Cohen, working with Thomas Rossing, has done laser interferometry on mandolins and they turn out (not surprisingly, in hindsight) to act a lot like guitars. As for banjos, I don't know of much research other than a chapter in The Science of String Instruments along with what you have presented here.
As a builder, I feel like I have some amount of control over plate and air mode frequencies when buiding guitars and mandolins, but for banjos, tightening the head allows for adjustment "on the fly" so to speak, and I'm a bit curious as to just what it is that I am doing when I tighten or loosen the head!
On guitars, mandolins, and violins, the lowest few modes of the tops have significant impact on the sound. On banjos, it's different. The only head mode that contributes quite distinctly from all the others is the lowest one. It couples to the Helmholtz mode of the pot and together contribute to the lowest frequency radiation. The builder and player have obvious ways of impacting its sound. However, unlike guitar, for banjo it's a tiny component component of what we hear. Instead, we react to the sound produced by the many closely spaced modes that are excited up to high frequencies.
The builder has many design choices and the player has many component and adjustment choices. Part of the challenge in understanding what's going on is that a given identifiable sound characteristic may be impacted by several of those choices, which work together in complicated ways.
The closest analog to shaping wood soundboards to control vibrational modes is banjo bridge design. Bridge weights and flexing modes do not appear as individual frequency peaks in the sound but as formants. Builders and players know this quite well in practice.
Tightening the head with all other things left the same does several things to the sound. Obviously, it raises all head mode frequencies. But it decreases head mode amplitude for a given string force, ultimately choking out the sound. It decreases the break angle of the bridge relative to the head, which is actually a bigger contributor to the total effect of break angle than the strings themselves, whose break angle increases with tighter head. Tightening the head also impacts the sound radiation efficiency. Over the relevant head tension range, what we hear is not so much a change in overall loudness but something more evident because of the sensitive frequency dependence of the sound radiation efficiency.
Years ago, while searching downtown Los Angeles pawn shops for the Holy Grail, Dorea Bantar (maximize the page & scroll down)
Edited by - monstertone on 04/19/2023 08:52:00
monstertone -- Reading up on John Dopyera, I found mention that he made banjos, too. This is the first I ever saw one -- or at least a picture. Thanks.
