by David Politzer
The banjo clearly has many features in common with other stringed instruments. It certainly has plenty of unique features, beloved of players and luthiers, alike. And the physics of much of this is well-understood. This would be the content of "Banjo Physics 101." E.g., what determines the pitch of a plucked string? If you're curious about that, you'll have to look elsewhere. What I hope to do here is report on my research efforts to explore issues of banjo acoustics, banjo construction, banjo mechanics, and banjo science more generally, addressing things I don't understand but believe I could. Why does a banjo sound different from a guitar? Or, even more to the point, why does one banjo sound different from another? It should be unnecessary to mention but unfortunately it needs repeating: the biggest differences one hears between performances come from the musician and not the hardware!
There are always some projects in the works. So, if you find anything here of interest, you might want to check back to see what's new since.
Here is something S.S. Stewart wrote about professional acousticians of musical instruments.
Banjo Drum Physics -- theoretical preliminaries is 30-plus pages thick with differential equations, Fourier series, and complex numbers (but no sound files). It is, of course, aimed at helping understand how banjos work. In particular, it presents the simplest way I could figure out to do the physics of the effect of the air inside the pot on the produced sound -- via its interaction with the head.
The goal is to gain some overall perspective. Correct, formal solutions of the equations have been known for over a hundred years, but to figure out what they're telling me, particularly as relates to the banjo, required a simpler approach than any I'd found in the literature.
DYI Mylar Flange for a More Mellow Banjo Head describes how you can cut a second mylar head and install it under your regular head to reduce some of the sharpest "ping" sounds --- fast, inexpensive, and totally reversible.
Here are the sounds of head taps before and after. For links to actual plucked strings (and instructions), click here for the write-up.
A Hoseus Banjo Restoration describes some simple, amateur efforts to bring a bottom-of-the-line 19th Century banjo back to life. It features an 1886 patented head support system that never really caught on. There's no physics, just banjo tomfoolery.
The accompanying sound files (also linked in the pdf) are: ("steel" refers to steel strings and a 2 oz. bridge; "fish" refers to fishing line strings and a 1 oz. bridge)
Banjo Rim Height and Sound in the Pot is a follow-up to the first endeavor in this banjo physics series. (See DECEMBER 2013, below.) That study focused on the two lowest frequency modes. The totally new material here is an iquiry into the effect of rim height on the whole spectrum. Measurements on the three different height rims bear out the standard calculation of sound resonances inside cylindrical containers. While this might not sound too impressive, just looking at the results tells you something very significant about the role of rim height in the transformation of string pluck to radiated sound. For the acousticians of musical instruments, a careful repeat of the 2013 measurements establishes a stark contrast between the banjo and the guitar (an other wood-topped instruments) regarding the Helmholtz resonance.
(That's an 8 MB file. If you're going to print it out on a B-and-W printer, here is a 6 MB version, already in grey-scale.)
Three sound files are linked in the write-up but are also available here:
frailed sample A
frailed sample B
(8/2/16: The discussion of FIG. 14 misidentifies which pot is which. If you're serious, you can get it right; you've just got to picture the actual pot geometries. Why didn't I fix it? This same manuscript is in two other "permanent" archives. It's hard to say whether it's worth messing with them.)
Air modes of the Bacon internal resonator banjo is a terser, more "professional" write up of the same investigation (14 pages of text versus 22 -- but you'd miss some great photos). It was summarily rejected by the Journal of the Acoustical Society of America. Apparently, "the conclusions are very weak and simple." It was faulted for not explicitly referencing relevant previous work. However, the only relevant previous work is over 150 years old and a standard part of the sophomore physics curriculum where I work. There also is no section titled "Methods," as well as other violations of the Scientific Method as articulated by Francis Bacon (perhaps no relation) in the 16th Century and taught to STEM junior high students everywhere.
There are sound files linked in the write-up, but I include the first one here as a teaser. What you hear are the taps of a piano hammer on four Deering Goodtime pots, tapping from center to rim. The pots, in order, are 1) an old wood rim, 2) an old wood rim fitted with a 1/4" diameter brass ring, 3) a new wood rim, and 4) a new wood rim fitted with a Bacon tone ring.
I found the differences to be noteworthy and something of a challenge to explain. The write-up is long but has no equations. It also has no triumphal confirmation of theory by experiment, but I believe that the suggested perspectives are enlightening in this context and more broadly.
You can listen to sound files of actual playing with those bridges on the same banjo here, in this directory. The bridges are identified there only by number. You can and should do a "blind" listening test and only consult the Banjo Bridge Wood Comparisons manuscript key (at the end of the paper) after forming your own opinions.
Design and weight certainly impact the sound. However, by matching bridges as we did, there's not much left to make a difference. The speeds of sound through the bridges may be different but are too high to matter acoustically. And the differences in hardness, which would impact flexibility, are largely compensated by the matching of weight. (I.e., the softer woods are less dense; so to make up the weight, there's more of it [in the "thickness" dimension].)
I came across a very relevant tidbit from Jim Rae. (See p. 5.) He writes, "At least 99% of a banjo's sound power occurs below 5000 Hz,..." Jim has done extensive measurements on resonator banjos, some in collaboration with Tom Rossing (e.g., see The Science of String Instruments) and some as consultant to Steve Huber in the development of the Huber "Truetone" rim and ring. That's why I initially only looked below 5000 Hz. Noting the measurements presented in FIG.s 2 and 3 in part 2:... (above), that's why overall loudness is hardly effected by the resonator but the resonator is a significant factor in tone determined by yet higher frequencies.
The accompanying Resonator Banjo sound file is here, as well as being linked within the article.
Also, this article is heavy on the physics (albeit fairly elementary) and very light on the music.
A couple of years ago, Jim made a wonderful documentary, The Librarian and the Banjo about a very important book, Sinful Tunes and Spirituals: Black Folk Music to the Civil War, and its amazing author, Dena Epstein. It is a major, pioneering piece of historical scholarship about an era and subjects previously largely ignored. Banjo history is really just only one small part of that story.
mute sound file
Simple Anti-Tone Rings for the Banjo: Do-it-yourself Electric, Surgical, and McGhee tone rings that can be easily and inexpensively installed to make modern banjos sound old.
This was my first Banjo Physics project, written up in December 2013: The Open Back of the Open-Back Banjo. There are four essential, accompanying sound files which you'll need to follow along with the manuscript. (You might want to save them on the side, to listen as you read.) They are:
head taps, while opening up
the sound of Banjo A
the sound of Banjo B
the sound of Banjo C
glass banjo by M. Desy; soft banjo by Sally Suzuki