Depth of body...?

[steve V. johnson]

What effect does the depth of the body of a mandolin have on the sound?

It seems that some European makers' models, and the Brazilian bandolims look to be deeper than most A- and F-style mandolins.

And, is the effect of the body's depth the same or different from what the volume of space inside the body 'box' does with the sound?

I don't really know what I'm talking about here, so I'm looking forward to being 'set straight' on this stuff... <GG>

Thanks,

stv

[sunburst]

I'm looking forward to it too!

I don't think anybody really knows. The depth obviously adds volume to the air in the mandolin as it increases, so, it would certainly have a similar affect to any other difference that would give a bigger air chamber, but possibly not the same affect.
I hope Dave Cohen lets us know what he has found out through his experiments, though I don't think he has done any specifically for air volume or body depth.

There is quite a bit of anectotal evidence that a deeper body sounds "rounder" or "more oval-hole like", while thinner has more "projection", but opionions vary.

[Paul Hostetter]

I don't think anyone really knows either. I've done lots more with this notion in regards to guitars than to mandolins, but I am only comfortable saying that body depth is important. So are a lot of other things, and I think the only way you'll get any meaningful glimpse is to make around 100 otherwise identical A-5s in several different depths and average the results. Small samples don't tell you very much, and untested theories are just so much verbiage.

I recently experienced an eye-opener: an adjustment rig for a Mastertone-type resonator banjo that allows the player to adjust the distance of the resonator from the flange. Just the 5/8" throw from one end to the other showed pretty dramatic results.

You can derive a helpful generality from a couple of well-known guitar models that exist in large numbers in two depths: The Martin J and the 0000, and the old Gibson L-OO and the Nick Lucas. I can't think of any analog in the mandolin world.

[Chris Baird]

The deeper body lowers the helmholtz(internal air) mode. #If it gets too low you can't get a strong coupling with the top and back plate and begin to get lots of sustain but little volume. As the notes are hanging in there longer (due to the fact that the string energy isn't being dissapated quickly because of poor coupling) the tones intermingle and give a more "complex" character. #I've found that the old Gibson ovals are right on the edge in terms of how low you can go with the A0 mode and still have structurally sound well coupled plates.

[Paul Hostetter]

I know it's tantalizing to invoke ideas like Helmholtz resonance, and the basic principle has some relevance (bigger box, decreased resonance frequency, etc.) but Helmholtz chambers (there are only really two: a rigid necked sphere with one opening, and a rigid box with one opening) are so utterly unlike musical instruments that the insights are probably more imagined than real. What about a chamber with a surface that actually flexes? One with multiple and irregular openings (I’m talking about violins). What about all these wondrous things John Monteleone spawned with large soundholes in the sides? There goes the Helmholtz stuff right out the window. The internal chamber has no boundaries. I recently had a chance to hear a Beardsell guitar played live and unamplified in a really good setting and it buried most of the other guitars. By the Helmholtz principles, it should not work at all.

I'm nonetheless still intrigued by the theoretical aspects that seem to apply, but I'm more convinced by instruments that really work than I am by the scientific jargon that professes to explain their success. The other downside is: if you were able to refine an instrument according to these principles, you’d end up with something no one would buy because it bore too little resemblance to a Loar. Drat!

[Chris Baird]

You are right in that Helmholtz as a strict observation is hard to get and really irrelevent to an actuall instrument. #However, the A0 mode, which is heavily influenced by the helmholtz, is a very serious consideration and takes into account every aspect of the instrument. The beauty of the A0 observation is that one doesn't need to know the myriad and seemingly infinite varibales that contribute to it in order to measure it. That measurement has been indispensable to my building process. I don't profess to have anything figured out but I don't think that it is impossible to get a grasp on what is going on in this way. It meerly takes a lot of data collection. What am I talking about?; I don't know. # # What would the internet be without folks willing to talk about what they don't know. One can take my advice as they see fit, perhaps it will be worth more down the road.

[sunburst]

While there may not be a "real" helmholtz at work in instrument bodies, especially multi-ported ones, there is something similar going on.
Understanding the basics of what Helmholtz is, and how the flexible plates and sides of a mandolin work together with it, has helped me visualize how the plate modes work with the air modes in the mandolin, and what it is I'm striving for when carving the plates.
I don't have a problem with the term Helmholtz being applied to instruments. Though it's not really the correct term, I feel like I know what that means, to some extent, at least, and it's useful for trying to describe what is contributing to the sound.
And, by the way, I don't know what I'm talking about either .

[peter.coombe]

The Helmholtz resonance is basic textbook physics, so you can't get away from it, but after all it is a mathematical formula that makes certain assumptions, and some of the assumptions are not true in a musical instrument. The sound chamber is not rigid, so that must be taken into account, but the basic principles remain. A0 is often called the Helmholtz resonance, hence much confusion. The frequency of A0 is definately important in the tone of a mandolin, but it is difficult to be certain exactly how it affects tone because there are so many other things that influence tone. In oval hole mandolins, if A0 is a G or lower, then you get a boomy, hollow sounding G string that is so characteristic of many of the old Gibsons. I try and tune A0 to G#, which gives the instrument a much more even tonal balance that I much prefer. F hole mandolins seem to be more complicated. I used to tune A0 to somewhere between C# and D (with a deeper rim), but now aim for D# as in the Loars. My arching has also changed so that introduces another complication. Note that the relationship between the air volume and the frequency of A0 (or the Helmholtz resonance) is a square root relationship, so you have to change the air volume a fair bit to get much change in the frequency. Same applies to the area of the sound holes. It is much easier to change the stiffness of the top and back.

[Dave Cohen]

"...and untested theories are just so much verbiage."

That statement would seem to dismiss science with one pompous blow, except for one thing; it betrays a woeful misunderstanding of science. Constructs don't get to become theories without a great deal of experimental verification. I cringe every time I hear someone say "It's just a theory". There is no such thing as an "untested theory". A hypothesis may not yet have been subjected to experimental verification or falsification, but a construct, model or hypothesis does not become a theory until it has been subjected to a very large amount of experimental testing. Theories include the likes of classical mechanics (Newtonian, Hamiltonian, & LaGrangian), quantum mechanics, statistical mechanics, thermodynamics, classical & quantum electrodynamics, stellar evolution, biological evolution, superstrings,.....etc.

The work of Helmholtz does fall within the bounds of classical mechanics, and stringed instrument bodies are essentially Helmholtz resonators, even those with multiple openings. There was a paper in CASJ several years ago about a "swiss cheese violin", dubbed "Le Gruyere" by the authors. The violin had multiple holes, all except for the traditional f-holes initially plugged with corks. As the corks were removed one at a time, the sound of the instrument gradually went south as the air mode frequencies gradually moved higher and coupling with body modes became weaker.

I could go on and on about this, but it is not my responsibility in this venue to defend science. Those who dismiss science should, imo, take the responsibility to understand whatever it is they so casually dismiss.

[leonardbakers]

Dr. Dave,

Geez, sounds like somebody ought to take a bolt-on neck, build a few boxes with identical tops and backs but use different depth sides on 'em. String 'em up white and play.

Would that do the trick?

[peter.coombe]

Mmmm, at first reading of this thread I thought "Oh NO not again!", and once again I find myself agreeing with Dr Cohen, although he has put it somewhat more forcefully. On re-reading my post it is a bit misleading. What I meant to say is that the mathematical formula applying to a Helmholtz resonator does apply to musical instruments, so the relationship between volume of air in the soundbox and surface area of the soundholes, and the lowest resonant frequency of the soundbox (i.e. A0) is exactly the same as a Helmholtz resonator. This is basic textbook physics and cannot be ignored if you want to know what effect changing the depth of the sides will have and hence what effect it may have on tone. It is not "some relevance", it is basic physics and hence is absolutely and vitally important. However, stiffness of the plates is also a factor in the mathematical equation for musical instruments (i.e. take the equation and add a factor for stiffness), but they are still basically Helmholtz resonators. It is absurd to say otherwise. If you want to understand how a mandolin works and use this understanding to improve tone, or more practically, to maintain consistency from instrument to instrument, this basic fact must be understood. Ignore it, and your results will be all over the place. Of course many other things affect tone as well, but at least the Helmholtz resonator principles are well understood.

[mandocrucian]

This book, written by Bart Hopkin who published/editted the now retired quarterly magazine Experimental Musical Instruments, has a lot of down-to-earth explanations of the physics involved with how/why various types of instruments function. #Don't know that I've seen it mentioned before on the board, but highly useful for ideas.

Musical Instrument Design
Information for Instrument Making
By Bart Hopkin with an introduction by John Scoville

This book is a key resource for anyone interested in musical-instrument making. It provides a good, strong overview of design principles for acoustic instruments of all sorts, with extensive, practical, hands-on information, generously illustrated. This is the only book that does this: there are many books that offer plans for making specific instruments, but no others that lay out underlying design principles in such a comprehensive way.

The book covers the familiar musical instruments, and a host of new and unusual ones as well. Scattered throughout the main text and the sidebars are ideas and informal plans for diverse instruments you can make. The chapter headings are: 1) Musical Sound Perception, 2) Acoustic Principles, 3) Tuning Systems and Pitch Layouts, 4) Idiophones, 5) Beaters, Scrapers & Friction Makers, 6) Aerophones, 7) Membranophones, 8) Resonators & Radiators, 9) Chordophones, 10) Special Effects, 11) A Few More Thoughts. At the end are several appendixes and charts with practical reference information that will make the book a useful handbook long after the first read-through. These include a chart laying out frequencies and wavelengths for pitches through the musical range, another chart giving the essentials for various western and non-western musical scales, an appendix devoted to tools and materials with an extensive where-to-find listing, another devoted to electric amplification systems (pickups and such), plus glossary, bibliography and index.

The writing is accessible and friendly without sacrificing seriousness of purpose, and the math, where it appears, is pretty benign.

Concerning the author's qualifications for writing this book: Bart Hopkin's own explorations in instrument-making have been extensive and highly varied, and he has the successes and the failures in abundance to show for all that he has learned. More importantly, since 1985 he has been the director of the publishing orgainzation Experimental Musical Instruments, and for fourteen of those years he was publisher and editor of the quarterly journal of the same name. In the course of that work, he has been in constant contact with musical instrument makers of all sorts, as well as acousticians, scholars and theoreticians. The cumulative know-how and experience of these people — particularly the several experts who read, critiqued and corrected the manuscript prior to publication — inform the text throughout.

Price $18.95

Niles H

[sunburst]

Thanks!
I didn't know about that book.
I put off buying Understanding Wood for so long that I figured I knew most of it by the time I finally bought it. Boy!, was I wrong! I didn't know there was that much to learn about wood!

Not only did I learn a lot about wood, but I learned a "life lesson".

I'll be looking for that book, and expecting to learn things that will make me wonder how I ever built instruments without knowing them.

[steve V. johnson]

Paul wrote: "I recently experienced an eye-opener: an adjustment rig for a Mastertone-type resonator banjo that allows the player to adjust the distance of the resonator from the flange. Just the 5/8" throw from one end to the other showed pretty dramatic results. "

What were the differences, Paul, from that 5/8" change?

Thanks,

stv

[steve V. johnson]

Wow, thanks for all the great data (and the rest, too! <GG>) !!

A few steps back from the physics, here's from whence the question came. #I think I should have left out the part about the volume of the box...

I have a Phil Crump B-II bouzouki, a two-point variant of the 'onion-on-a-stick,' or 'Celtic' shape. #The bouzoukis I had heard on recordings sounded like big mandolins, just lower in pitches. #The Crump is much deeper and more resonant than that, not quite guitar-like, but not like a mandolin either. # #When I have compared this with guitar-bodied zouks, the Crump is more mando-like than those. # In talking with some luthiers and listening to instruments from a lot of players, it seems that the one thing that I have eliminated several aspects that might have #been key in placing an instrument somewhere along a scale with 'guitar sound' on one end and 'mandolin sound' on the other: #Scale length and overall box volume don't seem to do nearly as much on this as the distance between the top and the back of the box.

Of course there are dynamic relationships all around...

As an example, that Italian octave mandolin that Tim O'Brien plays sounds very mandolin-like, but has a large body that is very shallow, so there's a fair amount of volume in there.

I love my Crump, and yet there is a sound I want that is somewhere to the mando-side of the gtr-to-mando continuum, and I'm searching for the physics and the language to use to work with a luthier to get it.

Thanks very much (Chris, et al) for the insights into the tuning of A0 and some basics of how that works, and also for the references to instructional books!

stv

[Dave Cohen]

OK, I'm back from having gotten my socks in a knot.

In principle, Helmholtz resonators come in many shapes and an infinite number of sizes, including stringed instrument bodies. The only thing that makes the main air resonance of an instrument body not a Helmholtz resonance is that it is coupling with the other vibrating components of the instrument,, i.e., with the wood and the strings. Consequently, the frequency is shifted from that of a pure Helmholtz resonance. Nevertheless, it is there, and it is important to the tonal character and bass/treble balance of an instrument. It is not necessary to produce sound (the chinese P'ip'a has no soundhole), but it certainly has an influence.

Body depth is a trade-off. A deeper body means a larger cavity air mass, which can (other things being equal) result in stronger coupling of the body modes with the air modes. But a larger body can also lower the frequency of the main air rssonance, which, depending on the frequencies of the lower body modes, may or may not be a good thing. In principle, if you enlarge the body, you can keep the main air resonance at the same frequency by enlarging the soundhole(s) - up to a point.

There is an article on the Helmholtz resonance in the latest issue of American Lutherie by R.M. Mottola. It seems to be OK, though I did find a mistake. He stated that a doubling of the soundhole radius should raise the frequency of the Helmholtz resonance by an octave, i.e., double the frequency. Not right. The Helmholtz resonance frequency is proportional to the square root of the soundhole radius, so doubling its radius will raise the frequency of the Helmholtz resonance by a factor of 1.414... Similarly, the Helmholtz resonance frequency is proportional to one over the square root of the body volume. So the dependence on the body depth is also not linear. In practice, guitar body air mode frequencies tend to decrease rather slowly with increasing body depth, as is the case with mandolin family instruments.

So what do you get out of all this? While the equations don't always give you something simple to work with, they certainly do give you the trends, which are mightily useful in and of themselves.

Your luthier should know this stuff at some level. Even if (s)he is not familiar with the formalism, (s)he may know it intuitively or empirically. There are also some good resources from the GAL. Tom Rossing had a few articles on the physics of guitars, and they are all in the Big Red books now. W.D. Allen had an important article on air resonances, which is now in the first Big Red Book.

http://www.erols.com/judcohen

[Gail Hester]

Back in 2001, Gibson built a mandolin for Stuart Duncan with a thicker body. According to the article below, “Stuart requested some customization of the instrument, adding a 1/8 inch thicker body depth for a different tone”.

http://www.gibson.com/whatsnew/press...01/mar29a.html

It would be nice to hear from Big Joe if that made any noticeable difference.

[steve V. johnson]

Dave Cohen writes: "Body depth is a trade-off. A deeper body means a larger cavity air mass, which can (other things being equal) result in stronger coupling of the body modes with the air modes."

Does everything that follows this rely on the deeper body giving a larger cavity air mass? Other body dimensions could change, that is, decrease, in some proportion to an increase in depth...

I tried to phrase the original question to separate the effect of the distance between the top and back of an instrument from the overal 'cavity air mass'. It's not bigger boxes or bodies I'm wondering about, but that distance between the top and the back, particularly in mandolins and especially in octave mandolins/bouzoukis. Oh, and specifically -not- with guitar-shaped bodies, too.

Thanks! This is fascinating!

stv

[steve V. johnson]

Thanks, Gail, maybe we can get his attention here...

stv

[steve V. johnson]

P.S. I would love to hear some anecdotal stuff from anyone who has experimented with body depths. The science is illuminating, but I'd love to learn 'what happened'.

Thanks,

stv

[Chris Baird]

I've done a lot of experimenting with my flat tops. The range being about 1/2". The shallow bodies are more focused with less sustain. The deeper bodies are more complex with more sustain. It basically can be said that deeper bodies give a more oval hole tone where as shallower bodies give a more F-hole tone.

[steve V. johnson]

Thanks, Chris!

Have you done any depth experiments with your OMs?

One of the prime motivators for me on this subject was repeated playings of the sampls of your walnut A and flat-top mandos.

Are they the same depths?

Thanks,

stv

[Chris Baird]

My walnut A-style is a totally different beast from the flat top. Different depths; different everything.

[Paul Hostetter]

Far from dismissing science with one pompous blow, I was simply trying to point out my belief that the makers who consistently generate the best instruments have always relied on good designs, well-chosen materials, good intuition and a high level if craftsmanship—and not any aspect of "science" real or imagined—to achieve those results. As it has been for centuries, building superior string instruments remains an art.

I was a charter subscriber to EMI and treasure every issue from first to last. I’ve sat through lectures by Carleen Hutchins and lots of other people of that school. I’ve listened hard to the talk, and I have listened hard to the instruments, and have had to temper my appreciation of those efforts because generally the instruments built with those scientific principles as a basis come up a distant second to ones made by artists who wouldn’t know an AO mode if it bit them in the keister. I’m not dismissing science at all. I continue to listen with respect and fascination to the folks who are exploring. But it hasn’t answered very many questions yet when it comes to building wooden string instruments. I hope and expect science will eventually help explain art, but I don’t think it’s much to go on yet on a practical level.

Steve asked a really good, clear question, and refocused it again when he said what if only one aspect changes: depth. The only people who can really answer that are those who either actually build the things in multiples both ways, or who can at least find a lot of them and play them directly. Chris Baird’s comment that "…shallow bodies are more focused with less sustain. The deeper bodies are more complex with more sustain…" was right on the money. It’s based on his own actual experience. Dave Cohen is of course right when he says "Body depth is a trade-off." It can be so shallow it can only sound thin and it can be so deep the sound simply gets lost in the big cave in there. We know this, or hope to, from real experience. To me it’s much more useful than being told that in a deeper box there is "stronger coupling of the body modes with the air modes."

BTW, Chris’s characterization is also congruent with the effect of deepening the Mastertone banjo pot with the adjusting screws I mentioned earlier, although there’s an additional factor to consider of how and to where the soundwaves reflect off the rigid curve of the inside of the resonator. Basically, the deeper it got, the more complex the sound became.

The guitar world offers lots to contemplate in this regard. I already mentioned two well-known guitar models that exist by the thousands which I think provide a good clue. I just took this photo off my wall and scanned it, pardon the glare:



Check the two guitars. One is a normal Washburn, an approximately O-size typical of the day, and the other is a Larson Brothers item that was originally offered as a lap steel guitar, also about that size. Many people played them Spanish-style however. If you have ever had a chance to compare these two designs, you appreciate that the thin one’s sound is not only extremely loud but surprisingly rich and complex as well. They were extraordinary guitars. It’s one of the gems from the fossil record that hasn’t been revived for some reason. The basic principles that underlie its worthiness—the proportions of the soundbox and the soundhole size—are a real lesson. Hands-on experience trumps any other way of evaluating instrument making.

[Dale Ludewig]

Although not specifically addressing the body depth issue, Paul's mention of the banjo experience reminds me of one of my own. Back in the 70's I made a number of banjos. The first one I made I still have. The back of the resonator was solid curly birdseye. I left the inside flat. It had lots of volume and the tone was certainly focused. About 10 years ago I got a lathe that could easily handle the diameter of the resonator and I decided to turn the inside into a standard concave shape. This, of course, added a little volume and a little depth. The change in volume was negligible, but the tone change was dramatic. Much more complex and bassier, if that's a word.