Acoustic Guitar Body Size: Soundbox Volume vs. Tone
How does modifying shape and volume affect tone

Pat McCarthy - 12:38am Jun 25, 1998

Hi, folks. Thanks in advance for letting me play in your sandbox. I'm sure I'm new to all of you, but have learned much from lurking here, and am familiar with most of you. (Hi, Deb!) I'm working on plans for a couple of 3/4 size guitars. I have LMI's "Martin size 5" plans, and was considering some alterations. I'm looking at a couple of possibilities, and wonder if any of you might have some knowledge of acoustic guitar design. My first question is: assuming the total volume of the box remained constant, how would extreme stretching or shrinking certain elements affect tone(i.e., tiple sized soundboard with 12" body depth vs. jumbo sized soundboard with 1/2" body depth, both with equal volume). My second question is: assuming you could increase/decrease volume of the box, which ONE dimension would need to be changed to increase a)bass, b)midrange, c)treble.

Thanks,

Pat McCarthy - Vicarious luthier

Good question!1 I'll assume that the more 'physics capable' will jump in, but it seems to me that depth affects the 'potential' sound, while top size (effective vibrating area) affects the actual sound production - in otherwords, volume is more of a reinforcing aspect. I certainly expect to have the error of my ways shown me - [lease be gentle (g)

I don't have an answer to your question but I can share my experience with a guitar that I just made. I made a classical guitar with a 8 foot radius top and back. This thing is very arched and it looks quite cool. The problem, however, was that in order to keep the thing from being too large at the waist I decided to make it have a shallower body depth at the neck and end block. (about an inch smaller than a traditional classical) The center of the spherical dome is just below the soundhole. One thing I learned from tapping a piece of veneer while bending it into and arch is this raises its pitch. This guitar has a very high voice, kind of a tenor range. it's very resonant and responsive but it's lacking the real low frequency range. I've thinned the top at the edges and shaved down some braces but it still remains very mid-range sounding. So, I don't know if this quality is a result of the thin body depth or the arched top or a combination.

I don't know if this quality is a result of the thin body depth or the arched top or a combination.
My experience with hammered dulcimers is that increasing body depth increases bass response, and decreasing it reduces bass response. But this also seems to be true of increasing and decreasing body *volume*, up to a point. As for arching tops, that seems (again on HDs) to increase resonance and sustain, and have little effect on the pitch of the instrument. Note that as you bend your top you make it functionally stiffer, raising its pitch.

But this also seems to be true of increasing and decreasing body *volume*, up to a point.
I agree, I've played some small body instruments that have a fuller sound than some really larged body instruments. Maybe there's a point when the body gets too large to support the low notes. (The resonant frequency of the box is below that of the low e string) ???

I don't know, Dean -- with HDs, if you make the box too deep it gets "boom-y" -- sort of hollow and unpleasant-sounding. The (apparent?) full sound of a good, small-body instrument (like a nice 000 guitar) may have more to do with a more even sound across the entire range than with a bigger instrument like a dreadnaught, which can be bass-heavy. <scratching head>

This discusion is very interesting to me since my son in law wants me to build a "travel guitar" and untill a few weeks ago I didn't even know how to spell gitter.

Sorry about the "travel guitar" requirement--the more easily transportable they are the less sound you tend to get. The better-sounding ones, like the baby Taylor, are really about 3/4 size. The small ones, like Martin's Backpacker, are easily transportable but have all the tone and volume of a wet shoebox. In the search for small, you have three dimensions--you can shrink the depth, the length, or the width. To shrink the length, you can redo the string attachments to eliminate the headstock and/or use a short scale--which usually is unsatisfactory for both tone and playing technique, and headless is often unesthestic. Less depth usually creates a "thinner" sound--very little low end response; lessening width has its obvious limits as the soundboard decreases in area. To me, the best travel guitar possible is a minimal electric. I've built a couple that are basically headless full-scale through-neck with detachable "wings" (I need these, as I can't get a good arm position on a 2 x 4) and a thinline Dobro pickup. I use a baby Marshall amp (battery power) and the whole thing fits into a plywood case about 27" x 3.5"x 5". You can get even smaller amps, like one for about $12 at Radio Shack. As far as acoustic-only, the best I've seen (heard) is the Epiphone El Nino; it's much like an Ovation miniature but a heap cheaper. They're also very difficult to find--even some Epi dealers have never heard of them. If you just have to do an acoustic, try doing a Danelectro-type hollowbody about the size of a Tele and about 2.5" deep. It's cheap, tough, and has surprising volume. Jed

This is all great, and much appreciated! As for my own observations, I've softly concluded that as per Deb, Kevin and Jed, body depth has a clear proportional effect on bass response. I've also heard that changing one dimension of an existing successful design can have disasterous effects (specifically - the Martin J is said to combine the worst elements of the D and 000!). I have never actually heard the Martin 5 design that I am attemepting, but am pretty sure that it leans heavily toward the treble end. At this point, I'm trying to offset that by increasing the depth from 3.88" to as much as 4.5", and using Indian Rosewood for the b/s and Engelmann for the top (WRC is far to soft for a travel guitar and Sitka too bright). My other design is a thin body along the lines of Kirk Sand or Rick Turner. Instead of routing out a solid block of hardwood, though, it will be made using traditional b/s construction for weight savings. Just as a side note, I will be playing this in hotel rooms at odd hours, so my goal is accuracy/evenness of tone over loudness [notice I didn't say volume ;^)]. Pat McCarthy - Vicarious Luthier

General rule is that a larger volume increases bass response. There probably is an optimum volume, but I suspect it interacts with a lot of other factors. I believe Jimmy d'Acquisto used to decrease the thickness of his archtops as the width increased.

A question nobody has raised and that I would like some input on is: How should the bracing vary as the size changes? X-bracing was (Ibelieve) developed for dreadnought size guitars. I'm not entirely convinced that it is the best possible bracing pattern for small bodied instruments. I've run across old parlour guitars that have only lateral braces which have plenty of volume and great tone. They are actually better for fingerstyle players than dreadnoughts.

To get even more esoteric, has anybody tried modifying Kasha bracing for small-bodied guitars?

X bracing was developed in the 1800s and first used on parlor guitars. It never came into its own until it was combined with steel strings.

A number of cool guitars have been made with ladder bracing. I've made single-0 size guitars this way and they are very satisfactory. They sound a bit brash, however, without the roundness of tone we have come to expect from X braced guitars. They seem to get both quieter and more trebly as the depth is decreased. Not that the trebles are accentuated, but that the bass is lost. Getting a satisfactory tone depends much more on what you are used to than what the guitar puts out. An open-minded person will find many more satisfactory guitars in the world than a demanding, closed-minded guitarist. I've learned from experience that it's possible to build a "failure" of a guitar that another musician will flip out over, and vice-versa. I love the fact that so many MIMFolks seem willing to experiment, but you have to be prepared for some failures, by your own terms, at least. I've tried every weirdness (in terms of design and materials) I could think of, and several instruments have gone into the campfire. There's a point where they're too embarressing to have around, especially if you make instruments for a living.

Thanks, John. I stand corrected on the origin of X-bracing. (By the way love your articles on Charles Fox's jigs. I'm working on a few things to speed up my own work.)

I agree with your comments on open-mindedness. Having a certain name on the headstock does not guarantee a great guitar. I make a point of playing all the odd-ball guitars when I walk into a music store. The "right" tone is a very subjective quantity.

Further question for discussion. Do body size and bracing interact differently with different soundboard materials?

Thanks, Robert. At Huss & Dalton we build regularly with Sitka and Englemann, and just recently with cedar. I've used a lot of cedar in the past, as well as some funkier woods not normally used for top plates. Despite many claims to the contrary, I'm not sure that guitars get a signature tone from the wood, either tops or backs and sides. The ones who would know are dealers of high end instruments, since they have a constant supply of good pieces and can compare them all day long. The trouble is that they as often as not will give you a line to make a sale, or they will follow the old mythology. As you know, several guitars can sound good to you at the same time, yet none sound the same. If you try too many at once your ear falls prey to overkill and you 're no longer a good judge. Think of it this way: can you listen to the guitars on a well-made CD and tell what wood they are made of? If you can you have a much better ear than I do. The guitar geeks who talk the best line are often the best read and the least experienced. Build what you want and follow your own intuition. It's not as easy to screw up as you might think.

I've built a real deep rosewood body classical as an experiment, since I was trying to improve the bass range of the guitar, and I found it had no more bass resonance than my shallow bodied Hauser style classicals, the sound seemed to get kind of lost inside the guitar, the thing didn't project at all. Did any of you ever experience that?

Readers of this discussion will benefit by going through the back issues of American Lutherie (articles by Allen, Caldersmith and Carruth) and Journal of Guitar Acoustics (available from Tim White, tpwhite@aol.com). I think it's great to experiment with many shapes and designs, but it's also great to appreciate what others have already done and then decide whether you want to make something up out of whole cloth...

A friend of mine who builds violins give me an interesting titbit on soundholes vs body volume. Apparently Helmholtz worked out that the optimum soundhole area is that of a circle of one-quarter the radius of the sphere that has the same volume as the body. This gives the loudest sound. Modern violin f-holes fit this criterion almost exactly, although I'd bet it was arrived at by trial and error rather than a mathematically inclined violin-maker.

I wasn't able to get as clear an idea on the effect of the shape of the soundhole. I've no doubt that changing the shape will change the sound somewhat, but are violin f-holes the way they are for any reason other than tradition? I know that D'Acquisto's later archtops have catseye soundholes rather than f-holes. This is supposed to improve the tone and volume of the instrument, but this is probably due to the increase in the area of the soundhole more than the shape. Simply scaling up the f-hole from a violin to an archtop guitar isn't going to work because of the square-cube relationship between surface area and volume. As Ignatius J. Reilly said, everything reduces to a question of geometry and theology.

Robert,

"...the optimum soundhole area is that of a circle of one-quarter the radius of the sphere that has the same volume as the body." [Clarification: Is 'one-quarter the radius of the sphere...' = the radius of the circle?]

Bruce: I didn't want to scare people off by using mathematical symbols but they do make things clearer, so here you go. Any soundbox has a volume V which is equivalent to a sphere of radius R such that V=4/3 pi R**3. If I understood the explanation correctly the optimum soundhole surface area A for a Helmholtz resonator will be that of a circle of radius r such that r=R/4 where A=pi r**2. As long as the surface area of the opening is correct it can be any shape you choose. I doubt that fifteen decimal places of precision is really necessary, but this should give the ballpark.

As Ignatius J. Reilly said, one needs to worry most about geometry and theology. He was half right, anyway.

Back to the Hemholtz discussion...

I built a small tenor guitar. I based my shape around a scaled down Hauser classical (from photos I found on the net). I don't have a set of plans but my scaled dimensions are average depth 3.4 in, soundboard surface area (as calculated by my viewer program) 212 sq in., and sound hole radius 1.7 in. The guitar sounds good except that the "D" string is a little dead above the 5th fret. It has excelent volume for a very small guitar. It has a 19 inch scale, and the body is about 9 in wide by 12 in long.

I have another one in the works and would like to improve the design. My sound board area is 84 sq in, and average thickness is 2.25 in, the sound hole raduis is 1.1 in. Using the Hemholtz calculations above I should have made the sound hole smaller (r = .89)

But... When I do a sanity check with the Hauser dimmensions, and using the formulas above, the full size Hauser sound hole radius should be 1.4 in (if you keep the area and depth constant), or the depth should be 6.2 in if you keep the soundhole and body shape (area) constant. Obviously the cube power on the raduis has a very strong influence.

Now the questions... Are my measurements accurate enough to be taken seriously. The advantage of the scanned method is that I can get an area calculation out of the computer (using AutoCad or FastLook). But garbage in equals garbage out. All of the calculations in the world won't help bad data. Has any one else done these calculations? Anybody have some data to contribute?

Should I also be subtracting the tailblock, neck extension, and possibly even the linings from the volume?

Is using an average body depth good enough? With more effort, I could take the top and back raduii and curveture into account.

Of course I realize that you can't build a guitar to a formula, but with as long as it takes me to build ....

John

A correction/ clarification to my previous message.

...I don't have a set of plans but my scaled dimensions are average depth 3.4 in, soundboard surface area (as calculated by my viewer program) 212 sq in., and sound hole radius 1.7 in....

These dimensions were for the Hauser

.... It has a 19 inch scale, and the body is about 9 in wide by 12 in , 84 in sq soundboard area, 2.25 thk, sound hole radius 1.1in ...

These dimensions were from my little Tenor.

BTW... Thanks to the folks here, on the internet news group REC.MUSIC.MAKERS.BUILDERS, and David C Hurd (and his informative WebSite). Having people to bounce ideas off of and get wide ranging advice from is invaluable.

John

John:You can get a pretty good measure of area by tracing the guitar on graph paper and then counting squares.

Determinining the size of the soundhole using the volume of the body and the Helmholtz formula was intended only to give a rough guideline. (If you really want an acccurate measurement of the body volume you could always fill it with water and measure how much it holds. Personally I find that overkill.) I would think that multiplying the surface area by the average depth would be accurate enough. After all, until somebody builds a spherical guitar a Helmholtz resonator is only a crude approxmation.

Incidentally, I found that I was wrong about soundhole shape. A circle provides the least resistance to air movement. The further you get from circularity the greater the effect on the frequency even if the area remains constant. I don't know that anyone has tried to quantify the effect of shape for anything more complex than an ellipse.

I'm currently giving myself a sound lesson in humility by reading through "The Physics of the Violin" by Lothar Cremer. I'm not sure how much of the contents I'll be able to apply to guitar building, but it's certainly raising a lot of questions I hadn't thought about.

I'll have that book in the MIMForum Bookstore in a few minutes.

I guess what I was really after is the calculation being done on a high quality guitar. This might give a sense of how acurate the measurement needed to be. With the radius being acted on by the cube power, I tend to think that is not a lot of room for error.

Can anyone contribute some dimensions? Use the squares method to get the area, give the sound hole raduis (or diameter), the body depth at the neck, waist, and heel. A short description of the guitar and its sound qualities would also help. Things like scale length and top wood will also help.

John

Deb: The Cremer book is one that you should add but you had better include a warning that it is NOT for the mathematically faint of heart. It was written for physicists and assumes that the reader is comfortable with partial differential equations. I've just browsed through it so far. To get the full benefit I'm going to have to sit down and work through the math myself. (Hey, guess that Ph.D. I spent so much time on may finally turn out to be useful after all.)

John: I can go measure my dreadnought to give you some ballpark figures.

Robert, can I talk you into submitting a brief review of the book (a few sentences) to add to the Bookstore page?

Deb, sorry to take so long, but I didn't see your request until a few days ago. Here goes.

Cremer's book is not about violin-making, but is an in-depth study of the physics of sound production in a violin, from bowing and string production to vibrational modes of the body. As the book is intended for graduate level physicists, it is not recommended for anyone who is not comfortable with partial differential equations and tensor analysis. Those with the necessary mathematical background will come away with a fuller understanding of the science behind the instrument.

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