I'm currently working on 4 "paddle box" style guitars/strummers/whatever.  I'm at the stage of shaping the tops and trying to decide on sound hole size and design.  I've looked online at a lot of technical discussions on Helmholtz resonation and such, all of which is way over my head.  I'm looking for a simple formula to get a general idea of calculating sound hole size to box capacity (if there is such a thing).

The second part of this concerns soundhole shape and whether that affects sound.  Most flat-top guitars have round holes.  Arch-top and bowed instruments (violins, cellos, etc) favor f-holes, and then there are luthiers that get creative and carve very elaborate designs.  Is it just personal preference?  Obviously round holes are easiest to make, but I'm trying to take my builds to the next level in terms of both workmanship and performance.

Any input is greatly appreciated!

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Hal,

There is actually such a formula, the one used to calculate Helmholtz resonance, which a guitar only approximates, and is found about halfway down the page in this reference:

http://www.phys.unsw.edu.au/jw/Helmholtz.html

There is also this paper, which you may have seen in your researches:

http://hal9000.ps.uci.edu/Weber%20H90%20Physics%20Paper.pdf

The size of the sound hole is proportional to the resonant frequency, so larger holes will cause the soundboard to resonate at higher frequencies. For a bassier build, use a smaller sound hole. Also, locating sound holes in the upper bouts or shoulders will result in lower frequency dominated builds. The size of the box (air volume) and string gauge will also have an influence. The 1-2" diameter sound holes typically found on CBGs should give you deeper sounding boxes, all other things being equal. Somewhere in this Group is a thread where the calculation was done for a CBG of known dimensions, using the above Helmholtz resonance equation. IIRC, the calc showed that a single 1.5" sound hole, located in the upper left bout or shoulder ( assuming a right handed player) enhanced the bass response.

Yep, round holes are easier to cut and shape; f-holes work on violins and jazzbo gits because they were originally cut into arched tops, allowing for different sides of the arch to vibrate and enhance different frequencies. Cutting them into flattops is more for cosmetic appeal. Cutting even more complex shapes makes the Helmholtz equation above even less relevant, since it assumes a cylindrical pipe to begin with, and a round guitar sound hole is just a relatively flat pipe. Interestingly, Antonio Torres Jurado, credited as the father of the modern classical guitar, experimented with sound hole tubes to enhance lower frequency response, but gave it up. (according to several sites I just read). Of further note is Planet Waves' Soundport for acoustic-electric guitars, which seeks to do the same thing, while also suppressing feedback.

Here's a series of build experiments: Build a few with varying sound hole sizes and locations. If you use a standard box size, then you could also use a series of soundboard templates (Torres used to do this), with
sound holes of varying sizes, shapes and locations, to test the best placement before finishing the box. This would work on neck-throughs or bolt on necks whose fretboards that do not extend over the soundboard. Once you find a design you like, further experiment by connecting a series of gradually longer tubes of the same diameter as your optimal sound hole, to the soundboard, mounted attached to and extending directly below the sound hole. This might function similar to a resonator. An even wilder experiment would be to try a series of graduated cylindrical tubes inside one another, with an annulus between each one, to see if multiple frequencies could be enhanced, volume-wise.

I bet your head hurts now. Basically, cut round sound holes the size of something between a US quarter and silver dollar, place t either in the center or in the upper left bout, use thicker strings, and you should be good to go.

I did the math, and I've attached a quick and dirty version of the Helmholtz equation in word format, with an example for a "typical" CBJ.  Hope this helps, or at least provides a starting point.

 

Attachments:

If you have more than one sound hole should they all be this size or add up to this size? For the box volume, should you subtract the losses from the bracing and neck mountings?

Hal,

The thread I was referring to above was in the Beginners Club forum:

http://www.cigarboxnation.com/group/thebeginnersclub/forum/topics/s...

An example of the calculation for an 8.5" long box gives the 1.5" sound hole answer I referred to above.

Oily

In earlier post I was looking at sound hole size and found these 2 formulas.

 I set up a spread sheet and ran both formulas listed below using these numbers

Dimensions      10 x 8 x 2

Frequency of 2nd lowest string     146.83

 Formula for calculating sound hole diameter returned a sound hole diameter of  1.684

Helmholtz equation for sound hole diameter for cigar box guitars returned a sound hole diameter of .824

 One of these numbers is about half of the other.  Am I calculating something wrong or am I completely missing something here.  Could  the Helmholtz equation be the radius instead of diameter.  Any clarification or help would be welcome.

 Formula for calculating sound hole diameter

    1.)  Calculate box volume(V) = Length * Width * Height
    2.)  Solve for the radius of a sphere of the same volume:  radius = ((3*V)/4*pie)^(1/3)
    3.)  Divide the radius by 4.
    4.)  This resulting value is the new radius of the sound hole.
    5.)  So, 2 x radius is the new sound hole diameter.

And came up with this example:  (2 * (((3 * 8.25 * 5.5 * 2.75) / (4 * 3.14))^(1 / 3))) / 4 = 1.55023303

 

Another post gave this formula:

Helmholtz equation for sound hole diameter for cigar box guitars

The equation is:

Sound Hole Diameter in inches = F2 x W x L x D x 0.00000023895

                                                                               

where:

W = box inside width

L = box inside length

D = box inside depth

F = frequency of 2nd lowest string in Hz 

For example:

The D string on a 4 string CBJ tuned to open G (GDGB) is 146.83 Hz

The inside dimensions of the cigar box are 8 x 10 x 2 inches

Substituting these values into the equation, we have:

Sound hole diameter = 146.83 x 146.83 x 8 x 10 x 2 x 0.00000023895

 

Sound hole diameter = .824 inches, or about 53/64”

 

Hal,

Even further Frequency enhancement and sonic tuning can be done, if using a thick enough neck inside the box, by boring holes of different diameters through the neck, either vertically or laterally. There are pics here somewhere that show a build like this, with laterally drilled holes, from either late 2009 or early 2010. One of my builds slated for early next year will have this feature, to see what effect it has. There are other pics here somewhere which show a build with relatively thick box sides, that have multiple holes drilled vertically into the two long sides; the builder reported good bass response and better volume on that one than on any of his previous builds.
Wow, Oily, you really thought about this.  And yes, my head hurts!  My paddle boxes measure about 8.5" x 10.5" x 3".  If I can find my calculator (me thinks the wife took it off my desk and hid it) I'll play with that formula, and use it to design something.  Actually, the quarter to silver dollar size seems on the small side - I have a teardrop shaped travel guitar that measures 15"x 9"x 2.5" and it has a 3" soundhole with good volume and nice bright highs.  Perhaps the answer is to calculate both volumes and size the soundhole as a percentage between the two,, i.e.; if my paddle box is 85% of the cubic volume of my other guitar, the hole size could be around 2.5", or a decorative hole with the same surface area.  I know there are other factors involved, but for our uses that may be a valid approximation.

Hal,

 

Yeah, I have a couple science degrees, so this kind of stuff is like breathing to me. I have a Martin Backpacker that has a relatively large soundhole, too, for its size. Yep, these tend to have bright highs. Reason I advocated a smaller soundhole is that many CBG builders seem to want to boost the lower bass frequencies, which many feel gives a "warmer" growlier sound that they associate with the Blues. The bright highs tend to sound tinny to my ears (which are undoubtedly damaged from years of exposure to high-decibel concert rock), and also make such a CBG sound "banjoey." That said, the reason I bought the Backpacker is because I needed a mandolin-like sound for a stage show I was doing years ago, and it was a far cheaper alternative than a real mando. Plus, it was my first "portable" travel guitar.

 

I'd use the Helmholtz resonance equation only as a rough guide to soundhole size, not as a specific remedy, because all it will tell you is the "optimum" frequency at which your soundboard will resonate best for a given volume of air (read box size). Brings up a question though: if you're gonna build several of these box designs, why not try at least one with a smaller soundhole? If you're not happy with it, you could always increase the soundhole size until you get what you like. If you go back and look at Rand Moore's original paddle box, and at similar Russian balalaika, and Chinese, Japanese, and some Indonesian 3-stringed instruments I've seen recently, whose names I can't properly pronounce, they all appear to have quarter-to-silver-dollar-sized sound holes. I've played several balalaikas and related instruments, and they always sound mellower and lower toned than my Backpacker with the smaller volume and larger soundhole. It might be worth a try, especially if you're gonna amplify them with a piezo or mag pup. That said, I also have a couple of Middle Eastern ouds, and the one with the larger and more numerous soundholes (3 in the case of my cheapo Iraqi oud, a large circular soundhole in the center, about the same size as a dreadnought acoustic soundhole, but covered in highly detailed "fretwork," and one smaller oval one either side of that, lower down, from which I removed the fretwork to increase projection) also sounds "tinnier" and focused toward the higher frequencies. I suppose this is to cut through the conversation at parties and coffee shops.

Hi Oily & Hal.

On my first paddle box stick dulcimer (the one documented in my discussion group "Home Made Resonator Boxes 101, v.2.0"), I decided to position the sound hole in the same relative location as Bob McNally does on his standard strumstick (mine I use as a kind of reference model). His instrument is a bit too high pitched for my taste, so I decided to build my sound box bigger (roughly 4 times bigger) and I put guitar strings 2, 3 & 4 on it to achieve a bass-ier sound. The size of my sound hole is 2 cm (7/8"), the same as McNally's strumstick. At the time, I thought I could always make the hole larger if needed, but I have never felt the need.

My second paddle box project (still in progress) is sized about halfway between the McNally Strumstick and my first paddle box. It has a 2.5 cm (1") diameter sound hole positioned in about the same relative position as the other two instruments. So, soon I'll see if a bigger hole makes much of a difference or not. Incidentally, this new paddle box will the a 4-stringer. The first 3 strings will be identical to a strum stick (will probably use banjo strings), and the 4th string is 3/4 length like the dulcijo, and will be the same diameter as string 1. So, essentially a 4-string dulcijo. Should be finished in a week or so. Still need to stain and finish the instrument, add the frets and finish stringing it up.

As far as the theories and formulas regarding optimal sound hole size, I just find the hole topic "over my head" and prefer winging it. On several of my instruments I started with small holes and on occasion widened them with fair improvement in volume. I also subscribe to the idea that if you hold your sound hole up to your cheek and tap on the back, you should feel a puff of air. If your hole is too big, you won't feel the puff. Not scientific, but better than no rules at all.

 

-Rand.

 

Been waitin' for ya to join the discsussion, buddy!

 

You touch on some of the same themes I was discussing with Hal: Small sound hole, relatively big box (more air volume), and thicker strings. I think your "puff" test is perfectly valid and scientific, at least in the sense that it is a repeatable test easily done by other "investigators," and I think could be supported by the mathematics. If we wanted to get all engineering technical (which might be fun, but not, certainly, what Hal, you, or even me, really wants to do), we'd have to hook up some pressure measurement device to the sound hole to measure the pressure of that puff (a dB meter might do it), and then investigate the same test with 1) same volume box, but different soundhole sizes (my soundhole template idea), 2) single soundhole template, but different volume boxes, and finally, 3) different volume boxes with different sized soundholes.

 

Then we'd have some data to cuss and discuss 'til the wee hours, while the glue is drying.

 

OK, here's a thought for the group: What sizes (LxWxH) do the majority of cigar boxes come in? I can make up an Excel table with that data, then take various soundhole diameters, and run scenarios using the Helmholtz equation. Will tell us the optimum resonance freq. Put it in musical terms: "This configuration resonates best at A2, so use strings 2,3 and 4 for a bassier-sounding git, or 3,4 and 5 for a brighter tone," or whatever.

 

Heck, I don't need most cigar box dimensions; I can just build a data matrix for all sizes, starting with a 1"x1"x1" cube (given a 1" wide by 1" deep neck, a git virtually no one would attempt to build), and soundhole sizes from 1/32" to, say, 8" (yet another set of likely-to-be-unplayable boxes), assume soundboard thicknesses of 1mm to 1/4," and see what freqs pop out! Then we could apply known string gauges to this data, and see what an "optimized" CBG might theoretically look like. Then, we use the idea of crowdsourcing by going through the thousands of build pics on the site, get dimensions of boxes, string gauges and soundholes, and I betcha we'd find that the monkeys have not only already written Hamlet, but have secured the movie and product distribution rights to it, as well!

 

But then, we could reasonably claim we'd know: "For a Padron box with dimensions X,Y,Z and a lid thickness of h, using string gauges l,m and n, the preferred soundhole size(s) for best volume and frequency response are..."

 

Back to y'all in a couple days with the Excel table. Anyone out there interested in some finite element analysis?

 

Yeah, me, too.

 

Oily

 

 

 

 

Hi Oily,

Sounds like you are a glutton for punishment (what advanced math seems to me). If you like to crunch all that data, go right ahead. Let us know if you find and trends and/or practical "rules of thumb" you can gleam from all this data analysis. Then maybe we can test the theoretical against builds we have actually done. Well, good luck.

-Rand.

 

Oily (the masochist) & Rand:

Like the Pirate who walks into a bar with a steering wheel stuck in his pants said,"Arrrrrgh.....It's drivin' me nuts!"

I've calculated that the interior volume of my paddle boxes will be approx 2/3 that of my travel guitar (which, BTW, I also can't play).  That would put my soundhole at about a 2" diameter, which may give me better projection, if bigger is better, with the added depth of the box making up for some of the bass loss.

I also realize that string selection will be very important.  I've had good luck with using .011, .016, .022' and .030" gauges so far tuned to DGBE with a scale length of 25.5".  Again, theses sizes tend to be brighter and will be even more so with a shorter scale (I'm planning on roughly 23" for these), so I may try larger sizes for a warmer tone.

I find it fascinating just how many variables come into play.  I wish I could understand them all.

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