sound hole

aloha all,
in the instruments that i have built, the sound hole dimension was always pre-determined by the build plans.

i cant help but wonder if there is a formula or some kind of sound hole voodoo that would give a basis for the sound hole dimension in relationship to cubic inches of air inside box or square inches on sound board.

does the shape alter the sound that much? the position of the hole important?

please give me any ideas, references, comments or your own experiences on the subject of sound holes. mahalo in advance

lokahir said:

i cant help but wonder if there is a formula or some kind of sound hole voodoo that would give a basis for the sound hole dimension in relationship to cubic inches of air inside box or square inches on sound board.

does the shape alter the sound that much? the position of the hole important?

Click to expand...

Yes! There is a relationship between size and characteristics (volume and tone). There is a relationship between shape and these characteristics also. Both relationships seem well documented from an academic perspective. It is definitely interesting to try to apply those academic findings to instrument design.

The relationship of size we know about thanks to Hermann Helmholtz, a scientist who studied the relationship between the volume of a chamber and it's resonant frequency. Larger chambers have lower resonant frequencies. Similarly, he studied the relationship between the size of an opening in the chamber (a soundhole) and the resonant frequency. A larger opening tends to shift the frequency higher, a smaller opening shifts it lower. You can google his name and get all the math; personally I don't think that's really required beyond understanding the basic relationship since things get "complicated" for oddly shaped chambers (i.e. a typical ukulele shape doesn't react exactly the same as a perfect cube).

Based on those basics, I've done some experimentation with soundhole size and I've drawn my own conclusions, I'd love to hear if others have as well. I've definitely gone down the rabbit hole but it would be refreshing to compare notes. I focus on tenor sized ukuleles almost exclusively. My goal has been to produce an instrument with a more pronounced midrange, since that's the tone I like, and I don't often find it in commercially produced instruments. To achieve that, I've reduced the size of the chamber slightly by building a little thinner than most people seem to (I taper from 2 3/4" to 2 1/2"). I also use a slightly larger soundhole than seems typical (2 3/4" diameter). My instruments built with these two changes, when compared to those built with more typical specs (3" to 2 3/4" body taper, 2 5/8" soundhole) definitely produce a subtle difference in tone, just what I had been looking for, so I've kept those specs. I would go so far as to say that these two changes make more of a difference in tone than many things that people seem to focus on in tone discussions (i.e. the change in chamber volume and soundhole size make a bigger difference than switching between redwood and spruce for the soundboard).

I have not yet experimented with soundhole shape at all on a ukulele, mainly because I like the way a circular soundhole looks. Shape seems to come in to play given that most air movement through a soundhole occurs right along the edge, so a shape that maximizes perimeter for a given surface area (i.e. an f hole) will have a different result than the same surface area in a round hole shape. Look at page 41 and 42 in this paper:

https://dspace.mit.edu/bitstream/handle/1721.1/61924/707340180-MIT.pdf;sequence=2

Also, there's a book called The Luthier's Handbook by Roger Siminoff which goes into a lot of detail about these and related subjects. It's not ukulele-focused but there is a lot of good reading material.

If you want to go down the rabbit hole of the science behind much of ukulele building then David Hurd has written a book called "Left Brain Lutherie". He's now retired but his website ukuleles.com is still up and has all kinds of info on it.

The late Graham Caldersmith wrote extensively on classical guitar acoustics, much of which is relevant to ukuleles. He developed a family of different sized guitars and establishing soundhole size to body volume (as well as all the associated resonances) was central to this. He wrote a number of articles for American Lutherie which can be searched for at the Guild of American Luthier's website luth.org. Membership of the Guild is very useful.

Cheers

dwizum

I to have gone down this rabbit hole. So my notes on this topic are ......
Thin the body and open up the hole. I have been fooling with these two dimensions for awhile.
Here is a link I did sometime ago but I still think it is on the right track and worth some thought. I have many ukes laying around to play... And the thin one is the one I always pick up to play, and I play it everyday. The soundhole is 2 3/4" The body is 1 7/8
"https://ukulelefriend.com/?s=Tom+Parse&post_type=video

Great video Tom! And very encouraging to hear a similar result to what I found. It seems like you've tended to an even thinner body than mine but the same soundhole size. Have you played with soundhole size at all, in conjunction with the thinner body? Or have you always used the 2 3/4" on all body thicknesses?

I spent the first 20 years of my building career making arch top mandos and guitars. One of the last operations you perform is to slowly enlarge the F holes to tune the frequency response of the instrument. Usually you start off with the holes small and a booming bass response and high strings rolling off quickly as you move up the fretboard. As you enlarge the holes, the low notes attenuate slightly and the high ones improve. You quit when things are balanced. With that background, I always make my sound hole smaller if I plan to add a side sound port. Most other luthiers I have talked to do not. Bridges and sound holes seem to garner little attention for some reason.
Brad

dwizum
No I have not played around to much with the soundhole size. I switched to 2 3/4" awhile ago and have just stuck with it for all of my tenors.

wow. thanks everybody for your comments. i cant wait to start experimenting with all the info provided. great starting point info. question, so do you all have a bunch of tops or completed instruments with a not very complimentary sound hole? already started looking for that sweet spot. much mahalo.

I suggest that you build a ukulele with a very small sound hole. Measure the body resonance and note the balance of notes from low to high. Enlarge the sound hole and repeat. That way you have eliminated all the other variables that could be misleading if you are comparing different instruments.
Brad

BuzzBD said:

I suggest that you build a ukulele with a very small sound hole. Measure the body resonance and note the balance of notes from low to high. Enlarge the sound hole and repeat. That way you have eliminated all the other variables that could be misleading if you are comparing different instruments.
Brad

Click to expand...

I'm sure I've read of someone experimenting by just taping pieces of card with different sized holes onto an existing soundhole. Obviously you can only go smaller!

I believe these were in line with received wisdom, that smaller soundholes enhance bass response while large soundholes enhance treble.

As the soundhole "tunes" the body resonance, which I think is mainly based on body volume, changing the depth of the sides should have a similar effect (more body volume = more bass, etc). But dwizum's experiment suggests that reducing the body volume and increasing soundhole size gives more mid-range response, rather than both working together to increase treble. This suggests that body depth is a third factor - anyone able to explain how the three interact?

I don't know if I can answer specifically how the three interact, but I did basically do the experiment Buzz suggested - I started with a really small soundhole and did not install a rosette. I enlarged the soundhole in steps until it was right up against the braces (I don't remember the exact size, but somewhere above 3") and played it at each step. I did this on my current body design, which has slightly shorter sides and also slightly smaller upper bouts - so it's maybe 15% less in overall volume than typical tenors (although there's a lot of variation there) and probably closer to an "ideal" circular shape since the upper bouts are smaller in proportion.

Below about 2 1/8" the instrument sounded bad. It just wasn't a useful tone, it sounded boomy and muffled. Like someone was playing it under a blanket. It woke up at 2.5" and sounded good all the way up to 2 7/8". Between those two sizes you got a useful range of tones, about what you'd expect according to the theory. Smaller was a little darker and scooped sounding, larger got more punchy. The tone never really got super trebly. At 3" it just sort of fell apart - it just lost body and volume. It sounded similar to what happens when you thin the top or shave the braces too much. At that point I destroyed the body and re-used the neck on another instrument. I bet if you wanted a really bright trebly instrument you could get there with a smaller body than mine, and probably a bigger soundhole (or two soundholes, or a more efficient shape like f holes). I feel like the round soundhole has a limit where you can't keep making it bigger past a certain point.

The only final thought I have is that while these experiments have lead to me getting what I was looking for, the major conclusion I came to is that tone is incredibly personal. It's difficult to talk about in words and outside of the obvious cases, it's difficult to claim one tone is "good" and one is "bad" - regardless of what the theory says, I feel like there's clearly a big range of "could be good to someone" tones possible on either side of the mathematically perfect design. Basically, I reached a point of dizzying confusion trying to understand the math behind all this (for instance: determining the "ideal" soundhole size for a given body volume) and decided to just trust my own ears. So after that experiment I settled on 2 3/4" since that had good mid punch, kept enough bass and volume, and wasn't too trebly.

I remember seeing an old and simple table for Ukulele dimensions. If one Googles ’ukulele scaling dimensions’ then it seems to come up in the search results. For sound holes sizes it gives 2&5/8” for a Tenor - the associated body dimensions listed seen small by today’s standards.
https://www.google.com/search?q=Uku...&client=safari&prmd=sivn#imgrc=Gatt_Wxk2ZbApM
It can be found here too: https://ukuleles.com/ukuleles/sounds/

A thread on Cosmos about tone woods had a particular comment in it that I found helpful. Soundboards have got to be thin enough (so flexible) to allow low frequency vibrations. I guess such soundboard response understanding is a given for most folks here but it was a ‘light bulb’ moment for me.

I wonder what I should be looking for in the design of a Soprano that indicates (before you ever play) that it will have a good base and mid-frequency response? Punchy and squawking Sopranos I do not like, IMHO the Ukulele is a musical instrument and should be melodic rather than cutting.

ProfChris said:

I'm sure I've read of someone experimenting by just taping pieces of card with different sized holes onto an existing soundhole. Obviously you can only go smaller!

I believe these were in line with received wisdom, that smaller soundholes enhance bass response while large soundholes enhance treble.

As the soundhole "tunes" the body resonance, which I think is mainly based on body volume, changing the depth of the sides should have a similar effect (more body volume = more bass, etc). But dwizum's experiment suggests that reducing the body volume and increasing soundhole size gives more mid-range response, rather than both working together to increase treble. This suggests that body depth is a third factor - anyone able to explain how the three interact?

Click to expand...

I think the basic concept of how this all works is as follows (please note that this comes from my knowledge of the design of ported loudspeakers, but I believe that the physics is going to be the same):

1. When you play a note on a uke, what you hear is the sum of the responses from the string, the top, and the sound hole. The string response is quiet compared to the other two, and can be neglected. There may be low-volume responses from the sides and back, but we'll also neglect them for this discussion.

2. The response from the top is directly excited by the string, and is mostly going to be a straightforward function of the fundamental tone plus harmonics.

3. The response from the sound hole is a little more complicated, conceptually. The air within the uke is going to be excited by any note played on the strings, but not every frequency will be result in an equal amount of volume coming out of the sound hole. The combination of the internal volume and the area of the sound hole will select for a specific frequency at which sound hole output will be highest.

4. If you measured and graphed the output of the sound hole across a range of frequencies, you would see that output from the sound hole is highest at the frequency selected by the combination of internal volume and sound hole area (i.e. sound hole resonance frequency). Above and below that frequency, output will drop off at a characteristic slope. As a result, frequencies far from the sound hole resonance frequency won't be strongly reinforced by the sound hole, and the sound hole output will be negligible at very high frequencies.

5. Since the total output of the uke is the sum of the top plus sound hole, you can alter the balance of sound by changing the sound hole resonance frequency. It's important to know the frequency of the lowest open string that will be on the instrument. If it's a low G and the sound hole resonates around low G or a little higher, bass notes will tend to sound boomy, or at least noticeably louder than notes played on other strings. If it's only going to be used for standard reentrant tuning, you might choose it to be a bit lower than open C, so bass from the C string is strong but not too strong.

6. Making the sound hole bigger (edit: *smaller*) than standard for that size uke will lower the sound hole resonance frequency, which at some point may seem to emphasize mid and upper frequencies. What's really happening there is that the sound hole resonance gets pushed far enough below the string frequencies that it starts to contribute significantly less to the overall volume of sound of the bass strings. So it's really less bass, not more mid and high.

7. As far as considerations of depth and body shape go, the most important thing is going to be the internal volume of the instrument. Skinnier depth and wider top is the same as deeper depth and narrower top, or longer or shorter body, if they all produce the same internal volume. There might be a difference if you had a shape that was much thinner than the norm, or with a very narrow transition from upper to lower bout, etc. Basically, if some internal part of the uke is narrow enough to have its own resonance frequency different from the sound hole resonance, that could change the bass response in an unpredictable or undesired way. Of course, differences in body shape change the size and shape of the top, which will have its own effects on the sound, how the instrument is braced, and so forth.

8. Incidentally, changing the shape of the sound hole, within reason, probably will have little impact on the sound if the area remains the same. I expect that f-holes on mandolins. violins, etc. could sound different if changed to round holes, because so much of the area of the f-hole is very narrow and long. But going from round to oval, square, or irregular, isn't going to matter much. Two smaller holes instead of one big hole probably isn't going to matter much either.

Uke-alot - good points! I have a few thoughts:

For your 6th point - I think you're describing the relationship differently than I've understood it, in terms of a Helmholtz resonator. Look near the bottom of this page, where a guitar soundhole is discussed:

https://newt.phys.unsw.edu.au/jw/Helmholtz.html

Let me see if I can get the formula shown there to reproduce here:



Radius and frequency are positively correlated - as you increase radius, the resonant frequency will go up (not down as you've explained). Or are we misunderstanding each other?

Also - one consideration I had on your 7th point is that body shape (at least in the sense of the ratio between depth and shape) isn't just about the resonance of the container or soundhole. A soundhole on an inert box that's shallow with a wide top may perform the same as a soundhole on a deep box with a smaller top, but for a ukulele, the top (meaning the soundboard) itself will definitely perform differently between the two, right? An instrument with a tiny top but a deep body will sound different than a wide top and shallow body, because the soundboard is a different size. So I don't think it's totally accurate to consider the box volume as the only factor that matters. I think that's part of the trick of ukulele design, and part of what separates them from designing a loudspeaker cabinet. We're playing with the soundhole as part of the top, so any change to the soundhole impacts the soundhole and the top itself. And separate from considering the soundhole, our "speaker cone" happens to be one wall of the box (the soundboard) - the very wall we're punching the soundhole in. I think the loudspeaker equivalent would be if ports were made by cutting holes in the speaker cone, instead of by cutting holes in the inert box it's placed in. For better or worse it's a much more complicated situation.

dwizum said:

Uke-alot - good points! I have a few thoughts:

For your 6th point - I think you're describing the relationship differently than I've understood it, in terms of a Helmholtz resonator. Look near the bottom of this page, where a guitar soundhole is discussed:

https://newt.phys.unsw.edu.au/jw/Helmholtz.html

Let me see if I can get the formula shown there to reproduce here:

View attachment 129864

Radius and frequency are positively correlated - as you increase radius, the resonant frequency will go up (not down as you've explained). Or are we misunderstanding each other?

Also - one consideration I had on your 7th point is that body shape (at least in the sense of the ratio between depth and shape) isn't just about the resonance of the container or soundhole. A soundhole on an inert box that's shallow with a wide top may perform the same as a soundhole on a deep box with a smaller top, but for a ukulele, the top (meaning the soundboard) itself will definitely perform differently between the two, right? An instrument with a tiny top but a deep body will sound different than a wide top and shallow body, because the soundboard is a different size. So I don't think it's totally accurate to consider the box volume as the only factor that matters. I think that's part of the trick of ukulele design, and part of what separates them from designing a loudspeaker cabinet. We're playing with the soundhole as part of the top, so any change to the soundhole impacts the soundhole and the top itself. And separate from considering the soundhole, our "speaker cone" happens to be one wall of the box (the soundboard) - the very wall we're punching the soundhole in. I think the loudspeaker equivalent would be if ports were made by cutting holes in the speaker cone, instead of by cutting holes in the inert box it's placed in. For better or worse it's a much more complicated situation.

Click to expand...

Ok, assuming the formula in the link is correct, then making the hole larger for equal volume should make the resonance frequency go up. (And I'm not disputing it; it's been a long time since I've gone back through the basic math of this. And there are more variables to consider in speakers, most importantly the length of the port, but also the air velocity in the port.)

To clarify my earlier post, the internal volume and sound hole area are the main things that matter to the amount of volume *produced by the sound hole.* As I acknowledged in my post, changing the size and/or shape of the top will have some impact on the sound of the instrument. But I think that's a really complicated topic, and it would be hard to create rule-of-thumb generalizations on that (at least, I can't), because things like the optimal thickness of the top and bracing scheme will also change.

If the question is keeping everything the same except the diameter of the hole, then you would have to consider the possible range of hole diameters and whether they produce a enough of a change in stiffness or radiating area to matter much in terms of how the top produces sound. I think the range of desirable hole diameters would be constrained by what happens at the extremes. At some point, the hole resonance frequency is low enough that it doesn't reinforce bass frequencies enough and the instrument sounds thin, or maybe it's too high into the midrange and the midrange ends up sounding unnatural. It would be interesting to do the math and figure out how big or small the hole would be between those extremes, and then one could make an educated guess about whether it's significant in terms of the sound the top produces.