Tone bar question

[peter.coombe]

My assumption on this has always been that they were trying to introduce some asymmetry in order to prevent the tonebars from vibrating at almost exactly the same pitch, possibly introducing some unwanted beats, sound cancellation, or other interference. By having the bass bar larger but tilted away from the longitudinal axis, it provides about the same longitudinal stiffness as the treble bar but vibrates at a different frequency. I may be totally off base here, so take this with a grain of salt

Your assumption might be right in terms of how they might have thought about it, but it does not follow the physics of how a mandolin vibrates.

[j. condino]

Lloyd was also a violin player who was very familiar with their construction. It makes sense that he tried to incorporate the asymmetry of their single bass bar plus a soundpost construction into some interpretation of function for his mandolins when he added the F holes.

[Graham McDonald]

Was it Loar or Ted McHugh, who ran the Gibson factory and who I suspect knew much more than Lloyd about building instruments. You only have to hold the neck of one of Loar's later Vivitone instruments to knock on the head any notion the Loar knew much about instrument construction.

[peter.coombe]

Reading through this thread again, I just can't let this go. In terms of tuning "tone bars", all you are doing is changing the stiffness and mass of the top, although because of the cube rule (stiffness increases according to the cube of the height), you are mostly changing stiffness, and it does not matter two hoots whether you call it a "tone bar" or a "brace", they are exactly the same, and do exactly the same thing, i.e. increase stiffness with little increase in mass. Changing stiffness will change the frequency of the normal modes of vibration of the top, be it free plate or an assembled instrument. However, with an assembled instrument changing the stiffness of the top changes everything, not just the frequency of how the top vibrates. One could say that a brace is a structural thing, but it does exactly the same thing, i.e. mostly increase stiffness, so I am at odds with Roger on this, they are exactly the same thing. After all, guitar makers "voice" their tops by shaving the braces on the top, not just the "tone bars" located behind the bridge. When "tuning" a tone bar, all you are doing is to change the frequency of one of the modes of vibration that you can hear (by changing the stiffness), but you are almost certainly also changing the frequency of other modes as well, you just can't hear them because of the way you are holding the thing and tapping it. The point is, whether it is a free plate or an assembled instrument, the thing vibrates as a whole thing according to it's mass, stiffness and Q. Basic physics. You can call portions of the instrument the bass bout or treble bout, but as far as the physics is concerned in how it actually does vibrate, bass and treble bouts do not exist. You can see this quite clearly by using laser interferometry or Chladni patterns. Laser interferometry is impractical for most of us (including me), so Chladni patterns usually must suffice. So, changing anything will affect the modes of vibration and hence sound. So free plates, top with ribs attached, assembled instrument are entirely different systems and will have different frequencies and shapes of the modes of vibration. These changes are mostly unpredictable, so in general you can't predict precisely what will happen in the assembled instrument from free plate modal frequencies. There is a correlation using relative frequencies that I have measured, but there is a fair amount of scatter which is what you would expect. Added to that, is the mass of the tuners, mass of the tailpiece, mass of the pickguard and how is attached, mass of the sides etc etc, all affect how the instrument vibrates (and adds to the scatter). It is a system with interdependent parts. Nothing is separate. You can't tune one thing and expect nothing else will be affected because it almost certainly is, and that is because that part changes the overall mass and/or stiffness of the vibrating system. You can learn a lot (I certainly did) from the guitar research pioneered by my late friend Australian luthier Graham Caldersmith because mandolins vibrate similar to guitars, just the frequencies are higher.

[Richard500]

I’m still trying to absorb the idea that an arched, f-hole, unbraced instrument top can be stable under string down-pressure. Especially with the grain running longitudinally. Is this because a mandolin bridge has such extensive cross-grain contact compared with, say other bridge types?
Also, the idea that reducing the mass of a resonant, vibrating element lowers the frequency.
And, I think it’s been covered before, but the idea of purfling as a way to reduce damping at the edges by effectively thinning the connection seems like a good idea, and related to enhancing sustain. Or is this taken care of by the general top graduation?
That’s the class for today.

[Dale Ludewig]

Reducing the mass of anything lowers its resonant frequency as far as my experience goes.

[HoGo]

Was it Loar or Ted McHugh, who ran the Gibson factory and who I suspect knew much more than Lloyd about building instruments. You only have to hold the neck of one of Loar's later Vivitone instruments to knock on the head any notion the Loar knew much about instrument construction.

I agree. McHugh was the boss and perhaps even designer while Loar was kind of acoustic "tinkerer". He traveled and certainly visited violin makers and the era was filled with loads of esoteric theories about old italian iviolinsand how they were made so he tried to persuade Gibson management to incorporate that into their work.
I believe the F-5 design was on drawings right from the teens when F style got it's final shape and factory processes were established. Loar was the one who persuaded them to build that thing despite the decreasing mandolin polularity and falling market.

It is clear that every part of instrument affects tone as I have seen during my tuning of instruments in the white. Sometimes in very unexpected ways (like reshaping of neck heel on some instruments). Modern violin makers don't seem to favor the tuning theories of Hutchins et al from decade or two ago and barely record pitches of vibrational modes of plates. The few that use them use them just as general pointer of distribution of plate stiffness (but mostly look for target weight range).
What is interesting that there seems to be almost NO dispute about bass bar tuning of violins, basicly everyone copies one of few time proven shapes and sizes (as used by reknown violin shops like Hills, Morel etc...). And bass bar on violins is much stiffer and affects structure (and thus tone much more than those tiny bars of mandolin). I guess htis was case of Loar mandolins. Factory workers didn't have time to do any tuning (and with the noise in likely still partly steam-powered plant it was plainly impossible) so they just followed succesful prototype.

[HoGo]

I’m still trying to absorb the idea that an arched, f-hole, unbraced instrument top can be stable under string down-pressure. Especially with the grain running longitudinally. Is this because a mandolin bridge has such extensive cross-grain contact compared with, say other bridge types?
Also, the idea that reducing the mass of a resonant, vibrating element lowers the frequency.
And, I think it’s been covered before, but the idea of purfling as a way to reduce damping at the edges by effectively thinning the connection seems like a good idea, and related to enhancing sustain. Or is this taken care of by the general top graduation?
That’s the class for today.

The top appears to be weak to folks especially if they handle free plate and feel how floppy it is. if you put the bridge load on such top it would crack, but once you fix the perimeter it will behave completely differently and feel very stiff (you don't have to glue it permanently, just placing fixed blocks around perimeter of plate that will not allow any movement will suffice). On finished instrument there is also the tension of strings that actually pulls ends of top against each other and the arch wants to counteract the downforce of bridge. So ideally it is in large part balanced system and the load is dispersed among most of the parts. You cannot say the top takes 80 pounds of force, the whole instrument does. Ever heard of honeycomb structures? Thin walls cleverly conected can produce very rigid structure especially for distributed load.

[HoGo]

Reducing the mass of anything lowers its resonant frequency as far as my experience goes.

It's not that simple. If you reduce mass of string the frequency goes up. Even on simple beam there are several modes (frequencies) and depending on where you reduce the mass some modes may go up some down. Instrument plate is much more complicated and oversimplifying never worked well.

[siminoff]

Berrnie... to your question on positioning of tone bars. Tone bars positioned nearer to the center of the sound produce a higher pitch than the same tone bar positioned further from the center of the soundboard (i.e., neared to the rib). If you have a soundboard hanging around, this is very easy to test and prove. The tone bars on the early F5s have the treble tone bar positioned nearer to the center of the soundboard (so they easily tune to a higher pitch) and the bass tone bar positioned further from the center of the soundboard so they easily are tuned to a lower pitch. Both bars are positioned so that they run beneath the bridge's feet.
Roger

[peter.coombe]

Reducing the mass of anything lowers its resonant frequency as far as my experience goes.

That is probably because when you reduced the mass, you also reduced the stiffness at the same time because you are removing material. If you reduce mass, but stiffness remains the same, the resonant frequency will increase, not decrease. You can demonstrate that by using blue tack to increase or decrease the mass. The stiffness of a piece of wood (or any other material) is proportional to the cube of the thickness, but the mass is directly proportional to the thickness. Thus by removing material, you are reducing the stiffness much more than the mass, and the resonant frequency will then go down. Basic physics.

Since the publication of the Gore/Gilet guitar books, which are largely based on Graham Caldersmith's research work, this idea that you need to tune the bass side lower than the treble side of an instrument (make it thinner or shave the braces lower) has been thoroughly debunked in the guitar world. Nobody believes that stuff any more. It is about time it was debunked in the mandolin world, since mandolins also vibrate like guitars. Tuning tonebars may produce a good sounding instrument by adjusting the modes of vibration to make a pleasing sound, and that has been determined empirically by trial and error what the optimum frequencies are. Much of what we do is trial and error and there is nothing wrong with that. It has been done for centuries in violins. However, for an accurate explanation of what is actually happening in the physical world you need to look elsewhere, e.g. the research papers by Cohen and Rossing, Caldersmith, and the Gore and Gilet books. There are enough references in those papers and books to keep you busy for quite a while.

[HoGo]

Here is one old thread with some info on position of tonebars in Loars:
https://www.mandolincafe.com/forum/t...18-Celebration
From my measurements and pictures the very earliest Loars had the bass-side bar 1/4" closer to centerline at larger circle of f hole and approximately 1/8" closer to centerline at upper end of f holes. The treble bar matches later position (as on my drawings) perfectly. Later Loars were very consistent. On the Loars where bars are shifted (see the pics in the linked thread) the relative position of the two bars appears to be the same just shifted to one side. On the one example with shifted bars in the linked thread you can see that the centerjoint is quite shifted as well from geometrical centerline so it is possible that position of tonebars was measured or marked with a template using center joint of top as reference and when that was off the tonebars went with it...

[sblock]

HoGo is correct, and the arch of a properly graduated mandolin top can withstand the down-bearing force of the bridge and strings, which can be up to 80 lbs. (60 lbs. is more typical). This happens in the context of a complete instrument, where the perimeter of the carved top is fixed to the ribs and neck, and indirectly through them, to the back, as well. He is right to point out that the top is part of a more complex structure whose integrity comes from the whole, not the part.

Personally, I don't believe that the tone bars play much of a structural role in an F5/A5 style mandolin. They certainly can stiffen the top to a degree (as discussed earlier in this thread), but this added stiffness is not a crucial factor in supporting the down-bearing load, even if it can change the instrument resonances, which is why some luthiers shave bars to "tune" the top. I say this for several reasons. First, many mandolins exist that are found to have cracked or loose tone bars, and yet their tops don't collapse altogether, even without the support of tone bars. Second, some Asian brands of mandolin have been manufactured that lack tone bars altogether. And third, F-style mandolins have been built using all manner of tone-bar patterns (x-braces, traditional two-bar pattern, radical 5-bar pattern, and more), and none of those mandolins suffer from collapsed tops, as a rule.

The chief cause of top collapse is thicknesss graduations that turn out to be too thin --- often accompanied by large changes in humidity that affect the wood integrity.

[siminoff]

Hogo and Graham:
Regarding Loar or McHugh, Ted McHugh was the key engineer during Loar's time. Lewis Williams ran the company and was a close friend of Lloyd's. And as I think you both know that when Loar left Gibson, Williams soon followed and they opened the Acoustic-Lectric Company. As Hogo suggested, while Loar lived in Kalamazoo, he was a traveling musician and was not at the plant all the time. And, as Hogo pointed out, Loar was deeply into violins and violas (which certainly speaks for the numerous violin attributes applied to the F5). Looking at Gibson drawings and patents, McHugh had his name on many, and Loar on a few. But clearly - from my findings - it was Lloyd's input - supported by friend Lewis - that dictated many of the developments of the Master Model Line.

Hogo:
You mentioned that Carleen Hutchins theories are no longer followed. Can you clarify that, please? I knew Carleen well (she lived one town away from me where I grew up in NJ and she played a major role in my interest in tap tuning - in fact, she was the first one to show me how it worked somewhere around 1969 or 1970). It's been my experience that her work on her "family" instruments, her writings in Sceitific American, and her work with the Catgut Acoustical Society have all been well respected. I'm interested to learn your perspective.

Peter C:
You said that "... since mandolins vibrate like guitars." Are you saying that the flat soundboard of a fixed bridge guitar works the same way as the arched and graduated sound of a mandolin? Can you please clarify that or were you referring to something else?

Good chat...

Roger

[j. condino]

2021 resolution: more time in the workshop & less time on the worldwide waste of time.......bye......

[Tom Haywood]

I’m still trying to absorb the idea that an arched, f-hole, unbraced instrument top can be stable under string down-pressure. Especially with the grain running longitudinally. Is this because a mandolin bridge has such extensive cross-grain contact compared with, say other bridge types?
Also, the idea that reducing the mass of a resonant, vibrating element lowers the frequency.

I don't buy for a second that an unbraced arched mandolin spruce top can be stable, unless it is so thick that the instrument will sound like c$@p, or it is plywood (same comment about sound). I think anyone who repairs mandolins has seen that tops frequently collapse when braces quit supporting. Parallel "tone bars" are support braces for that reason.

Braces are also "tone bars". The mere placement of a brace on the top creates tonal differences from the unbraced top, and helps to control the vibration and tone. This can be heard clearly when altering the size, shape, number and location of braces on a guitar top. Most of the braces on a Martin D 28 top, in my view, do not provide any necessary support, but they do control the tone produced by the top, mostly by controlling the vibration in specific areas of the top.

Using the guitar example, it is easy to see that the main "X" braces are the primary support for the top. These two braces can be shaved or "scalloped", resulting in emphasized lower frequencies from the top - the more bass heavy booming sound of a bluegrass cannon. Measuring the frequencies produced by tapping the top over the brace as it is shaved shows that the frequency is lowered as mass is removed from the brace. I know it seems counter intuitive. Tap tuning the mandolin top shows exactly the same thing.

There is no doubt that braces add stiffness to the top and removing wood from the braces may also reduce stiffness, which also directly affects tone. It seems to me that the entire process of making a good arched mandolin top is to remove mass and stiffness by thicknessing the plate, then adding mass and stiffness (and raising the resonance) with braces, then removing mass and some stiffness (and lowering the resonance) by shaving the braces. The only reason I can see for this circular process is to give greater control in arriving at the desired top resonant vibration.

So it is not a simple thing to discuss in terms of physics. I suggest that the discussion and debate continues because all of the physics answers to the experiential questions have not been discovered yet (and may never be). There is plenty of good stuff to pursue regarding standing waves and nodes, but imo all the answers will not be found there.

[Richard500]

Gosh; I didn’t intend to start a vibratory war, so apologies. Just the frequency of a simple harmonic oscillator (or a plucked string, or a flat plate or a tuning fork) is definitely inversely related to the square root of the mass. Sure, lots of other complications exist in these less than simple structures, including very much the way the vibrating thing couples acoustic energy to the surrounding air, and we’re not hearing the isolated fundamental.
My other question, answered most interestingly by Adrian, was related to the ‘strong enough with no braces’ because it’s arched. Looking at the item in question, it’s pretty clear the f-holes eliminate the transverse support in the critical area around the bridge, so some, or a lot, of the strength is the fore-and-aft arch.Good, so far. Then, the idea that this arch is maintained against collapse by the string tension pulling the body together, which counteracts the downward pressure. Intriguing idea. Very easy to test.

With good intention, it has just been pointed out that oversimplifying is bad; but actually, starting with the simplest model is the approach my tribe uses. Sure, a spherical mandolin may be nicely described by some Bessel functions, and symmetry is always our friend, but we can go much too far: I remember my frosh physics book stating ‘walking is similar to rolling’. So no, the first step in the analysis is to simplify a system, and then add in details, verifying the model by experiment if possible at each step. On the other hand, if empirical evolution has given us a mandolin we really enjoy, and building such a thing is, if not easy, but possible, we don’t have to do anything more; unless we want to develop something different.

[peter.coombe]

Peter C:
You said that "... since mandolins vibrate like guitars." Are you saying that the flat soundboard of a fixed bridge guitar works the same way as the arched and graduated sound of a mandolin? Can you please clarify that or were you referring to something else?

Cohen and Rossing did the research mostly on arch top mandolins, but they also measured others and found the same thing but at different modal frequencies. So, yes a graduated carved soundboard does vibrate similar to a flat soundboard fixed bridge guitar. However, from the measurements I have made, it looks like a flat top mandolin is more similar to a flat top guitar and a carved top mandolin is more similar to an archtop guitar. They vibrate in the same way, but the relationship of the top to the back is different. So, when you measure free plate modal frequencies, you need to tune the back higher in the flat top mandolins (and guitars) to get the same relationship as the arch tops in the completed instrument. This gets you closer to what Gore and Gilet call a "dead back". They claim that in their experience the optimum relationship is a 4 semitone difference. I get bang on that by tuning the free plate ring modes to the same frequency, but on the flat top mandolins the ring mode of the back needs to be about 8-9 semitones higher than the top. The back needs to be so stiff and heavy that it is difficult to implement, but they sound much like a carved and graduated mandolin but louder because the top is lighter. It is a massive improvement in sound (sound quality overlaps my carved and graduated mandolins), and it is something I would never have guessed if I had not read the Gore/Gilet books. Making the back heavier and stiffer on a flat top mandolin changes absolutely everything, including the sound in a profound way. So, mandolins really do work similar to guitars. Note that what I have done has been on oval hole mandolins, F hole mandolins are different, the main back mode is about 6 semitones above the top on the ones I have measured, but they still vibrate the same way as a guitar.

On the other hand, if empirical evolution has given us a mandolin we really enjoy, and building such a thing is, if not easy, but possible, we don’t have to do anything more; unless we want to develop something different.

Absolutely correct, empirical trial and error works and will get you there in the end, eventually. However, I have done something completely different with my flat top mandolins, and that required some knowledge of how guitars work. I would never would have guessed it (what most luthiers call intuition, I call educated guessing). I started out with a challenge. Flat top guitars can sound wonderful, so you should be able to make a wonderful sounding flat top mandolin, but in general they don't have a very fine refined sound at all. They range from just plain awful to not too bad but somewhat rustic sounding. I started out making them like Gibson, and they measured similar to a vintage Gibson flat top and sounded better but not in the same ballpark as my carved and graduated mandolins. Eventually I came to the conclusion that Gibson got it wrong. Obviously Gibson did not get it wrong with the Loars.

[John Bertotti]

Cohen and Rossing did the research mostly on arch top mandolins, but they also measured others and found the same thing but at different modal frequencies. So, yes a graduated carved soundboard does vibrate similar to a flat soundboard fixed bridge guitar. However, from the measurements I have made, it looks like a flat top mandolin is more similar to a flat top guitar and a carved top mandolin is more similar to an archtop guitar. They vibrate in the same way, but the relationship of the top to the back is different. So, when you measure free plate modal frequencies, you need to tune the back higher in the flat top mandolins (and guitars) to get the same relationship as the arch tops in the completed instrument. This gets you closer to what Gore and Gilet call a "dead back". They claim that in their experience the optimum relationship is a 4 semitone difference. I get bang on that by tuning the free plate ring modes to the same frequency, but on the flat top mandolins the ring mode of the back needs to be about 8-9 semitones higher than the top. The back needs to be so stiff and heavy that it is difficult to implement, but they sound much like a carved and graduated mandolin but louder because the top is lighter. It is a massive improvement in sound (sound quality overlaps my carved and graduated mandolins), and it is something I would never have guessed if I had not read the Gore/Gilet books. Making the back heavier and stiffer on a flat top mandolin changes absolutely everything, including the sound in a profound way. So, mandolins really do work similar to guitars. Note that what I have done has been on oval hole mandolins, F hole mandolins are different, the main back mode is about 6 semitones above the top on the ones I have measured, but they still vibrate the same way as a guitar.



Absolutely correct, empirical trial and error works and will get you there in the end, eventually. However, I have done something completely different with my flat top mandolins, and that required some knowledge of how guitars work. I would never would have guessed it (what most luthiers call intuition, I call educated guessing). I started out with a challenge. Flat top guitars can sound wonderful, so you should be able to make a wonderful sounding flat top mandolin, but in general they don't have a very fine refined sound at all. They range from just plain awful to not too bad but somewhat rustic sounding. I started out making them like Gibson, and they measured similar to a vintage Gibson flat top and sounded better but not in the same ballpark as my carved and graduated mandolins. Eventually I came to the conclusion that Gibson got it wrong. Obviously Gibson did not get it wrong with the Loars.

I'm copying this to my computer, mind if I give those measurements a try?

[peter.coombe]

I'm copying this to my computer, mind if I give those measurements a try?

Go for it.

[John Bertotti]

Go for it.

Thanks, one question if you will, rather than just amke a back thicker to make the semitone difference you are looking for have you tried using any bracing instead?

[peter.coombe]

There are a number of ways to do it. You can make the back thicker or use hefty braces, or use a dense wood, or laminate the back, or any combination. I am still learning what the optimum approach is, but the best sounding mandolin so far has a really heavy back (Ebony) and hefty bracing (6mm wide, 16mm high made from Douglas Fir, 3 braces). The best analogy I can think of is a see saw. If one person on the see saw is a lot heavier, the lighter person will move a lot more. You need to move the fulcrum to get it to balance. The same thing is happening if you make the back heavier. The top is much lighter so it moves much more than the back. The node of the main top mode (the fulcrum) moves outwards so it sits right on top of the ribs, or sometimes even on the ribs. What that means is the entire top is vibrating like a speaker cone, the ribs are not moving much at all so the top is a is a more efficient sound producer. If the back is lighter and floppier the node is usually about 2cm in from the ribs, so the ribs are vibrating, and that is wasted energy. The back is heavier so not much sound comes from the back because it takes more energy to move a greater mass. You can see the node move outwards from the Chladni patterns. When you do this, everything changes, all the modal frequencies go up, even the main air mode goes up in frequency and you need to be careful it does not end up on a note of the scale (usually G,with oval soundholes). The main air mode can be adjusted by using a fingerboard overhang and change the size of the overhang to make the adjustment, but you can't elevate the fingerboard or it won't work. I assemble the instrument and try different fingerboard templates to get the air mode frequency I want, and then use that template to make the fingerboard. That is it in a nushell, only took me 10 years to work it out!

Don't try this on a carved and graduated arch top mandolin. Flat tops only.

[John Bertotti]

There are a number of ways to do it. You can make the back thicker or use hefty braces, or use a dense wood, or laminate the back, or any combination. I am still learning what the optimum approach is, but the best sounding mandolin so far has a really heavy back (Ebony) and hefty bracing (6mm wide, 16mm high made from Douglas Fir, 3 braces). The best analogy I can think of is a see saw. If one person on the see saw is a lot heavier, the lighter person will move a lot more. You need to move the fulcrum to get it to balance. The same thing is happening if you make the back heavier. The top is much lighter so it moves much more than the back. The node of the main top mode (the fulcrum) moves outwards so it sits right on top of the ribs, or sometimes even on the ribs. What that means is the entire top is vibrating like a speaker cone, the ribs are not moving much at all so the top is a is a more efficient sound producer. If the back is lighter and floppier the node is usually about 2cm in from the ribs, so the ribs are vibrating, and that is wasted energy. The back is heavier so not much sound comes from the back because it takes more energy to move a greater mass. You can see the node move outwards from the Chladni patterns. When you do this, everything changes, all the modal frequencies go up, even the main air mode goes up in frequency and you need to be careful it does not end up on a note of the scale (usually G,with oval soundholes). The main air mode can be adjusted by using a fingerboard overhang and change the size of the overhang to make the adjustment, but you can't elevate the fingerboard or it won't work. I assemble the instrument and try different fingerboard templates to get the air mode frequency I want, and then use that template to make the fingerboard. That is it in a nushell, only took me 10 years to work it out!

Don't try this on a carved and graduated arch top mandolin. Flat tops only.

Very interesting have you tried varying rib height to change the internal volume rather than your fingerboard overhang? or a third kerfing mounted between the top and back on the rib. Maybe stiffen them a bit but also reduce internal volume which might be changing the note? Just some thoughts and probably way off the mark. Who was it that had the ribs actually tapered from the neck to the tail, which changed the internal air volume? This also makes me wonder more about cylinder backs. I have only heard a couple but they both sounded great. Thanks for sharing all that information!

[peter.coombe]

Very interesting have you tried varying rib height to change the internal volume rather than your fingerboard overhang? or a third kerfing mounted between the top and back on the rib. Maybe stiffen them a bit but also reduce internal volume which might be changing the note? Just some thoughts and probably way off the mark. Who was it that had the ribs actually tapered from the neck to the tail, which changed the internal air volume? This also makes me wonder more about cylinder backs. I have only heard a couple but they both sounded great. Thanks for sharing all that information!

Of course you can change the internal volume by changing the height of the ribs or adding bits internally, but the main air resonance frequency is difficult to just about impossible to get exactly the same from instrument to instrument. So you can't predict what it will be after the mandolin is assembled. Every piece of wood is different. So what is needed is something you can adjust externally after the instrument is assembled because internal access is difficult. The fingerboard overhang reduces the effective area of the sound hole which lowers the frequency of the main air mode, and it is something that is easy to do. You can also take a knife to the sound hole and enlarge it to raise the air mode frequency, but it takes a relatively large change in area to make much difference.

[sblock]

Of course you can change the internal volume by changing the height of the ribs or adding bits internally, but the main air resonance frequency is difficult to just about impossible to get exactly the same from instrument to instrument. So you can't predict what it will be after the mandolin is assembled. Every piece of wood is different. So what is needed is something you can adjust externally after the instrument is assembled because internal access is difficult. The fingerboard overhang reduces the effective area of the sound hole which lowers the frequency of the main air mode, and it is something that is easy to do. You can also take a knife to the sound hole and enlarge it to raise the air mode frequency, but it takes a relatively large change in area to make much difference.

It should probably be pointed out that this observation applies only to oval-hole mandolins, not to those with f-holes. The fingerboard extension and support does not affect the air cavity resonance on an F5 (or A5) style mandolin.