What happens when the f-hole is bigger?

[Timmando]

I notice on my Morgan Monroe MDM-2 that the f-holes are bigger than on my new The Loar Lm700VS. How does that affect the volume and overall sound? Is it better to have a bigger or smaller f-hole?

[Marty Jacobson]

It is not intrinsically better or worse. It's just part of the system. I imagine that on that particular instrument, I suspect there is more going on than just a different f-hole size, so it's almost impossible to know what type of effect they have. Generally, bigger sound ports emphasize higher frequencies... all other factors being equal.

[sunburst]

Bigger aperture lowers Helmholtz frequency. It depends on the main resonant frequency of the top and back what that will do for the sound. Hint, it takes a very large change in aperture size to make a small change in Helmholtz, so in the case of your two mandolins, I would not expect any difference attributable to the aperture size because any difference that might be there would be dwarfed by the many other differences between the two mandolins.

[greg_tsam]

Hint, it takes a very large change in aperture size to make a small change in Helmholtz, so in the case of your two mandolins, I would not expect any difference attributable to the aperture size because any difference that might be there would be dwarfed by the many other differences between the two mandolins.

I've read previous threads in the builder's section about this. How much change are we talking about? For the sake of this example, if the typical f-hole is 1 inch would an increase of 1/4" affect the sound? Or 1/2"?

[Denny Gies]

Sunburst continues to be a great source of information. Thanks.

[sunburst]

There's a formula, something exponential, I don't know it (or care to) off the top of my head, that we can use to predict the change in Helmholtz from a known change in aperture size (in square inches of square mm or whatever). All that predicts is the change in Helmholtz, though, and how that may or may not affect the sound of the mandolin itself is impossible to predict unless we know quite a bit about the rest of the instrument. (Things like body mode frequencies, plate mode frequencies, and anything else we can quantify about the instrument. Generalizations are nearly impossible.)

[greg_tsam]

My buddy has a Gibson Flatiron and the raking of his fingers across the treble f-hole has caused it to double in size. The result is it is one of the loudest and sometimes piercing mandolins I've ever been around. The guy is a beast of a player, both hard charging and extremely talented, so he pulls it off. I often wondered how much difference the f-hole erosion made on his mando.

[dcoventry]

My buddy has a Gibson Flatiron and the raking of his fingers across the treble f-hole has caused it to double in size. The result is it is one of the loudest and sometimes piercing mandolins I've ever been around. The guy is a beast of a player, both hard charging and extremely talented, so he pulls it off. I often wondered how much difference the f-hole erosion made on his mando.

It's called the Willie Nelson Effect. Trigger Happy!

[eadg145]

I would not expect Helmholtz effects to dominate the sound of a mandolin. This is only one resonance among several in a musical instrument (think of the top, for instance). As to the parameters in play, the volume of the air cavity (in this case the instrument box size) also plays as much of a role in Helmholtz resonance as the aperture size. I would be very surprised to learn that calculations of Helmholtz resonance is used at all in mandolin lutherie, except as a back-of-the-envelope starting point. More likely build experience and the luthier's ears over many tweaks is the dominant factor in consistent sound.

[Bertram Henze]

Bigger aperture lowers Helmholtz frequency.

On the same body volume, the resonance frequency rises with the 4th root of the aperture area, approximately (assuming the aperture depth L is small against the diameter D). Thus, it takes 16 times the aperture area to get double the resonance frequency.

[sunburst]

I would not expect Helmholtz effects to dominate the sound of a mandolin. This is only one resonance among several in a musical instrument (think of the top, for instance). As to the parameters in play, the volume of the air cavity (in this case the instrument box size) also plays as much of a role in Helmholtz resonance as the aperture size. I would be very surprised to learn that calculations of Helmholtz resonance is used at all in mandolin lutherie, except as a back-of-the-envelope starting point. More likely build experience and the luthier's ears over many tweaks is the dominant factor in consistent sound.

That sums it pretty well. "Reverse engineering" plays a large part in the progress of many luthiers, not hard calculations.
Some people enjoy the speculative game of wondering what little visible changes will do and ascribing sounds they hear to what they can see (scalloped guitar braces, "forward" X braces, large sound holes, varnish finishes, etc.), but if we learn even a little bit about how instruments really do work we can skip over things like changing F-hole size by small amounts. Small amounts of change are just about all we have to work with, if we are staying anywhere near a traditional appearance, when we consider how much size change it takes to affect other things.
I, for one, am very thankful for the work of Dave Cohen and others who have done the studies and written it down for the rest of us to learn from, if we just will. Rather than "back-of-the-envelope", aperture size is barely back-of-the-mind for me. This is the most time I've spent thinking about it at all in quite a while. If I can make any more large improvements in the sound of my mandolins if will come from something other than the F-holes. I can know that because I have a basic (that's all really, basic) understanding of how the aperture size works with the rest of the instrument.

[sunburst]

Oops, my bad. Larger aperture = higher Helmholtz.
(As I said, this is the most time I've spent thinking about it at all in a while.)

[f5loar]

A bigger F hole allows you to put in a bigger rattlesnake tail which should relate to bigger volume, more sustain with plenty of bark.

[John Soper]

... and the rattlesnake tail allows you to play with a biting tone. :-)

[Dave Cohen]

"I would not expect Helmholtz effects to dominate the sound of a mandolin."

As Bertram pointed out, you have to make profound changes in either the total ff-hole area, the body volume, or both to significantly change the Helmholtz resonance frequency. But I would not go so far as to say that the Helmholtz resonance does not play a large part in the sound of any plucked string instrument. In fact, the interaction of the main body mode(s) with the Helmholtz resonance is responsible for much of the low frequency sound radiation in any string instrument, let alone mandolins. Higher frequency sound radiation, e.g., above 2-3 kHz, is another matter.

In ff-hole type mandolins, the Helmholtz resonance typically occurs at around 280-300 Hz. The first body mode, aka "trampoline" mode, or (0,0) mode, occurs first at anywhere from 250 Hz to 300 Hz or even a little higher. It occurs again at anywhere from about 340 Hz to ~420 Hz. In both cases, the motion is like a trampoline, in that both plates are moving with no amplitude at the edges and maximum amplitude at the center. That is, there are no nodes in the motion of either plate except at the edges. In the lower frequency trampoline mode, the plates are moving like a bellows. When the top plate is moving inward, so is the back plate. In the upper trampoline mode, the top and back plates are moving in the same direction at the same time, i.e., when the top plate is moving inward, the back plate is moving outward. Air is pumped in and out of the ff-holes by the lower trampoline mode, whereas little or no air is pumped by the upper trampoline mode. At frequencies below 2-3 kHz, the interaction of the trampoline mode(s) with the Helmholtz air mode is the "main event" in string instruments. There are certainly other events. F'rinstance, there are higher air modes, one around 750 Hz, another up around 1 - 1.1 kHz, and presumably more at still higher frequencies. There are numerous body modes, and there are neck modes which interact with some of the body modes. Nevertheless, none of those are as important to low frequency sound radiation as the interaction of the trampoline modes with the Helmholtz air resonance.

If you want some examples of instruments with weakened main events, look at domras and Neapolitan mandolins. In both of those, the Helmholtz resonance frequency is low, ca 140 Hz or lower, and the lowest body modes are at 500 Hz or higher. Those instruments do not have very projective low ends. They are pretty low mass, and make up for their deficiencies some at the high end, where they can radiate quite well.

http://www.Cohenmando.com

[greg_tsam]

A bigger F hole allows you to put in a bigger rattlesnake tail which should relate to bigger volume, more sustain with plenty of bark.

... and the rattlesnake tail allows you to play with a biting tone. :-)

Thank you for saying this. I have two large rattlesnake tails in my BreedLove right now for extra bite!

[Willie Poole]

I have heard the theory about a rattlesnake tail helping with the sound and I figure if they did make a difference what a big difference the whole snake would make, I`m still trying to get it in through the Ff holes, I wonder if killing it first would be a good idea?...I did kill the one that I have on my hat band....

Willie

[Steve Ostrander]

[QUOTE][/My buddy has a Gibson Flatiron and the raking of his fingers across the treble f-hole has caused it to double in size.QUOTE]

Your buddy needs to trim his fingernails....

[Ivan Kelsall]

The Northfield 'Big Mon' model of mandolin has enlarged 'f' holes. I often wondered if there was any real benefit of having larger 'f' holes,Northfield seem to think so. I've wondered many a time if it was just a way of pandering to people's thinking that larger holes = more volume. Not many people immediately think of Helmholz resonances when buying a mandolin,but Northfield seem to have a lot going for them re.their quality of build & sound,
Ivan

[lgibjones]

When I hear a mandolin with "pop", I have been attributing this a helmholtz resonance- does this sound correct?

Also, my understanding is that the equation above assume there is no deformation or damping in the sound chamber. Can the thickness or damping properties of the wood have a significant impact on the helmholtz contribution to a mandolin's sound?

I hope I am asking this in a clear way, thank you for your time, and thanks for a great discussion.

[Bertram Henze]

When I hear a mandolin with "pop", I have been attributing this a helmholtz resonance- does this sound correct?

Also, my understanding is that the equation above assume there is no deformation or damping in the sound chamber. Can the thickness or damping properties of the wood have a significant impact on the helmholtz contribution to a mandolin's sound?

I am not sure what "pop" means - if it does mean a strong percussive projection, then the answer is no; for instance, banjos without a resonator back have that also, but they haven't really a Hemholtz resonator function. It has more to do with how the strings are coupled to the top via the bridge and how well the top is converting solid oscillation into air oscillation. Good coupling = "pop".

The same applies for damping: Helmholtz resonance is an air thing, and if you stuff a pullover into the sound chamber that will hamper Helmholtz resonance, of course. Thicker wood, however, only hampers top oscillation, i.e. blocks the converter and thus the way of sound energy into the air, and it would do that with or without a sound chamber. It would also not be correct to call that "damping", because damping is supposed to annihilate sound energy into heat, while a bad coupling only contains the sound energy within the instrument for a longer time; that's why electric guitars have such a long sustain - they can't get rid of their sound energy.

[Tavy]

On the same body volume, the resonance frequency rises with the 4th root of the aperture area, approximately (assuming the aperture depth L is small against the diameter D). Thus, it takes 16 times the aperture area to get double the resonance frequency.

That's not the formula I'm used to seeing, but I think it works out the same

Either way, L is normally given in terms of D (L ~= 0.85D), which means the frequency is proportional to the square root of the diameter. Or the forth root of the area. So you only need 4x the area to double the Helmholz.

By way of example, oval holes normally have the Helmholtz around the open G string (196 Hz) giving a "tubby" sound. F holes have roughly double the sound hole area, so increase the Helmholtz by a factor of root-2 to around the open D string (294Hz).

[greg_tsam]

Here's the mando I'm talking about. There's more DNA than varnish on that thing but it's a hoss.

[Dave Cohen]

Couple of things:

First, the total area of two typical mandolin ff-holes is about 4.0 sq. in. The area of most of the vintage mandolin oval holes I have measured has been in the 3.0 sq. in. range. Suffice it to say that the area total area of mandolin ff-hole is not twice the area of an oval hole. Also, the formula that should be used for the Helmholtz resonance of a string instrument is that for a neckless Helmholtz resonator (cf Fletcher & Rossing, 2nd ed., p 15). The difference between results for the formulae is admittedly not great, except for ff-holes. A better formula for the Helmholtz resonance frequency for ff-holes (or for anything with two holes) would have to be derived based on two air masses acting as pistons (in respective soundholes), each attached to the same spring - the spring in that case being the air in the body cavity volume. I have used the formula for the neckless Helmholtz resonator, but I was careful to note that the agreement with measurements was not good. You have to be mindful of the fact that the result of the calculation will be at best a crude estimate.

Second, oval hole mandolins typically have their Helmholtz resonance frequencies at around 210 Hz. The frequencies of the lowest trampoline modes were typically found in the neighborhood of 200 - 207 Hz. That makes the coupling a bit different in oval hole mandolins than it is in ff-hole mandolins. In the latter, the two trampoline mode frequencies bracket the Helmholtz resonance frequency more symmetrically, i.e., the lower trampoline is as far below the Helmholtz resonance as the upper trampoline is above it. In oval hole mandolins The Helmholtz and the lower trampolines are pretty close in frequency, while the upper trampoline mode is remote, typically occurring at around 400 Hz or higher. I'm not sure without doing either radiativity experiments or some modeling which type instrument has the stronger coupling. Rossing thought it was stronger in ovals, but that was his guess. As always, experiment decides.

Helmholtz resonance formulae are for containers with completely rigid walls. When the walls move, as they do in string instruments, the air resonance becomes "perturbed", i.e., altered a bit. It is no longer considered a Helmholtz resonance, but is still very similar to one. When both air and plates are moving in vibrational motion, damping is not the first thing I think of. If their modal or resonance frequencies are close enough, they steal energy from each other, and that is coupling. The wood resonances have internal damping ("Q") and the air resonances do also. But the main effect of the interaction between the two is not necessarily damping.

http://www.Cohenmando.com