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The Helmholtz formulae optimize the lowest order air resonance for a rigid enclosure (Think stereo speaker box).

In his article, Mottola calculated the Helmholtz resonance for a small-body steel string guitar of his, and compared that to the actual resonance. The actual resonance was 16% lower than the predicted value, principally because the sides are not rigid.

Yep, there's optimal, but science doesn't get us there - yet.

But if the research falls a little short of the mark, there is nothing wrong with relying on tradition. "There is nothing new under the sun." applies. What works best is what survives. In 150 years of classic guitar history, the size of the soundhole - given the size and shape of the guitar - hasn't changed a whit. We still make 'em like Torres 'cuz we like the way they sound. Same goes for Martin.

As for location, McPherson puts their soundhole on the side, and I talked with a player who thinks that they have the best sound of any guitar he's played. Adamas(sp?) makes a guitar with several small soundholes. The theory, of course, is that there is more uninterrupted soundboard to provide more....

My belief? There are trade-offs. It all depends on what you are looking for, and what you are willing to give up to get it.

Larry

I've calculated the volume of my 000 plan to be approximately 412 cubic inches. According to the Hemholtz formula: V=4/3piR**3 where R is the radius of a sphere. Solving for R = 4.6. Then the idea sound hole radius is r=R/4 which results in a r = 1.15 approx. Now how many 000 guitars do you know that have such a small sound hole. Is the formula wrong, my math wrong or in practice is the formula ignored?

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A higher purpose for wood.
Rich Smith
Issaquah, WA

Regarding the size and how it got that way, I've heard that the only reason for it is that the guitar had a worn area on the edge of the hole, and someone cut it out bigger to get rid of the chewed up area and get it back round. True, I dunno.

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Brad Tucker

Ricardo asked:
"Is the formula wrong, my math wrong or in practice is the formula ignored?"

The formula is correct, as far as it goes, but when you're talking about guitars it leaves a lot out. In practice, it's ignored.

The Helmholtz formula only applies when you're talking about a more or less spherical vessle with rigid walls. If you use it for something that is cylindrical, like a trash can, the hole has to be pretty much in the center of the lid, and the walls can't be too low, like, say, a cat food can. The hole 'should' be round, and not a slot or something. Even with all of the conditions met you're only goig to get a pretty close approximation. That's because Helmholtz had to simplify the heck out of things to come up with a formula that he could solve. Even now, with good computer models, it's hard to come up with a precise answer in many cases, or so I'm told.

On the guitar the flexibility of the top and back (and, to a lesser extent, the sides) serves to drop the 'main air' pitch to something considerably lower than the Helmholtz formula would lead you to expect. How much the pitch will shift is difficult to predict, since it's not simply a functinoof how flexible the walls are, but of the resonant pitches. When the 'main top' and 'main back' pitches are close together the 'air' pitch drops more, and small changes in the stiffness or mass of one of the plates can alter the 'air' pitch noticably.

If it's any consolation, some researchers have decided that the exact pitch of the 'main air' mode is not all that important anyway. I'm not sure I totally _agree_ with them on that, but then, I'm just a guitar maker. Is there any reason why 'close enough' won't do in this case? You can usually get that just by eyeballing the soundhole size to 'normal' standards.

Alan thanks, there are many things that I'll only learn from experience. Lacking experience, I'm attaching a lot of weight to what I can glean from others. I'm sure I'll have screw ups, but I'd like to minimize the pain. I appreciate your answers.

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A higher purpose for wood.
Rich Smith
Issaquah, WA

Could we see what science is behind this claim? And does "parabolic" here mean actually following the graph of a quadratic equation, or is it a fancy way of saying rounded over?

BTW, on the Univ. of New S. Wales site, there is a nice article about why the guitar is sort of a Helmholz resonator, except in the ways it's not.

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Howard Klepper
http://www.klepperguitars.com

When all else fails, clean the shop.

Is there a guitar about which some player has not said this?

Ye Olde Curmudgeon

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Howard Klepper
http://www.klepperguitars.com

When all else fails, clean the shop.