Official Luthiers Forum!

Hi Everyone

I've had Al's DVD for quite a while now and recently purchased the Gore/Gilet books.
I have learnt a great deal from both of them and highly recommend them.
I finally took some time to do some hands on research on one of my finished instruments
and was hoping for some help sorting a few things out.

The guitar in question is my take on the Norman Blake model, a 12 fret 000.
Sitka Top
Figured Bubinga B&S

At the edge thinning stage Audacity showed the following data.
*I must admit at this point that when I took these I had only a rudimentary
understanding of what I was doing, so the following three values could be suspect.
Main Air 117
Main Top 151 (hole plugged and back damped)
Main Back 210

On the finished guitar with strings damped I got 3 main monopoles or at least that is what
I thought they were. These are coupled.
A well defined MA @ 112
An Ok MT @ 202
A wimpy MB? @ 215
I also got 3 very audible resonances @ 255, 285 & 375 but no discernible pattern.

Then just for hellery I checked out the back and got what I presume is a ring+ @ 256.
As it seems to me the previous results didn't quite add up, the MT & the MB are too close.
Here's a pic of the back. It's a little hard to se as I used tea leaves.


Do you think it's safe to assume that the resonance I heard but did not see on the top at
255 was actually the Main Back, as the results on the back are so close at 256?

If so, does it indicate that the back is not efficiently coupling with the top as there was no
evident pattern shown on the top @ 255?

Any idea what the wimpy monopole @ 215 might be?

Is finding the ring+ (if this indeed one) a reliable method of checking the Main Back frequency?

Thanks for listening!

Cheers
Bob Hames

Huh?
Nice looking back!!

Trevor's probably going to disagree with me, but what the heck...

You have to understand that you're working with a very complicated system here, that's more or less tightly coupled whether it seems as though it 'ought' to be or not. The coupling moves things around in ways that are hard to predict accurately with simple models. As has been said:
"It has been exhaustively demonstrated that, under tightly controlled conditions, carefully selected pieces of wood will do pretty much what they dang please"
Anyway...

I like to look at the 'main top' and 'main back' modes of the assembled guitar with the soundhole open, simply because that's the way it's going to be when it's in use. Doing so introduces coupling of various 'air' resonant modes, which can shift both the 'wood' mode frequencies as they appear on the top and back, and also the output peaks that you hear. The result is that you don't always see the 'wood' patterns at the same pitches as the peaks in the output.

To think about this, imagine a simple case of a rigid cylinder that's fairly long relative to it's diameter, that has a piston with a hole in it. Obviously, if you move the piston into the cylinder, it will compress the air inside, and it will flow out of the hole in the piston. If the area of the hole is half of the cross sectional area of the cylinder, the air flowing out of the hole will just flow in to the place where the piston was fairly quickly, and there will be little pressure left over to produce sound. There will be a 'Helmholtz' frequency for this resonator, and at that pitch you'll get some output.

As you go upward in pitch from that 'Helmholtz' frequency the relative phase of the flow through the hole changes with respect to the piston motion: instead of the air flowing out of the hole as the piston moves in, the air starts to flow out of the hole as the piston moves out. Now, instead of cancelling out, the two motions add up, and the overall result can be more sound produced. However, you have to remember that the overall pressure change inside the cylinder produced by a given motion of the piston is dropping off fast as you get off resonance. Overall, the output as heard or measured out in front might be highest at a frequency very slightly higher than the one that gives the most flow through the hole: the 'actual' Helmholtz frequency.

Let's assume that the piston is mounted on a spring inside the cylinder, so that it will tend to bounce at some frequency, which we can say is higher than the 'Helmholtz' pitch. As the piston approaches it's resonant frequency the amplitude rises (assuming a constant input of power), and it moves more air through the hole, as well as moving more itself, and with these motions in phase, the output as measured in front rises quickly. When the piston reaches it's resonant frequency, the output will probably be higher than it was at the 'Helmholtz' frequency, and above that frequency it will drop off.

I'll note that a special case of this is seen in 'bass reflex' speaker cabinets. Ideally in that design the Helmholtz resonance of the box is tuned to the same pitch as the 'free air' resonance of the speaker. The result is that, as you rise in pitch toward the Helmholtz/speaker resonant frequency the output goes up, but it peaks at a pitch that is below the resonance. At resonance there is actually a relative 'dip' in the output, which then rises again to a second peak before falling off. Since the speaker itself is highly damped (because it's light and has to move a fair mass of air), and the box itself is also usually well damped, the difference in output between the peak and the dip can be around 3dB, which is only just noticeable as a change in loudness, and the overall curve can be quite 'flat'. This produces a sound that is fairly high in fidelity, at the cost of using a lot of power to overcome all that damping. This is a mechanical/acoustic version of an L-C 'Butterworth filter'.

When you introduce the back, things get more complicated, as they do for every 'new' element that's added, such as the various other resonances of the air and wood, the sides, and so on. What does not change is the general point that the output maxima may not appear at the same pitches as the maxima of any of the resonances involved. What you're seeing in the output is a sum of all the inputs, with various phase lags introduced by the damping.

So: your MA, MT and MB numbers with the hole plugged and the opposite face damped make sense, and the changes in the modes with the hole open seem pretty much in line.

You say you got a 'very audible resonance' @255 with 'no pattern', but a ring on the back at 256. Isn't that close enough? The back is pumping air through the hole, and also pushing on the top, which is maybe not moving enough to make the glitter dance, but can still produce sound. (BTW, you won't see a 'ring+' on a fixed plate, only on a free one).

Why do you think the MB and MT are 'too close'? The back is usually more massive than the top or the air, and the frequency shifts less in general between the 'closed' and 'open' hole conditions. I see them like this a lot. I'd bet you'll see the MT drop a bit in pitch over time and with playing, which is probably not bad, as it gets you further out of 'wolf' territory.

The 285 resonance could be the second Helmholtz type resonance, although that's higher than I usually see it. In this one, the air pressure in the box does not change in the upper bout to speak of: it seems as though the waist and the soundhole just above it 'short out' the flow into the upper bout, so the air just goes to the lower bout. I'll note that the only model I've see that shows this is a very complicated finite element model that was published in the old Catgut 'Journal' by Elejabarrieta et all back in November of '01. The model used a fine mesh, and took into account both wood and air. See if the sound is coming out of the soundhole rather than off the top. This often shows up as a 'dip' in the output out front because of 'phase cancellation'.

The 375 Hz peak could well be something similar: a couple between the top 'long dipole' resonant mode and the 'A-1' air resonance. In this case each mode can show up at two different pitches, with somewhat different configurations, and the peaks of the 'wood' modes might not match the 'air' peak frequencies exactly. One of the 'air' modes will have it's node/null up near the lower edge of the soundhole, and not radiate well, while the other will have the node/null down closer to the wide part of the lower bout, with large pressure changes at te hole and consequent strong radiation. The top might not be moving much at all, but it can be applying a fair amount of force because the top is moving 'in' below the bridge as the pressure there is rising. This is another complicated deal, since it seems to depend on top motion as well as soundhole placement and a pronounced waist. You often don't get this on Dreads, for example, and don't see in on those guitars that have the soundhole up in the upper corner of the top.

Your guitar is not behaving simply, but it does make some sense.

I don't know about disagree, but I'll be briefer, hopefully!

A 000 with a MA at 112Hz suggests to me that you do not have a "live" back. My instruments of that size with live backs come out at ~95-100Hz for the fully coupled MA (T(1,1)1). So therefore I would also suggest that the wimpy "MB" at 215Hz is a peak that is not due to the back. I've seen similar small peaks around that frequency quite often and never bothered chasing down for sure what caused them, but I did a few tests once and got the impression that it was either a corpus mode or a "short circuit" air mode of some sort.

I suspect your true "MB" is around 256Hz, which again would be fairly normal if you're using a fairly typical 4 bar ladder braced back. The easiest way to check this is just to tap the back (middle of the lower bout, sound hole open, mic'ing the back) into Audacity (or VA etc.) and you should see a very obvious main peak which will be at a frequency slightly lower than where you should look for the T(1,1)3 when you tap the top, but generally in the vicinity of 256Hz. The 285Hz and 375Hz resonance you heard are possibly the long and cross dipoles, though which comes first will depend on how you dealt with the bracing.

There's a lot of guessing and assuming by me going on here, but you having gotten this far, my money is on you getting to an answer before too long using either or both of Al's or my responses.

_________________
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Good Morning

Thank you for the replies Gentlemen!
While it's true that I have learnt a great deal so far, it's obvious
I've a long way to go. It will take a bit of time for this old brain
to digest this, but after gathering my thoughts........
I'll be back!


Thanks Alan

Cheers
Bob

Hi

I think I'm beginning to see things a little clearer.


When I compared my original figures for MT & MB at 151 & 210 to the ones
I got using the Chladni patterns namely 202 & 215 it seemed to be too much of
a change. It would appear though that my actual MB is around 256 which would be more
desirable, would it not?


Al, I seem to remember you saying, either on the DVD or another post, something about not being
able to use Chladni data reliably on backs, but I can't remember in what context. Although the
pattern I produced on the back was not a ring+, it was a very definite pattern, and it would appear
that it was at the MB frequency. So just out of curiosity would you say this a reliable method to check
the MB results against a spectrum plot?


The back is a 4 bar ladder with braces a light 1/4"x3/4" tapered from top to bottom.
I took your advice Trevor & tapped the back and recorded into Audacity. The result was from 262-266.

Although I am happy with the sound of this guitar and some very skilled players liked it, there's always
room for improvement I think. I would like the low end to be a little fatter and this exercise has revealed
some interesting facts.
Trevor, you mention in the book that smaller bodied guitars with a MA above 120 sometimes exhibit a 2nd
harmonic that is stronger than the fundamental and this can result in a thinner sound on the lower notes.
I did notice when I was tuning the guitar with Strobosoft that the fundamental would start strong and then
decay fairly rapidly while the 2nd harmonic did not. Although my MA is 112 do you think perhaps this is
happening here?

Thanks Again Fellas
Bob

Well, a 000 is more of a medium body size. Small body guitars, e.g. Martin 00 size and smaller can tend to have a "middley" voice due to a lack of bass (which is often why they are liked, because the mids cut through). Also, because we tend to pluck strings at the quarter length point, the second harmonic is excited more than the first and so there also tends to be a relative lack of fundamental due to that reason.

If you want more bass out of a medium or small body guitar the basic recipe is to go for high monopole mobility (high responsiveness) which will give you a high T(1,1)2 peak, which you temper back and control by making sure you have a lively T(1,1)3. The combination of the responsive top and live back then gives you a "soft" Helmholtz vessel and so the T(1,1)1 drops also. Hence you can get a medium body 90Hz, 170Hz, 214Hz guitar which sounds more like the next body size up, but louder. They're great guitars if you pull it off well.

_________________
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Bob Hames wrote:
"Al, I seem to remember you saying, either on the DVD or another post, something about not being
able to use Chladni data reliably on backs, but I can't remember in what context."

Trying to 'free' plate tune backs gets frustrating. Given the wide range of properties of back woods, and the generally higher relative cross grain stiffness, I have yet to find a single bracing system that allows me to reliably tune them in the same way as the top. On the other hand, using relatively 'normal' back scantlings and bracing usually gets the 'main back' resonant mode pretty close to where you want it if you're careful. Since that's the only one that seems to contribute directly to output power, and trying to maximize it does not seem to make a lot of difference, just so it's there, I don't worry so much about tuning the backs. Basically, on those, I try to get the modes to be clean, and any 'rings' closed if it's not too difficult.

Once you've got the box together you can use Chladni patterns to look at the resonances, and to fine tune frequencies if you like. As Trevor says, the closer the 'main back' pitch is to the 'main top' frequency the 'softer' the box isin the bass reflex range and the lower the 'main air' pitch tends to be. Getting them too close invites 'wolf' problems. I usually find that on my guitars the 'main top' pitch drops about 1/2 semitone when I put on the bridge, and another 1/2 semitone or so in the first month of playing, so if the top and back match closely before the bridge is on that's not usually a problem. What I don't like to see is the back below the top by a semitone or two before the bridge goes on: that's asking for trouble IMO.

Often enough with 'normal' ladder bracing on the back I'll see two 'ring' modes on the closed box; one from the lower edge to about the waist, and another, a bit higher in pitch from the lower cross brace to the upper one. The lower one is probably the one that couples most strongly with the 'main top', and the higher one can show as a peak in the output spectrum sometimes. This might not be as 'efficient' in reinforcing the 'main air' mode as a single, larger and more powerful 'ring' in the back would be, but it seems to work well enough, and can add some
'interest' to the sound.

Trevor writes:
"If you want more bass out of a medium or small body guitar the basic recipe is to go for high monopole mobility (high responsiveness) which will give you a high T(1,1)2 peak, which you temper back and control by making sure you have a lively T(1,1)3. The combination of the responsive top and live back then gives you a "soft" Helmholtz vessel and so the T(1,1)1 drops also. Hence you can get a medium body 90Hz, 170Hz, 214Hz guitar which sounds more like the next body size up, but louder. They're great guitars if you pull it off well."

Yup. Getting the 'main back' and 'main top' working together gives you the equivalent of another half size on the box, I think: a 000/OM can start to encroach on 0000 or Dread territory in the bass, and still have the trebles of a 000. Making sure that the 'cross dipole' is not too low helps as well, as it tends to give a 'fuller' sound: the cross dipole is not as effective a sound producer as the monopole, and if it's close in pitch it 'steals' energy from the monopole and reduces it's output. This can cut off the monopole peak in the high end, and a tall, narrow monopole peak in the output is associated with a 'cutting' or 'harsh' sound. Flamenco guitars are built to have low cross dipole pitches which helps them 'cut', and even classicals tend to be lower than steel strings to help get some 'brightness' out of the nylon strings. Steel string guitars don't need this, and X bracing tends to move the cross dipole up in pitch to get it out of the way of the monopole.

"I did notice when I was tuning the guitar with Strobosoft that the fundamental would start strong and then
decay fairly rapidly while the 2nd harmonic did not. Although my MA is 112 do you think perhaps this is
happening here?"

A 'main air' resonance at 112 is close enough to the pitch of the open A string to cause some issues with it. Is that the one that has the fundamental drop out? How's the intonation?

Well looks like I've got some new goals, gents.
One thing for sure, I'm going to start keeping better records.


I think I noticed it on all strings but I will check it out again.

Bob