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I have been thinking a bit about how backs act in an acoustic guitar. As much has been written, they can act as a diffuser or reflector or somewhere in between. If EIR has a density of about .75 g/cm3 . . . Brazillian about .85 g/cm3 . . . koa about .65 g/cm3 . . . . Does it make sense to thickness a back in an inversely proportional way to its density? My thought is that a very dense wood may require to be thinner in order to be a diffuser type back, and a mahogany back may need to be kept thicker - in order to achieve similar response from the back in terms of it level of reflectance / diffusion.

Does anyone have any experience with this question? If so, I would love to hear your findings/thoughts.

Thanks!
Peter

Hi, I would say your idea is quite ok, but actually you can not put the density equal the stiffnes, so i think adiffernt approch would be to test the stiffnes / defelction by bending by hand and feel the right point ( for your construction) of thickness.

best regards, alex

I think it is hardly an uncommon practice, at least for classical guitars. Two examples: it is normal to make a light maple or cypress back as thick as 2.7mm or even more in order to match the weight of a regular rosewood back. Same for the very heavy rosewoods, they are thinned more. I made sides as thin as 1.5mm in order to reduce the excessive weight and make them flexible enough to be bent safely.

You should not forget that densities shown around websites are just an average. Each species varies a good deal so you need to asses each set. And people often throw this "Indian is lighter than Brazilian " thing around too lightly while in real they are probably much closer especially when one handles a lot of high grade tight Indian.

My measurements so far show Indian rosewood ranging from 0.78 to 1; The various Madagascar species from .67 to .95; Brazilian from .79 to 1. I measure everything I get: bridge blanks, backs, sides, FBs. Most of them fall somewhere in between 0.8 and 0.9, maybe 0.95. Bridge blanks seem to average noticeably higher than backs, especially if hoarding high grade tight pieces. The other suspects such as cocobolo, amazon, honduras, ABW and the Asian ebonies should average a fair deal higher.

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Build log

I'm not sure what you mean by a 'diffuser' back. If the back has a main resonance mode that is close in pitch tot he 'main top' mode, it will couple strongly, both with that top mode and with the 'main air' resonant mode. The result is more output at the 'main air' pitch, and a broader spectral peak at the 'main top' pitch. This doesn't 'diffuse' the sound, in the sense of spreading it around in different directions, it just alters the spectrum of the guitar.

The problem with making a lower density back thicker is that it would tend to raise the pitch of the 'main back' resonant mode. This would move you more in the direction of the 'reflector' back, and away from the 'coupled' one. You might want that, of course.

Another related problem I am facing right now is the stiffness. I just finished the maple back for my next guitar. At 2.5mm thick it is a good deal lighter than my rosewood backs, but it feels so stiff that I am not confident it will take the arch with only reasonable force. So my instinct is to keep thinning.

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Build log

I dot not quite understand reflectance/diffusion. However what you describe is exactly what I do. The numbers given for wood densities are not always accurate, and in any case there is a fair amount of variation, so those numbers should never be taken verbatim.
My approach is a lot more intuitive. I do believe there is an ideal thickness for a given back to work in a given guitar. When thicknessing the back (and that works for the top too), there is a point when the wood becomes musical, for lack of a better term. I operate within certain ranges for different woods, certainly a cocobolo back will be much thinner than a walnut back, for example. But, as noted above, a heavier wood is not necessarily a stronger wood, although there definitely is a correlation.

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

Double post again…

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

Thanks everyone for the comments and insights. What I gather:

Be careful about assuming common density among a species of hardwood.
Yes, less dense woods may need to be left thicker and more dense woods may need thinned.
There is a point of musicality (I have heard this too).
Density does not necessarily equate to stiffness and the pitch of the back should be considered.

One follow-up question if anyone has some thoughts . . . Is the species of wood or the density of a piece of hardwood more telling of its tonal characteristics? My reason for the question is that many other dense woods (e.g., Osage Orange) are often mentioned as similar sounding to rosewood. Are the tonal characteristics of Brazilian, for example, more connected to its density or more connected to its species-specific molecular structure? Any insight would be appreciated.

Fun conversation,
Peter

It is easier to generalise per species, variations exist, but most of the time they're pretty slight. Density does not necessarily lead to a specific tonal signature, although it can. Internal damping would be a more useful device to think about all this.
For example, two extremely dense woods, African blackwood and Macassar ebony (although Macassar can be all over the map in terms of density), are at opposite tonal extremes. While African B'wood rings like a bell, literally (very little internal damping), Macassar tends to tap like wet cardboard (a lot of internal damping). Brazilian RW has the advantage of having very little internal damping and of being very light for a rosewood. A characteristic shared by some Madagascar RW, and to an even greater extent by Panama RW (tucarensis).

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

But damping varies too. My experience with ABW is the opposite, having samples from 3 different trees. All have a dull tap, only marginally (if at all) better than typical ebony.

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Build log

Alexandru, are you sure you have AB? It is with pernambuco, without any doubt in my mind, the most resonant wood around.

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

This is very helpful! Thanks. Variables I was not looking at.

Peter

It is unquestionably ABW...Came for LMI and Gilmer but even if it was random ebay, it definitely looks and feels like it should. I guess just my luck of the draw. I still want to buy some more. If dull again, a cedar top should fix it I guess

At first I was surprised, since I kept hearing how good it sounds. I asked around some more, and while some people said it sounds tremendous, I found others reporting only a moderate taptone too.

I really don't have much wood stashed yet, but Madagascar and Bois d'Rose have been usually very very glassy for me. Maybe 1 or 2 are only moderately nice sounding out of some 12 sets. Out of some 20 Indian, half sound very nice and the others are at least nice. Only one is dull as maple or worse. One Macassar and one mahogany, both very dull. One maple, not too bad. Padauk, nice.

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Build log

Laurent,

I hope this isn't derailing the thread too much, but can you expand on what you mean when you say, "there is a point when the wood becomes musical". I think I get what you're saying, but not having thinned any tops myself, maybe I just have to do it to hear it.

Here's a YouTube video where the subject is thicknessing a top plate. He doesn't talk about musicality, but he thicknesses until the top takes on a sort of sheet metal like sound when you flex it rapidly in your hands. You can kind of tell how as the top gets thinner and thinner it gets louder in this regard: http://www.youtube.com/watch?v=xDDJVAaD9n8

Do your tops and backs take on a similar quality once they start to become "musical"?

Thanks for any help you can provide.

Erik

Listen to Al. Remember, the stiffness is increasing as the cube of the thickness. In other words, a back that is twice as thick will be 8 times as stiff. This will raise the frequency quite a bit. I find it much easier to make a responsive back that couples with the top using higher density woods.

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Randy Muth
RS Muth Guitars Website
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If I want to use mahogany for the back/sides yet and I want to try to couple the back with the top, it sounds like I need to be cautious about leaving the mahogany too thick else it will be too stiff. So I'm guessing the back should be left thinner and let the bracing make up for any lost stiffness.......sound right? It that is true, is there a guideline for how thich to leave the back? I'm familiar with a range of thicknesses for rosewood backs.....but not for mahogany.

I was able to get back and top coupling on my current (my first) build. I used EIR at 0.10" and used the old school, wide and thin Martin style braces in the lower bout and it was easy to get the frequency of the main back resonant mode down where I wanted it (OM body). My next build is a 00 using Cuban Mahogany and it won't be that long till I thickness the back so I'm curious what guidelines to use to know when to stop.

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Formerly known as Adaboy.......

Darryl,

The problem is this: the less weight the back has, the higher the frequency. So this has to be compensated for by reducing the stiffness of the entire back system, including bracing. There comes a point with low density woods where it might wind up being floppier than you want. You can, and should, still keep the upper bout of the back relatively stiff to help resist rotation about the headblock, but you may have to accept some deformation/flattening in the lower bout of the back.

The Cuban that I've had experience with was denser than typical Honduras mahogany, so that helps.

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Randy Muth
RS Muth Guitars Website
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Al, in this situation wouldn't the peak at main air resonance be taller and narrower than if the top and back were less strongly coupled? Why would the peak at main top pitch be both taller and broader? I thought you tend to get more of one by lowing some of the other.

Yeah, "diffuser" is a bad choice of words if it means a back that is free to move a lot at its resonances. From a couple of things I've seen on forums lately, I think Ervin Somogyi uses it in his book. So it's probably something we'll end up having to live with.

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Howard Klepper
http://www.klepperguitars.com

When all else fails, clean the shop.

IMHO .100" for EIR seems really excessive for a pre-war Martin style OM, unless it is really spongy EIR. My range would be more between .070" and .080".
Cuban tends to be denser than Honduran, generally, for a 00 I would probably not go under .085", and certainly not over .110". It all depends what you want the back to do, the bracing and the specific piece. It is easier to get better bass response with the wide low profile lower bout braces, but even easier with a lighter back plate.

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

Laurent, did you mean to say thinner back plate. Frequency is inversely proportional to the square root of the mass. So the lighter it is, the higher the frequency. But as you thin it, the stiffness drops dramatically which of course lowers the frequency.

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Randy Muth
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Howard Klepper asked:
"Al, in this situation wouldn't the peak at main air resonance be taller and narrower than if the top and back were less strongly coupled? Why would the peak at main top pitch be both taller and broader? I thought you tend to get more of one by lowing some of the other."

Systems of coupled resonators can do things you would not expect offhand. The problem is trying to describe what's going on in less than 60000 characters of ASCII text.

When the top and back are strongly coupled they move rather like a bellows at the 'main air' pitch: both moving 'in' or 'out' at the same time. This, in effect, makes the box look deeper: there is less pressure change for a given amount of air flow at the hole, since some of the energy that would have shown up as pressure is being converted into momentum in the plates. This tends to make the peak look 'spread out' relative to it's height. However, since there is actually a lot of air being pumped through the hole, the peak is really a tall one, but it's reasonably broad too.

When the top and back are tuned such that they are far enough apart in pitch to be effectively isolated from each other, you get two peaks in the output spectrum. These can be fairly narrow, or not, depending on the loss factors involved.

When the two peaks are closer in pitch, so that they are within each other's 'half power bandwidth', they will couple strongly. They share power, and also share losses. With things like the relative phase changes that happen between them, the result in the output can look like that of a 'Butterworth filter': a configuration of two fairly tall peaks with a dip in between. The peaks in the output will be higher and lower in pitch than the peaks of activity of the two elements that make up the couple. Quite often, in fact, the lowest part of the 'dip' is at a frequency where one element or the other is _most_ active. At any rate, the area under the output curve(which is sort of the 'total available horsepower' of the system) will tend to be greater for a coupled system like this than it would be for the same two elements uncoupled.

In the guitar it's actually more complicated than it 'could' be, since there are two mechanisms by which the top and back can couple. Not only can they pass energy back and forth through air pressure changes in the box, they can also push on each other through the sides. These two coupling mechanisms have different strengths, and they are out of phase with each other. The result is that you will often see three peaks in the output around the 'main top' and 'main air' pitches, and rather than the sort of classic Butterworth 'dromedary humps', you get the three peaks that Evan Davis dubbed the 'king's crown'. This can result in a peak that is fairly tall, and almost square.

I'll note that at least one of the uncoupled peaks would most likely be taller than any of the peaks in the coupled system. However, we have to remember that a single narrow peak is a strong note; usually with less sustain than the ones around it. Since we are not very sensitive to large changes in volume the note dosn't sound twice as loud, it just has half the sustain. Individual notes in the coupled system may not be as loud, but they are more even, there are more of them that reach a fairly high level, and they don't tend to lack sustain.

Thus this sort of coupling can allow you to have your cake and eat it too: you can build a system with low losses and high output that is not 'peaky'.

Thanks Al.

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Howard Klepper
http://www.klepperguitars.com

When all else fails, clean the shop.

Alan - I'm not sure I follow what you mean by "push on each other through the sides". Would you mind expanding a bit on that thought?

It sounds like the goal in tuning the top and back plates is that they should be tuned to the same frequency so that the "couple" to each other; is that correct? Is it also ideal that they should be tuned to the same frequency as the main air pitch, or is that not possible or desirable?

Do you think tuning the plates to the same or different pitches has an impact on overtone production?

Thanks, and sorry for all the questions.

Yes Randy, this is exactly what I meant, sorry for the confusion.
Charlie, it is when the top and back are too close in frequency that issues arise, like wolf tones for example.

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Laurent Brondel
West Paris, Maine - USA
http://www.laurentbrondel.com/

CharlyT asked:
"Alan - I'm not sure I follow what you mean by "push on each other through the sides". Would you mind expanding a bit on that thought?"

If you look at a 'glitter' (Chladni) pattern on the top or back you'll see that the stationary 'node' line is a little way in from the edge. For the 'main top' mode, for example, that line is about 1" or 1/1/2" in from the edge of the lower bout. This line is like the fulcrum on a see-saw: when the center of the top is moving 'up', the outside edge is moving 'down'. If that edge is moving the side has to be moving along with it, and that means that the sides are pushing on the back around the outer edge. I've measured this motion: I wasn't sure at first that it could make a difference, but it seems that it does. If you load the sides the output spectrum of the guitar changes noticably.

Backs are usually heavier than tops, are often made of materials that have lower losses than the top wood, and generally have somewhat different resonant pitches. The back can thus act like a 'flywheel', storing some energy and feeding it into the top at the back's resonant frequencies, both through changing the air pressure in the box, and by pushing on the sides.

People who use rigid or massive sides find that they get a different sound than with 'normal' sides, and often they feel it's louder. I think that having the sides in the game helps produce a more complex, and therefore 'interesting' sound, but that's just my opinion.

As Laurent says, getting the top and back tuned too closely to each other can cause 'wolf' problems. I generally hope to end up with the 'main back' resonant mode about a semitone higher than the 'main top' mode. This is close enough for good coupling, and far enough apart to avoid problems. It's also more likely to avoid troubles than having the top tuned higher than the back: tops often 'play down' in pitch over time, so a guitar with the high top pitch could get too close to the back.

The 'main air' resonant mode on most 'normal' gutiars is enough lower in pitch that you'd have trouble getting the top and back tuned to it. I once made a small guitar, based loosely on a Panormo, for my daughter, in which the 'main top', 'main air' 'main back' and 'neck' modes were all within a semitone of each other. It proved to be very difficult to alter any of those pitches: there was a sort of 'exclusion principle' happening, where they each forced the others into a certain niche. It was a nice little guitar though...