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I have two Red Spruce top sets, both are 0.130 thick right now. The stiffness with the grain feels essentially the same in both, but the cross grain stiffness is very different between the two. One is quite resistant to bending and the other is easy to bend. Big difference.

Assuming all else equal, what difference if any could the difference in cross grain stiffness be expected to have on the sound of the guitar?

The other thing that I'm wondering about is that, even though the dimensions of the two plate sets are almost identical, the set with high cross grain stiffness weighs 400 g and the low cross grain stiffness set weighs 350 g which seems like a substantial difference. Assuming final thicknesses for both sets that give the same with-the-grain stiffness, maybe the lighter set would be more responsive? How would the lower cross grain stiffness figure into that?

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Once in a while you get shown the light in the strangest of places if you look at it right - Robert Hunter

Is everyone stumped, busy making sawdust, or gone fishing?

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Once in a while you get shown the light in the strangest of places if you look at it right - Robert Hunter

I expect the less stiff top to produce more bass. In general, stiffness along the grain is more or less proportional to density, so you would get a higher stiffness to weight ratio with the lighter wood.
Cross-grain stiffness in softwoods is greatly affected by the verticality of the grain. Stiffness falls off rather quickly when the grain is only a few degrees off vertical.

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John

I guess John was not busy making sawdust, or gone fishing.

Stumped. But I'll give it a shot

As John says, long grain stiffness typically goes up with density, but in this case it hasn't. I'd give the lightweight top a higher score on the wood-good-o-meter. I'm not sure if one would have more bass than the other or not, since the lower cross grain stiffness should lower the frequency some, but the higher weight on the other will lower it some too.

I'm not convinced that high cross grain stiffness is always a good thing. I've had good luck using 45 degrees off quarter for harp ukuleles, which is the most floppy across the grain as you can get. I do need to build one with vertical grain to see how it compares, though. And build two guitars with 45 degree (one wide and one narrow).

Logically, high cross grain stiffness should be good on wide guitars like jumbos, but not so important on narrow ones like parlors. My harp ukuleles are narrow relative to their bridge width, so that makes sense that low cross grain stiffness sounds good on them. But I haven't collected enough data to verify anything.

Adjusting the angle of the braces can compensate for low cross grain stiffness.

This brings up something I was wondering about. Does cross grain stiffness that's substantially lower that the with-grain stiffness need to be compensated for? Would it be desirable to do so? The guitar I would be using the top for is 15" across the lower bout.

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Once in a while you get shown the light in the strangest of places if you look at it right - Robert Hunter

I would think so.Why else would ladder bracing have been used? For classicals adjusting the angle of the fan bracing can adjust the cross grain stiffness of the top. With "X" bracing moving the "X" higher or lower and opening and closing the angle of the "X" as well as adjusting the angle of the tone bars adjusts the cross grain stiffness. When a lightly built guitar develops a bulge behind the bridge (thin weak bridge/plate) a "Musser" brace is sometimes used to flatten the soundboard -effectively increasing cross grain stiffness.
The shape of the guitar with a pinched in waist should also increase cross grain stiffness.

Virtually none. According to my modeling (and borne out by the fact that I can always hit the target modal resonances I want, using the same modeling techniques), a 50% change in cross grain Young's modulus yields only a 3% change in the modal frequencies for an orthotropic wooden panel. Long grain stiffness (being 15 to 20 times higher) dominates the system to such an extent that cross grain stiffness can largely be ignored. I'd be reaching for the low density stuff, as for the same modal frequencies, it will produce the lower mass top, therefore more responsive. Standard X-bracing provides plenty of cross grain support.

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

http://www.goreguitars.com.au

I noticed something in Hurd's 'Left Brain Lutherie' that supplements Trevor's information. Hurd worked out a method of 'backing out' the long- and cross'grain Young's moduli of tops (within limits) using deflection tests. However, when he applied his method to older guitars the results seemed inconsistent to me. It occurred to me that 'cold creep' of the wood in the cross grain direction could negate that stiffness over time, at least as regards static stresses. In essence, the cross grain stiffness might help the top to withstand the torque load of the bridge at first, but over time it would take less and less of the load. If that is the case, then making a top thinner because it has high cross grain stiffness might cause problems down the line.

OTOH, the cross grain stiffness should have the same acoustic effect (more or less) throughout the life of the guitar. This shows up in 'free' plate tuning with Chladni patterns, which can be quite sensitive to the stiffness ratio of the wood. Mark Blanchard did a lot of work with this some years ago, and decided that changing the brace angles is not as helpful on the 'free' plates as you'd think it might be. He takes the position that 'the sound is in the wood', with the bracing being unable to correct for more than small differences. He's worked out a method of selecting tops based on their stiffness ratio that essentially reserves the ones with high cross grain stiffness for wider guitars, like Jumbos, and saves the ones with the lower cross stiffness for narrower platforms. It does seem to work.

Trevor, I am confused. If cross-grain modulus has almost no effect on the sound of the guitar, then why would most luthiers care so much about it, and about top wood being very close to on-quarter? I got a different impression of your thinking in sections 4.1.4 and 4.2.1.(WRC), for example.
And, is it fair to say that the sound of the guitar body is almost exclusively a function of the usual (low frequency) modal resonances? I would imagine some higher frequency resonances (and perhaps their damping) could be more sensitive to cross-grain stiffness?
Clarifications appreciated.

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David Malicky

I'm also confused. I've been trying to tune bracing using th Chladni patterns for years. I even bought your DVD on the topic. Are you saying you no longer believe that to be a useful technique for achieving a desirable tone?


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Alan Carruth wrote:
Mark Blanchard did a lot of work with this some years ago, and decided that changing the brace angles is not as helpful on the 'free' plates as you'd think it might be. He takes the position that 'the sound is in the wood', with the bracing being unable to correct for more than small differences.

I'm also confused. I've been trying to tune bracing using th Chladni patterns for years. I even bought your DVD on the topic. Are you saying you no longer believe that to be a useful technique for achieving a desirable tone?



Small differences make all the difference between a great guitar and a mediocre one. One reason Science can only take you so far.

Good point and one which has frequently exercised my mind, too. I've even asked questions on fora like this as to why people prefer high cross grain stiffness, but have never seen a persuasive technical answer. It certainly has little effect on the low order resonances and the modes above ~1000Hz are in "resonance continuum" country where it's pretty difficult to isolate what does what to what. What I can say, though, is that higher monopole mobility gives greater responsiveness across all frequencies, but they can be "killed" with thick finishes.

One of the top woods I use fairly frequently is Engelmann spruce. With a sample size of ~50 sets, the mean Ecross is 0.8 GPa with a standard deviation of 0.18 GPa. That's a pretty wide dispersion and I can't say that I've been able to put any sound differences down to variations in cross grain stiffness. The lowest I've built with was 0.3GPa. That's a guitar that lives locally so I get to see it reasonably often (its owner drops in for jams) and it looks and sounds great.

On quarter has greater stiffness, but it also is more stable, has tighter looking grain and shows medulary rays, so looks better. Don't underestimate that!

Structurally, there may be some benefits in terms of print-through of the bracing. Certainly for classical fan bracing, the braces are largely long-grain oriented. The higher the cross grain stiffness, the less print-through you see. But most X-bracing is angled such that you don't get much by way of print-through, even though there can be grosser distortions.

Long grain damping and cross grain damping are basically unrelated (according to my data). I have a chart (which I haven't published) plotting long vs. cross which is basically a "sneezogram". R^2 = 0.153 (i.e. very little correlation between the two). That was for samples of European spruce and Sitka spruce.

Regarding WRC, 0.1GPa difference in Ecross gives me a just perceptible difference in print-through for falcate braced SS guitars. Cut way off quarter, WRC won't hold up its own weight at soundboard thicknesses without seriously drooping, with Ecross measuring up well below 0.1GPa. That basically means massive print-though for me, which would be finish fractures and wood failure very early in the piece if I built with it. So I don't.

Alan has a point though, about the ratio long vs. cross. WRC has amongst the lowest ratios of Elong/Ecross, which means that they typically end up stiffer (flexural rigidity-wise) cross grain than spruce tops. I really like the sound of my cedar-topped guitars and maybe that's one contributing factor (along with lower overall mass, lower damping etc etc. in general).

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

http://www.goreguitars.com.au

When I started out with 'free' plate tuning the prevailing notion was that those frequencies would more or less translate into the frequencies of the assembled top. I'm not saying that doesn't happen in some sense, but mapping from one to the other is far from a simple proposition.

My last real 'matching' experiment, which was some years ago, didn't work out. I made two Classicals with all the wood cut 'in flitch', controlling everything I could think of, and they didn't sound the same when I got done. They were darned similar, but not the same. I had matched the first ten 'free' plate mode frequencies in both the tops and the backs to within a couple of Hz, and the assembled modes were the same, so it seemed as though something else must have been the issue. What was different was that the mode shapes of the two tops were not quite the same; particularly the 'ring+' modes, and the higher order ones above that, possibly due to slight differences in the fan braces, which were not split out. The one with the 'better' mode shapes had the 'better' sound. This prompted me to change my thinking, and pay more attention to the mode shapes than the pitches.

Mark and I have had a number of conversations about this over the years, and have come to parallel conclusions. At one point he tried to graduate the thickness distribution of the bare tops to get them to have the same mode shapes before putting on the bracing. The thought there was that you could then standardize on the brace profiles, and simplify things. He said he wished he had back all the time he spent on that one. What he found was that, if you look at the Chladni patterns of a bare top there are several modes that come very close to what you'll see on a braced and 'tuned' top. In particular, the 'ring+' will be there, more or less 'closed' in the lower bout depending on the stiffness ratio of the wood and the aspect ratio (width/length) of the outline. He found that if the 'ring+' did not 'close' on the bare top, it would be very hard to get it to do so with bracing. We both feel that we get the best results with a 'closed', or, at least, nearly closed, ring+, so it makes some sense to choose wood that will facilitate this.

Mark likes to start out taking the wood to some thickness that's 'way over what he's going to want. He then cuts it to his largest outline and checks the modes. If it doesn't meet his targets, with a certain pitch relationship between some of the modes that he associates with the tone he likes, and a reasonably 'closed' ring+, he'll cut it down to the next narrower shape, and try again. I've been measuring the stiffness ratio of my top woods directly (Mark doesn't), and have been monitoring my tops to see how they compare with his, to establish the range of stiffness ratios that will work on my patterns. It takes a while, so I'm not ready to give out hard and fast rules as yet. However, the general rule of using wood with higher cross grain stiffness on wider tops is an easy one to remember, and works pretty well.

When I made that plate tuning video I checked out the tops beforehand using what I call the 'Blanchard modes', and knew which would be the easiest to tune and which the most difficult. I'm pretty sure I included that information in the video. At any rate, it worked out just as expected: one went really easily, two were pretty simple, and one was a real trial. Since I wanted the video to include just such a range of things that worked out fine. All of the guitars, BTW, sounded good in the end.

My thinking at this point is that what we're seeing in the 'free' plate modes could be thought of as a state of 'balance' between the braces and the plate. Since an unbraced plate will give you pretty much the same sort of modes as a braced one, you could just leave the top thick enough to get the stiffness you want, and let it go at that. One obvious issue there is that it would end up really heavy, even discounting the problematic nature of the neck load on the upper bout without an upper transverse brace or equivalent. Bracing exists to add stiffness without commensurate mass. On the other end, you can go with a really thin top, simply to act as a membrane to move air, and cover all the structural bases with bracing. That works too, and gives a light top that produces plenty of sound if you do it right. It's not the same sound as you get from a more traditional structure, though. From what I can see, the best 'traditional' instruments have found a point of balance, where both the top and the bracing are carrying their share of the load (whatever that is), and working together to produce the sound. My experience suggests that the best tops are the ones that have the largest number of well-formed free plate Chladni patterns. I take this as a sign that none of the bracing is too heavy or too light, which would distort the mode patterns. So I certainly do use 'free' plate tuning these days, but with a bit of a different focus than perhaps I used to.

It's entirely possible that I'm fooling myself on this.

I've never kept accurate records of cross grain stiffness. I have chosen the wood for, and done the voicing/thicknessing/carving freq mapping on about 140 guitars over the last three years, and have deliberately used some tops with very low cross grain stiffness, and have noticed no correlation to good/bad tone. One day I'll look into it further.

I think that there are far more valuable things to focus on, especially if you're just starting out, than worrying about cross grain stiffness...

Not saying it's irrelevant, but if heavyweights like Alan and Trevor can't make a case for it's vital significance, I wouldn't lose any sleep over it.

One thing I keep meaning to add to my record keeping is trying to chart a correlation between cross grain stiffness and cross di/tripole freqs. It seems just plausible to me that tops with lower cross grain stiffness might possibly have lower di/tri freqs at the same monopole freq than tops with higher cross grain stiffness. But that's wild speculation with no data, and even if it were true, I wouldn't really care.

meddlingfool wrote:
"I've never kept accurate records of cross grain stiffness."

I'm not sure how important an exact reading of that is, in any case. From what I can see there is a fairly broad range of stiffness rations that will work well for any given shape, so anything that gets you into the ballpark on that will probably be close enough once you learn what works. It's sort of like damping: you can't really hear much difference between a Q value of 80 and 110, and it probably has less of an effect on the sound of the guitar than a lot of other things, so an exact reading may not be worth the effort. Ollie Rodgers used to use that as a sort of rule of thumb: if you can't hear a difference when you've made a change, then it's not acoustically important, even if you can measure it and think it 'ought' to be.

Exactly. Better to pay attention to things that make differences you can hear...

In process control loops the rule of thumb is to get an effect you can see you double or halve PID parameters. Small changes don't amount to too much.

printer2 wrote:
"In process control loops the rule of thumb is to get an effect you can see you double or halve PID parameters. Small changes don't amount to too much."

...except when they do.

One of the most helpful 'science' projects I've seen regarding guitar acoustics was Howard Wright's thesis, given under Bernard Richardson at UWales/Cardiff in 1996. It was based on a computer model of one of Richardson's Classical guitars. They were able to model the original closely enough to get a respectable sound, and then made modifications that would have been difficult on a 'real' guitar. Recordings were compared at random to see what changes people could actually hear.

One of the changes they made in the first run was to alter the 'main back' resonant mode pitch, raising and lowering it by 26% and comparing the new sounds with the original. In the case where they lowered the pitch all of the seven listeners heard a difference when an E chord was 'played', and none with a D chord. With the back mode raised in pitch, two people heard an difference, and one did not.

The starting pitches for the back and top were 215 Hz and 185 Hz, respectively; a little below A for the back, and F# for the top, so there was a difference of just under three semitones. Raising the back pitch took it to 270 Hz (if I read them right), between C#-D; almost seven semitones higher than the top pitch. A three semitone pitch separation is enough to give fairly low coupling between the top and back modes. Seven reduces it even more, but seems not to be enough of a change to be audible. Lowering the back pitch as much as they did put it at 160Hz, between D#-E, a bit more than two semitones below the top, so there could be a bit more coupling with the top, and also with the 'main air' mode. This could give a stronger 'main air' mode at a bit lower pitch, and could well account for the increased audibility of the change. Exactly what this particular change did to the spectrum is not clear in the report I have; they did not consider the 'main back' pitch to be 'significant', and didn't elaborate.

In my experience, the strongest practical couple happens when the 'back' mode is about a semitone above the 'top' in pitch. Any closer and you risk a 'wolf' note. In this case, that would have meant a 'back' mode pitch of about 196 Hz; the pitch of the open G string. They went right past it, so in my estimation this is a case where a smaller change would have had a greater effect than the large changes they made. It's not really a linear system, and those rules don't always apply.

Definitely deviating from the subject at hand....

But:


How are you measuring this, Al? T(1,1)2 vs T(1,1)3; Uncoupled top vs. uncoupled back; back tap vs top tap, etc. etc. And how are you judging the strongest coupling?

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

http://www.goreguitars.com.au

Knew it could be taken the wrong way. Tuning loops are usually done with a PID controller, effectively adding gain to a system. You have coupled elements that are similar to the top, back and hole along with their resonances and phase shifts. I was thinking more dampening rather than frequency changes in my comment.

Trevor Gore asked:
"How are you measuring this, Al?"

First: I got this idea from the late great Fred Dickens back in the late 80s. He got it from an equivalent circuit study he did at Bell Labs, where he worked, so the pitches in that case were of uncoupled L-C resonators. What he found was that having the uncoupled 'main back' mode a semitone above the uncoupled 'main top' resonance gave a spectrum output that was most like the guitars he liked. This was all from personal communication, BTW, so I can't cite a paper for you, although he may have mentioned it in an interview at some point.

As you know, translating that into wood is far from trivial, if not downright impossible using 'shop' approaches. A close approach that Fred used was to block the sound hole to eliminate the 'Helmholtz' resonance, and find the tap tones or Chladni patterns of the top and back. This doesn't really eliminate the coupling, of course, but it's a quick and dirty close approach. That has been my method of choice since.

Again, via Fred, the pitch of the 'main air' resonance can be taken as a reasonable indicator of the strength of the coupling between the top and back, all else equal: the strongest coupling will tend to give the lowest 'air' pitch. Again, you don't want to go there most of the time, since this can give rise to a very nasty type of 'wolf' note. The semitone separation is a useful target, yielding a strong and low pitched 'main air' resonance with little risk of a 'wolf'.

In the end this is a complex and strongly coupled system, so there are no really 'independent' variables in practice. Or, if there are, they're hard to isolate. In the end what counts is what the guitar does, and a practical and quick test that gets at that seems to me the most useful, even if it's hard to justify theoretically.

Thank you, Trevor, for the detailed reply -- very interesting. Based on your post and Ed's, it sounds like we want reasonably on-quarter, but we don't need to worry about the last 5 degrees difference between AA and AAAA, for example.
That's also helpful to know that long and cross grain damping have low correlation.

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David Malicky

Thanks, Alan. The 4-DOF model produces similar output of both the uncoupled and coupled resonant frequencies. And you need that depth of analysis if you want to really figure out where things will land. Typically, the net of the "repulsion effects" widens the separation of the T(1,1)2 and the T(1,1)3 by two to three semitones, but the T(1,1)2 can also end up "clamped" by the repulsion effect on it of the air resonance upwards and the repulsion effect downwards due to the back, so the T(1,1)2 and the uncoupled top remain at the same frequency.
Yes, I find that works reasonably well, most of the time.

I'm more inclined to look at the magnitude of the shifts between coupled and uncoupled rather than an absolute frequency. It seems to follow the movement of the coupling constants in the 4-DOF model, though I can't say I've had a really close look at it.

Anyway, best get back to normal programming... Thanks again.

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

http://www.goreguitars.com.au