Effect of plate thickness on archtop guitar power

[Brian Evans]

I am reading an MIT article on violin evolution, and it has an interesting observation - as the renowned makers evolved their instruments, they varied the f hole size and the thickness of the back plate. The thickness of the back plate got thicker and resulted in greater power, which they were able to measure and confirm, but they don't take the discussion (that I've been able find so far) to "why?" Anyone ever done any experiments on this with archtop guitars? The top has a whole "needs to hold up the strings" structural deal, but the back just has to sit there. I've tried to loosen up the back with the recurve but I've left the field of the back around .200" thick. At the same time I always wondered if thicker or thinner would make a difference... Any thoughts?

As always, and in keeping with the 20th birthday, thank you for your support of my tiny efforts in lutherie!

Brian

[Barry Daniels]

The back can couple with the top to add power and tonal complexities to the instrument if it is able to vibrate at a corresponding frequency compared to the top. I am using Trevor Gore's book to measure and adjust these frequencies in building flattops, but I know this also applies to archtops. If your really want to get in deep into the science of this get his books.

[Alan Carruth]

Another thing that comes out of Gore's work (although he's not the first to think of it) that is germane here is that the effective mass of the ribs matters it how much power the instrument puts out. If you look at the way the top vibrates in it's lowest resonant mode, say with Chladni patterns, you'll see that the stationary node line is in from the edge. This means that, as the center of the top moves in one direction, the outside edge moves the opposite way. If you think about the top as a loudspeaker, with most of the sound coming off the center, then it's smaller than it could be, and there's an area around the edge that's canceling it out to some extent by moving out of phase. He adds weights to the sides to cut down on that movement of the outside edge, increasing the effectiveness of the top and the power output.

The back's role in this is complicated, of course, but to a first approximation it is attached to the sides, and can add both stiffness and mass to them. In the simplest case; a back made of concrete that was super massive and stiff, all of that mass is added to the sides, giving the same effect as Trevor's side weights. In real life if the lowest back mode is tuned close in pitch to the lowest top mode the two will tend to be moving as a 'bellows' over a fairly broad range of frequencies. The mass of the back is, to some extent, added to the mass of the sides in pinning the top edges. In theory that should make the top more effective at making sound.

To get this to work to best advantage you need to look at both the mass and stiffness of the back, to get the tuning right. There are, of course, a lot of opinions as to what 'right' is, but that's a start at thinking about it anyway.

From what I've seen, however it works, the back seems only to be able to add to the power of the guitar in the lowest frequency range. As you go higher than that any energy that is driving back vibration is extracted from the top in one way or anther, and since the top is the most effective sound producer that hurts output. It's not all about power of course; those back vibrations do add 'color' to the sound, and that's important.

Always keep firmly in mind that guitars, even archtops, are vastly different physical systems from violins. The post alone is a radical departure that makes comparison tricky. Although we can learn from out bowed cousins, there's a lot of translation needed.

[Barry Daniels]

I think one of Gore's most important additions to the science is the application of certain tools to measure plate resonances. I am talking about computer software and a USB microphone. The software plots a chart of frequencies recorded during tapping the completed box. This shows frequency peaks that can be easily assigned to the back or top and then you start to make certain adjustments to move the peaks into optimum positions. It is really fascinating. I found a freeware program that has real-time analysis that immediately shows the results of covering the soundhole or deadening certain elements. It's a new window into the craft.

[Alan Carruth]

"I think one of Gore's most important additions to the science is the application of certain tools to measure plate resonances."

That's not original by a long shot, although he's done a lot to spread the word.

When I worked with Carleen Hutchins in the '80s she had about $20,000 worth of lab-grade B&K equipment for making spectrum plots of instruments. Every once in a while a bunch of us would bring in stuff for her to test and she'd be stuck in the lab all weekend running charts. As soon as they started putting sound cards into computers people were using them to do the same. I still use a DOS freeware FFT program called FFT4WAV3 that was written in the days when the 386 processor was just coming into use. It's quirky, and limited in some ways, but also does some tricks that no other software I've seen will do.

Carleen used a sweep signal to drive the instrument for her plots. Since she was not using a computer there was no way for her to derive the spectrum from an impulse. In many ways the impulse test is superior, and it's certainly easy to do. As with everything you do have to understand the limitations of it to get meaningful information; so what's new?

[Craig Bumgarner]

.... In real life if the lowest back mode is tuned close in pitch to the lowest top mode the two will tend to be moving as a 'bellows' over a fairly broad range of frequencies.

The lowest modes being the monopole modes? What constitutes "close"? Gore & Gilet talk about the back couple monopole being tuned no closer than four semitones above the top monopole for good separation and clarity. If they get closer, the sound becomes muddy. Much more than that, the back is pretty well inactive. When I started building the four semi tone difference in, it made a noticeable difference in clarity.

That said, a lot of great guitars have less separation, some have backs that have significantly lower back monopole resonances than the top (!!!).

FWIIW, I started out using Visual Analyzer for Windows and a USB mic as Barry describes, but have since gone to FFF by Six Digital, an iPhone app ($10 last I checked). Much easier to use which means I use it more often and seems every bit as accurate. Saves files easily, or use one button click to save a snapshot.

[Barry Daniels]

Alan, I didn't mean to imply that Gore was the first to use these tools, but that he was the first to put this information where it was readily accessible to the public.

Craig, I couldn't find FFF in the App Store.

[Craig Bumgarner]

Sorry, typo. FFT, not FFF.

[Barry Daniels]

Craig, does that app allow you to set limits on the chart axes, and does it quantify frequency peaks? A lot of different frequency analyzers don't do that and I see it as necessary.

[Craig Bumgarner]

You can set limits on the axes, but the setup does not stick, the next time you open the app, you are back up to full scale. But, it is very easy to adjust the scales and limits by typical smart phone gestures. Two fingers spreading apart/pinching horizontally zooms the frequency axis in/out, two fingers vertically adjusts the amplitude axis. You can both zoom and scroll. Occasionally, my fingers get confused and the wrong thing happens, but the curve is not lost, just have fuss with it some more to get the view you want.

To quantify the peaks, you can pull a guideline from the side with your finger and move it to the center of the peak. The frequency is shown next to the guide line. You can zoom in and steepen the peaks for more accurate ID by means of the gestures above. For me this is all easier in FFT than VA.

You can take a screen snapshot with a one button click on the screen and they save to your photos app on the smart photo, so they are easy to access and share.

Snapshots are just pictures though, not interactive. For future interrogation, you can save the curve in the FFT app, to be recalled later where you can apply all the interactive bells and whistles, You can also recall and overlay multiple curves easily which is handy if you want look at coupled vs. uncoupled, or before and after installing bridge, etc.

The app is supposed to allow exporting the curves to a PC, but I've never been able to get that to work. I don't know what I would do with them over on the PC anyway in that as far as I know, there is not PC version of the app. So, I back up my phone periodically.

Anyhow, I've not used VA now for over a year. FFT was okay on my little iPhone 5, much better on my 7+. It would be good on an iPad too, but the 7+ is always with me, so super easy to use. This is very helpful, not only in the shop, but also in the field when you encounter a killer guitar you'd like to investigate, takes about 10 seconds to setup, tap and save. Now if I could just find a similar app for taking top deflection readings.

[Barry Daniels]

Thank you Craig, that was very helpful. Now back to the original discussion

[Brian Evans]

Not so fast, me bucko... This is way better than the original question! Craig, are you really saying that you can tap a guitar, use the internal mic on an iPAD to capture a sample and get a read-out that has useful information? I may have to get an iPAD. For fun, can you guys do some analysis of that capture you posted, and tell me what useful information you get from it, and what you might do with it?

Thanks, Brian

[Alan Carruth]

Craig Bumgarner wrote:
"The lowest modes being the monopole modes?"
Yes.

" What constitutes "close"? "
Trevor and I have some differences of opinion on this whole issue, probably largely based on the fact that we tend to measure things a bit differently, I think. You have to keep in mind that the 'mode frequencies' are not some fixed thing that never vary. The fact that they interact, and indeed must do so, means that each affects the other, and then there's the influence of the air in there. How you support the instrument when you take the measurement, and how you drive it can also make a difference. This all gets very confusing from time to time.

The most basic definition of the modes is the one that isolates them as much as possible. Rossing did something like this with flat top guitars many years ago. He packed them in sand with just the hole open to look at the 'air' modes of a guitar shaped box. Then he set up a backless guitar with a stiffened rim edge to mimic the stiffness of the back without enclosing air to see what the top would do. After that he tested the air and top modes of a real guitar that was suspended somehow, to look at the changes when the top and air couple. I don't think he did the same with the back; the more stuff you include the more complicated the evaluation gets, and he was looking at the main stuff then.

Fred Dickens, among others, did computer modeling to tease some of this out. He used a program that could evaluate equivalent circuits to predict the overall resonant behavior. He could set up LCR circuits that would work more or like isolated parts, such as the top and back, and then link them together to see how the whole assembly worked. This could be compared with the output of real guitars to get an idea of what the parts 'should' be doing. This is more or less similar to Rossing's work, only with models instead of wood. Naturally the models are simpler, but they're also much easier to modify in specific ways, so you can learn some basic stuff fairy quickly if you know how to work with the models. In his work the models that mimicked the 'best' guitars most closely had the 'main back' resonance a semitone above the 'main top' mode.

Fred also pointed out something that Trevor has said: that plugging the sound hole comes reasonably close to isolating the main top and main back modes from each other, so that the pitches in that situation are fairly close to the 'real' ones. This would be more accurate if the back and top were not linked through the sides, but, of course, that's not the case. Trevor goes into some of the outcomes of that. In the current context, one thing this means is that if you hang the guitar up by suspending it from the head, as I do, that gets a somewhat different result than supporting it in a more 'realistic' way that damps the sides. One issue with the 'realistic' support is that it matters a lot just exactly how you do it, and so it goes.

Ultimately, this is a system of coupled oscillators. What constitutes 'close' in such a case depends not only on the oscillators and their frequencies, but also how tightly they're coupled. The top and back of the guitar are pretty tightly coupled, both by pressure changes of the air in the box and by the stiffness and mass of the sides, with the two working out of phase in a lot of cases. The frequencies of the different elements don't have to be al that close for them to couple usefully. What's more important is what constitutes 'too close', and that's a matter of judgment that may well differ from one case to another. It's fairly easy to know when you've gotten things too close: that's practically the definition of the 'wolf' note, in all of it's varieties. In general, the more tightly things are coupled the more 'interesting' or 'productive' in some sense the instrument is, but at some point it crosses the line to being a problem. In some sense it's more important to know how things work, and how to fix them when they don't, then to have some sort of number to look at. There are just too many variables for any one number to be useful in all cases.

[Craig Bumgarner]

This all gets very confusing from time to time.

Amen to that! Guys like you and Trevor are light years ahead of me. I'm just an aging builder trying to use a bit of this to get ahead of the traditional "well son, you just have to build a lot of instruments" curve.

Thanks for your explanation. It is interesting to me that different researchers have come to seemingly different conclusions. Given their differing investigative methods though, it is not surprising that they might get different results. These research methods would be hard to replicate in field testing and as you say do not necessarily duplicate the playing condition.

The best I figure I can do is test in manner that is generally consistent with the playing condition and maintain this standard over all my testing. I hold the guitar by the head block and rest the tail end on my thigh. I tap in the same location near the bridge location. I am less concerned about how properly this fits a model than being consistent and seeing changes that show up as differences I can actually hear. I take FRC and top deflection measurements of good examples of the guitars I like and compare them against what I'm building. After 4-5 years of doing this, I have developed my own understand of what kind of sound I might expect looking at a set of FRC and deflection results, at least in my rather narrow range of guitar styles.

But....., every time I start to think I know what is going on, along comes a ringer that throws me for a loop. As I have heard you say, "things get complicated real fast"

Thanks as always for your insights!

[Eric Knapp]

Sorry, typo. FFT, not FFF.

There seem to be two apps that you might be referring to. Here's a screenshot of them on the App Store.

Which one do you have? Both might work.

Thanks,

-Eric

[Craig Bumgarner]

Which one do you have?

The second one, FFT by Andrew Smith, is the one I use. I did not research others, some one recommended FFT to me and it has worked well enough that I have not looked for alternatives.

[Eric Knapp]

The second one, FFT by Andrew Smith, is the one I use. I did not research others, some one recommended FFT to me and it has worked well enough that I have not looked for alternatives.

Thanks!

-Eric