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I am about to start bracing the back of an Imbuia SJ I recently started and want to incorporate the information contained in recent posts by Al Carruth and others regarding coupling the back and top to maximize the responsiveness of the guitar. My understanding is that the resonant frequency of the back should be a semitone higher than the top in order to move in that direction and at the same time avoid wolf notes. Furthermore, the addition of the bridge to the top has the impact of reducing the top’s resonant frequency by a semitone so it would seem that the resonant frequency of both the top and back should be close prior to gluing to the rims anticipating the contribution of the bridge.

My question is – not having the equipment or knowledge to verify Chladni patterns, would you used the pitch of the tap response of the braced back and top as an indication of the resonant frequency of both? - - Shape the top braces for an optimal response and then begin reducing the back brace cross sections and length of brace thinning at the perimeter until the tap pitch is similar to the top tap pitch?

Would you also tap the top and back once they are attached to the rim and, based on the pitch response of both, potentially thin the edges of the back plate if needed until the back pitch matches the top pitch (assuming it is initially higher)?

Could a simple guitar tuner be used to determine the tap pitches for comparison purposes?

Am I understanding this all correctly?

Sorry if the questions are a bit sophomoric but I’m trying to gain a better understanding of this top/back coupling issue before the shavings start flying.

Thanks

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Doug Mills
Chicago, Illinois

Unless you make the back out of concrete, and pretty thick at that, it _does_ couple with the top around the 'main air' pitch. However, if the 'main back' and 'main top' pitches are much more than a musical third apart the coupling will be relatively weak. The main effect of the coupling is to drop the pitch of the 'main air' mode, and make it more active. Since the 'main air' mode is the lowest pitched resonance that can contribute in a major way to the sound output, this is what gets you the bass response.

As I say in another post, it's sort of hard to relate the tap tones or Chladni patterns of a 'free' back to anything it does once the guitar is together. I usually find that backs are rather over braced, in terms of their frequency response: often you have to take a lot of wood off the braces to drop the 'main back' tap tone. Those low, wide Martin braces actually make a lot of sense in this way. Shaving the ends down is less effective that dropping the height of the center at lowering the pitch.

There are ways other than Chladni patterns to 'look at' the resonant modes of 'free' plates, but they do require some understanding of Chladni patterns to sort out, IMO. When you listen to 'tap tones' you're hearing some mix of all the different modes that could be activated from the tap point, and that are not very active at the holding point. I can't sort these out very well by ear, but you might be able to. If you know what the patterns look like you can hold and tap in a number of places and figure out which pitch is what. Recording the taps on a computer that has some sort of Fourier Transform software (such as 'Wavesurfer' available free from :
http://www.speech.kth.se/software/) will allow you to find the frequencies of the resonant peaks, so long as the mic is in a good spot to 'hear' them.

You could even revert to Chladi's own methods on 'free' plates: he used to support the plates on four points (try pencil erasers) and bow the edge with a violin bow to activate the modes. His problem was finding the pitch, but a tuner or computer can do that for you now. Come to think of it, some sort of light, stick-on pickup, a speaker, and an electric guitar amp could also find modes on the assembled box by feedback. Stick the P/U on an active area of the mode you want to find, put the speaker in the same spot, crank up the gain, and tap. You should be able to get it to ring out at least for long enough to form a pattern.

Alan you mention musical third. Can I ask some clarifying questions?

When the box is assembled how does one isolate the top note versus the back note? I assume you have to learn this information AFTER the box is assembled.

If the top note is say...G#...then the back note should be B# (A flat)?

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There is no difference between the man that thinks he can....and the man that thinks he cannot.

Al - Thank you for your detailed answer. I am still groping in the dark a bit however. Back in April, you gave another detailed and very interesting response to a question asked by Chris. In this thread you described a hide and seek search for a buzz that ended up being the result of the main top and back resonant modes being too closely matched. You discovered that the modes were within 7 Hz from each other which ended up being the root of the problem. Did you determine the exact front and back frequencies by tapping and checking the resonant peaks with a program like Wavesurfer that you describe above? Am I understanding correctly that this approach might also provide comparative information for the back frequency relative to the top frequency even if these frequencies shift once the top and back are attached to the rim?

Chris – in several posts where you have confirmed your top resonant frequency to be A or G or G#, are you determining this by tapping and watching the response on a tuner or using a Wavesurfer type program or noting Chaldni patterns at those particular frequencies for the top and back plates prior to rim glue-up?

thanks

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Doug Mills
Chicago, Illinois

Doug - I'm really shallow in this regard (modes, tapping, so on). In the past I have simply held an assembled box up to a tuner...tapped the area of the box where the bridge would be...and watched what the tuner did. I think the 'note' the tuner registers is the main air mode...but I could be playing fooz ball in the left field of a soccer game. I've never used a program or Chladni pattern.

_________________
There is no difference between the man that thinks he can....and the man that thinks he cannot.

Chris asked:
"If the top note is say...G#...then the back note should be B# (A flat)?"
Last I looked, B# was C!

On my guitars I like to have the 'main top' and 'main back' modes _no more than_ a musical third apart. I count of that particular relationship to get the bass response I'm looking for, since I usually make my tops a bit on the thick side. YMMV! I've heard good guitars with the backs a third above the top, and even a fifth above the top. They just don't sound like my guitars. Some people even like them better: there's no accounting for taste.

This rapidly gets to be a semantic jungle: since everything is coupled to everything else it's just about impossible to find the 'real' frequency of anything. Once you assemble the box the top, back, sides, and air _have_ to work together, and the pitches you hear or measure and the patterns you see are all the result of some series of interactions among the various parts.

When I'm looking at the modes of the completed box I do try to isolate things as much as is conveinient. Blocking the soundhole, for example, eliminates the pressure changes in the box from the Helmholtz air mode, and largely decouples the top and back. There is still some coupling from higher-order air modes, and through the sides, but that's not as strong at low frequencies. At any rate, since you can't get rid of it, you just have to live with it.

That guitar with the seven Hz difference was an assembled instrument, and I found the frequencies of the 'main top' and 'main back' modes using Chladni patterns. It's been a while, but I may even have done so with the soundhole open. This, after all, was the condition of the guitar when it gave the problems, and closing it may well have altered the pitches I was looking for. You could find those pitches using 'Wavesurfer', or maybe even with a good tuner, but the patterns give you information about how the plates are moving, as well as the pitches.

Again, there is _no_ reliable relationship between any mode frequency on the 'free' top and back and any mode frequency on the completed guitar. I used to think there was, but now I'm pretty sure there is not. You can't use one to predict the other beyond a rough generalization: tops with high 'free' mode frequencies tend to have high pitched tap tones when the box is assembled, but the exact pitch is not predictable.

One of the problems with using a microphone to find mode frequencies is that the output of the mic will depend very strongly on where it is relative to the mode shapes. To find the 'main top' mode, you'd want the mic right over the bridge and on the center line, since that area is most active for the 'main top', and least active for the usual next mode up, the 'cross dipole'. Too close to the hole and you'll indeed get the 'main air' mode pitch as your strongest and lowest peak. That's why I say that it's nice to have an idea of what the modes look like, and where they tend to be on the pitch scale. It makes it easier to sort things out. Obviously, the more 'normal' the guitar the more 'as usual' the modes and pitches will be.

(sigh)...I don't know why I typed A. I know better.

Thanks again Alan.

_________________
There is no difference between the man that thinks he can....and the man that thinks he cannot.