String energy transfer in steel sring guitars

[LPMark]

When thinking about the bridge/ bridgeplate and X brace placement, does the strings vibrational energy transfer more at the saddle point or at the tension anchor which would be the bridge plate/bridge pin?

I've heard some builders say the bridge pins should be located right in the center of the bridge plate, inferring that was the axis of rotational energy, not at a point under the saddle as it would seem to be.

I see that the typical placement of bridge plate results in pins roughly in the center of the plate [and center of mass] and saddle much closer to the edge of the plate.

Thoughts?

[Rodger Knox]

The energy transfer happens at the saddle, anything past the saddle is essentially static.
The purpose of the bridge plate is top protect the top from the ball ends of the strings, so they should be in the middle of the plate. While the plate does add some stiffness, that is not it's primary purpose. It's right under the bridge, which is the stiffest brace on the top.

[Ned Milburn]

Not to disagree with Roger, but offering some different thoughts... ;-)

Certainly one of the important functions of the bridge plate is to offer protection from the pressure of the ball ends of the strings. But I don't think it ends just there.

The sandwiched lamination of the bridge plate, top, and bridge, aid a great deal in preventing the bridge torque from pulling the soundboard upwards behind the bridge, and help the torque from pulling the top away from the x-braces. This can be evidenced in guitars with poorly fit bridge plates showing greater warping of the soundboard AND bridge, and sometimes even pulling away from the x-braces. These warps can usually be rectified to "like new" condition by removing the old bridge plate and adding a new bridge plate that fits flush to the edges of the x-braces. The bridge plate needn't be notched into the x-braces; simply a flush fit is enough. Guitars with narrow bridge plates (front to back) often display greater amounts of warping in the bridge and surrounding soundboard area. Some bridge-plates extend past the back of the bridge profile, and others do not extend past the bridge profile.

Even some classical builders use bridge plates. Certainly, they aren't doing that because of bridge pin wear. Again, the extra lamination adds extra stiffness and if oversize when compared to the bridge footprint, can help diminish the amount of soundboard warping.

Another factor with bridge plates is weight. The heavier the bridgeplate, in general, the slower the attack of a note (slower acceleration of movement due to greater mass). But there could be a gain in sustain due to the momentum of extra mass, but that would depend upon the rest of the soundboard design. A light bridge-plate/bridge combination will tend to offer a different sound than a heavy bridge-plate/bridge area.

And finishing off with the OP's question, the main energy transfer is in the total function of the bridge & bridge-plate & saddle (& soundboard for that matter). The strings transfer their energy into the saddle, primarily, but the saddle is embedded in the very stiff bridge, and the total energy transferred by the bridge to the soundboard is again related to the total function of the aforementioned parts. The bridge/bridge-plate transfer this energy to the x-braces, which then help constrain certain bridge & soundboard movements and allow other movements freedom of vibration.

The location of the bridge pin holes, is IMO a matter of lesser importance than the dimensions, shapes, and masses of the bridge, saddle, bridge-plate, x-braces, soundboard, etc. Main consideration is to make certain the pin holes are located far enough from the saddle to avoid an overly sharp break angle to avoid premature saddle wear. It shouldn't be hard to find a happy medium by studying a bunch of classic "tried and true" guitar bridges.

(Written quickly at Tim Hortons while waiting for son at Karate practice. Hope it came out clearly...)

[printer2]

Actually never thought about the plate preventing the soundboard from warping. Gave me some ideas that I will have to try.

[redir]

The saddle is a lever so the rotation starts right there.

Bridge plate as Ned said absolutely helps keep the top from warping. In fact the bridge itself helps to keep the top from warping. It's a good idea to think of the bridge itself as one of the braces in your tops bracing system.

[Alan Carruth]

redir worte:
"The saddle is a lever so the rotation starts right there."

If you're talking about torquwise motion of the bridge as a driver of sound on the guitar, it's only a very small contributor. Raising the the string height off the top by a lot (from 11 mm to 18 mm in my test) gave audible changes in the tone, but not any significant increase in overall power. The tone changes are easy to explain when you know the different forces the vibrating string puts on the top of the saddle. That's where the work happens.

Some recent modeling data I've seen suggest that the loading from the strings at the bridge pins is on the nature of a 'column load': the strings compress the wood between the ball ends and the top of the slot. The upward pull of the strings at the top of the slot is distributed by the stiffness of the bridge/plate assembly, so that the actual 'lift' is felt at the back edge of the bridge, not at the pins. Of course, there's an equal and opposite down force on the saddle.

The overall stiffness, mass, and damping of the top/bracing/bridge/saddle/plate determine the complex 'impedance' of the string termination at the top of the saddle. There are plenty of variables to go around, and you can get all sorts of arguments about which one is the most important. It's the relationship between the impedance of the strings and that of the top system that determines how the energy gets transferred at a particular frequency. I agree with Roger that the primary function of the plate on steel string guitars is to resist wear by the ball ends of the strings, but there are not too many parts of the guitar that only serve one purpose, or don't have ancillary effects beyond their intended use.

[LPMark]

Thanks all who posted. Fascinating stuff. The saddle, bridge/bridge plate, X brace IMO is the heart of string vibration energy transfer to the top and therefore dominates string vibration dynamics.

I have started feathering the edge of the bridge plate [butt end] and I see that the stiffness of the bridge would render that ineffective unless the plate extends a fair distance beyond the bridge.

I read somewhere that the ideal placement of the saddle is at the X brace intersection to give max power, but pins would have to clear the braces.

Thoughts?

[murrmac123]

Originally Posted by LPMark

I read somewhere that the ideal placement of the saddle is at the X brace intersection to give max power, but pins would have to clear the braces.

Thoughts?

Not really feasible, for several reasons, but mainly because the X braces need to support the bridge at the ends ... that wouldn't happen if the intersection was directly under the center of the saddle.

[sirwhale]

I have found this thread interesting, especially as my Blackbird Luck 13 doesn't have a bridge plate. The newer versions do, I wonder what affect this has on the sound of the guitar.

[Bruce Sexauer]

I view the bridge, including the bridge plate and the saddle and the pins and the strings before they pass over the saddle as a solid entity. To a limited degree they are not actually, but from the standpoint of understanding how the energy from the strings is passed on too the top they functionally are. I believe those who will argue against this view, which I have held for years and expressed before, are picking nits, and taking this view is extremely instructive. Viewed from the side the bridge becomes a triangle, a lever with a broad base, which cantilevers its force into the top, pushing the bridge down in the front and lifting it in the rear. The pressure down on the saddle, from the top's POV, is nothing, it is the torsional rotation on the top and the varying tension of the string as it vibrates that the top reads. In this perspective it is the structural integrity of the whole and its mass that are important. Or that are able to make a difference, one might say. A much greater (and more controllable) variable is the location and strength of the X (assuming they exist) braces, and then other braces in near proximity. When viewed as a rigid mass the bridge is the major top brace and it becomes apparent that no more structure is needed at that location, a "fact" that I do not see reflected in many of the bracing patterns I have observed..

The bridgeplate adds mass, but is not essential to the guitar except as a support for ball ends (could be MUCH smaller) and as an aid to clamping on the bridge. When it is bigger than the bridge itself it caused the "hard" spot the bridge represents to become larger, and adds mass where a thinking person may find it least desirable. Mass at the bridge (center of the responsive top) diminishes response, increases sustain, balances response at cost to liveness, and tends to lower the tonal center of the individual notes (makes the guitar sound mellow at cost of being interesting).

All opinion and my thinking based on observation and experience.

[Alan Carruth]

Bruce Sexauer wrote:
"The pressure down on the saddle, from the top's POV, is nothing, it is the torsional rotation on the top and the varying tension of the string as it vibrates that the top reads. "

I must disagree with that point, although the rest of your argument is good. I base my disagreement on two things: measurements of the relative signal strengths of the vibrating string on the saddle top, along with the mobility of the top under those forces, and also a series of experiments on how altering the string height off the top affects the sound. As always, this stuff is more complicated than it 'ought' to be, but I can summarize the main points.

The vibrating string produces two main force signals at the saddle top (apart from the static force). There is a 'transverse' force, across the line of the string, in the direction that string is vibrating, and a 'tension' force pulling the top of the saddle toward the nut. The tension signal is 'frequency doubled'; it pulls the bridge in twice per full cycle of the string, once when it's 'up' and again when it's 'down'.

The string can vibrate 'vertically', perpendicular to the plane of the top, or 'horizontally', across the top, or, of course, at any angle in between. When it's going 'vertically' the transverse signal is pushing the top in and out of the box, like a loudspeaker cone. When the string moves horizontally the transverse force produces almost no motion of the bridge at all. On the other hand, the 'tension' signal works the same no matter how the string vibrates.

The transverse force is small relative to the static tension of the string: maybe 5% or so. In terms of the relative magnitude of the signals, the transverse force is generally the larger: on average it's about seven times as large as the tension signal. This varies depending on the the string material and construction, and how tight it is. A plain steel high E will have a Tr/Te ratio of maybe 8:1, while the same string tuned down to the open G pitch will be closer to equal. Hint: the more compensation the string requires the greater the tension signal is relative to the transverse.

For a given force you get a lot more sound out of pushing the bridge in the loudspeaker mode, as the transverse signal does, than you do from rocking it, for two reasons:
1) The loudspeaker motion of the whole lower bout is very effective at pumping air, both through pressure changes in the box that moves air through the hole, and also by producing sound directly off the top. By comparison, bridge rocking pulls the lower part of the soundboard up as it presses the upper part down, so there's some cancellation of effort there.
2) We build tops to move as easily as possible in the loudspeaker mode, while trying to make them to resist bridge torque. You get much less top motion for a given force rocking the bridge than you do for the same force pushing it in, particularly at low frequencies.

Coupled with the generally lower force produced by the tension change signal, the result is that much less sound is produced from tension change than from the transverse force when the string moves 'vertically' with respect to the top. I did a couple of experiments driving strings in different ways that allowed me to at least start them out with motion only on a single plane. When the strings moved across the top, so that only the tension signal was driving it, I got about 20 dB less sound output (1/100th of the power) than I did when the strings were driven vertically, with both the tension and transverse signals to do the driving. You don't have to get very far off horizontal for the transverse signal to take over producing sound.

It makes some sense that if the strings are further off the top the tension signal will gain leverage, and produce more sound. I ran a series of experiments on that, as well, using a Classical guitar, although the results should hold in principle for steel strings as well. I used a mechanical plucker to get the same input force in the same place and direction on the open strings (six plucks for each string for each setup) , and recorded the output of the guitar for different string heights off the top, and also different break angles. I analysed the sounds produced, looking at harmonic content, peak amplitude, and rise and fall times. I also made up 'synthetic strums' of the recorded sounds, which were played back in random pairs through good ear phones to see if folks could hear the difference. A friend helped me with the statistical analysis.

In the objective measurements there was no significant difference between plucks in terms of power: the rise and fall times, and peak amplitudes were the same in every case. There was a difference in harmonic content: the sound had relatively more of the second partial when the string was higher off the top, due the increased leverage, as expected.

I also looked at break angle as a variable in this, and in the listening tests people were just guessing when it came to detecting any difference due to break angle when the string height stayed the same. When the string height off the top was changed almost everybody could hear it.

Again, that's the main lines of the thing. There are other things going on that contribute to the ability of listeners to pick up a change in height off the top, most particularly the high frequency 'zip tone' of the string (which is also a bridge rocker), but that's a whole other complicated post. The important part of the take away is that it's the transverse force that makes most of the sound: bridge torque produces 'tone color' but not power.

In all of this I'm going on the results of my own experiments. These were done as carefully as possible, and I'll be happy to share the method and data. Indeed, I've been trying for some time to whip this all into publishable shape, and hope to get some time to work on that soon. Still, no experiment is perfect, and if anybody comes up with different results that prove me wrong, I'll acknowledge it. I'm going to require some convincing, though....

[LouieAtienza]

Originally Posted by LPMark

Thanks all who posted. Fascinating stuff. The saddle, bridge/bridge plate, X brace IMO is the heart of string vibration energy transfer to the top and therefore dominates string vibration dynamics.

I have started feathering the edge of the bridge plate [butt end] and I see that the stiffness of the bridge would render that ineffective unless the plate extends a fair distance beyond the bridge.

I read somewhere that the ideal placement of the saddle is at the X brace intersection to give max power, but pins would have to clear the braces.

Thoughts?

I think the closer the saddle to the intersection, the more it can "move" somewhat independently of the bracing. Whether that gives more "power" I'm not sure. I would think having the bridge wings "tie in" to the bracing and the bridge plate below "unitizes" that crucial area and gives it strength. In fact I do try to make my bracings such that it is very stiff from the bridge to the soundhole in that area directly between bridge and fretboard, which I feel allows me to make the bracings and soundboard to the side and back toward the butt end of the guitar as light as I can.

Of course now, moving the saddle changes the where the neck joins the body, and then there would be discussion about having the X-brace intersection closer to the center of the soundboard, or more toward the neck...

[Bruce Sexauer]

Al, you do realize that since you were responding to my thoughts I actually had to read your whole post?

Nothing you said seemed to decouple the function of the saddle from the triangle I view it as an integral part of. I disagree with nothing you said except that you disagree with me. You do not seem to. The saddle amounts to a convenient way to vary the height of the triangle. By the way, changing the length of the base makes a noticeble difference too!

I do think that if the saddle has any movement whatsoever independent of the bridge then that is a problem that needs to be addressed for it is wasting otherwise useful energy, probably creating counter forces I call distortion.

[Alan Carruth]

Bruce:
I may well have misread your post. I realize I used a lot of words to address the point, but, after all, I did a lot of work to check it out.

The first part I agree with:
"I view the bridge, including the bridge plate and the saddle and the pins and the strings before they pass over the saddle as a solid entity. To a limited degree they are not actually, but from the standpoint of understanding how the energy from the strings is passed on to the top they functionally are. I believe those who will argue against this view, which I have held for years and expressed before, are picking nits, and taking this view is extremely instructive."

Again; agreed. Sure, people can talk about the flexibility of the saddle or the bridge as possibly affecting the sound, but I think for the most part that's going to be small potatoes on steel string guitars.

"Viewed from the side the bridge becomes a triangle, a lever with a broad base, which cantilevers its force into the top, pushing the bridge down in the front and lifting it in the rear. "

This certainly describes the static forces on the top. The sentence that follows seems to extend that into a dynamic argument, and that's what I'm disagreeing with:

"The pressure down on the saddle, from the top's POV, is nothing, it is the torsional rotation on the top and the varying tension of the string as it vibrates that the top reads. (my italics)

Again, the vertical force on the top as the string vibrates is 'small' relative to the tension on it, but large compared with the mass and stiffness of the top. If the strings exert, say, 180# of pull all told that's more or less the equivalent of standing on the top if that were a vertical load. No feasible top is going to take that. The top itself would be sufficiently strong to handle the string load if the strings were in the same plane as the top itself and pulling parallel to it; the bracing is there to support it against the static torque, while allowing scope for the small vertical force of the string vibration to produce sound.

If I misread your post, or misinterpreted it, I apologize. Again, I put in a lot of work checking this all out, in part because there are folks in the guitar community who argue the other side, and I wanted to have my facts straight . I've always felt that knowing how things actually work is a good way to avoid making mistakes: even if it doesn't necessarily help you make 'great' instruments it can help keep you from making bad ones.