Official Luthiers Forum!

Seems there is no end to questions on how a guitar functions! So here is another one I would appreciate your opinions on.

As you gain experience and hear ideas, it seems one builds a more and more complex model of the guitar and how it produces sound. We hear sound from the air pressure fluctuating on our ear drums. The sound from a guitar is created by components of the guitar varying the air pressure by vibrating. Most would likely agree that the bulk of the sound is produced by the soundboard. Assuming a Martin style bridge with pins to terminate the strings, I would venture most consider the bouncing and rocking motion of the bridge due to string vibration as a primary source of most of the soundboard vibration (though there seems to be differing opinions whether rocking or bouncing causes most of the vibration).

Focusing on the rocking action of the bridge, what plane of the bridge do you think is the center of the rocking motion? Without thinking this concept through, in my mind the center of the rocking rotation was the saddle. However, watching Kent Everett's voicing DVDs, he seemed to be proposing the plane of the pin holes where the strings terminate is the center of rotation (at least that was my understanding). And thinking about it, he may be correct. This area is dynamic and possibly the center of rotation is constantly moving......but it couldn't move far could it? Has any one filmed the motion of the bridge with a high speed camera to answer some of these questions?

So what plane do you consider the center of bridge rotation? Is the rocking motion of the bridge remain parallel to the strings?.......or is it parallel to the saddle?.......or is it parallel to the bridge pin holes? If the bridge rocks parallel to the bridge pin holes and you angle the bridge pin holes parallel to the saddle to keep a consistent break angle, it seems it would change the sound slightly compared to the bridge rocking parallel to the strings.

Isn't there a TV show on Discoverychannel that does nothing but high speed photography? We need to have them film the motion of a Martin dreadnaught with traditional X bracing and a traditional classical guitar with nylon strings using their high speed cameras. Do you think the motion would be similar?

I ask these questions as it seems that if you have a radiused (or domed) soundboard, you would get maximum rocking motion of the bridge if the center of rotation were located at the apex of the dome (relative to the plane of the strings).

Thoughts?

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Formerly known as Adaboy.......

Hi Darryle,

Is this one of those "inquisitive minds just gotta know" things?

Dave

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God, Family, Carreer

You got it Dave!

I do think this is a key area for producing sound and understanding how the bridge works and how it needs supported might lead to either better sounding instrument, or more consistent instruments, or an instrument that stays stable for decades yet still provides a good tone.

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Formerly known as Adaboy.......

First: why are you concentrating on bridge rocking?

I spent 'way too much time a few years ago measuring the forces the plucked string puts on the top of the saddle; the driving signal for the bridge. It turns out that for most strings the 'transverse' force is much greater than the 'tension change', and it's the tension change that rocks the bridge.

If the string is moving 'up and down' relative to the top the transverse force is pushing the bridge 'down and up', causing the top to move like a loudspeaker cone. This is the most effective way for a top to produce sound, in part because the whole lower bout is moving in the same direction at any one time. When the bridge rocks part of the top is moving up, and part down, so there's some cancellation going on between the two areas.

It has been argued that the string moves mostly in the crosswise direction. I think that's a mistake. For one thing, if it was not moving vertically, why would it buzz on the frets? I'm pretty sure that there's usuallt some 'vertical; and some 'horizontal' motion, and the resulting force on the top of the saddle is at some angle. But remember, if the transverse force of the string is much much greater than the tension change, it doesn't take alot of 'vertical' component in the string motion for the 'up and down' force on the top to exceed the 'rocking' force on the bridge.

Besides, it much easier to move the bridge up and down than it is to rock it. After all, we build tops to resist rocking of the bridge, AKA 'bellying'. I rigged up a driver and pickup setup that could push the bridge on a guitar in any direction and read the motion. You get a fair amount of motion at all frequencies in the 'up and down' direction, much less when it's rocking (except at one particular frequency), and much less than that in the 'crosswise' direction (as you'd expect).

That one frequency where the bridge rocks about as much as it moves in the vertical direction is the pitch of the 'long dipole' resonant mode of the top. If you drive the top at that one frequency with a pure tone, and sprinkle some sand or sawdust or glitter on it, you'll see that there are two areas moving; one behind the bridge and one in front of it. If the area behind the bridge is going 'up' the one in front is going 'down', and the bridge is indeed rocking. Like all resonant modes, this one has some 'bandwidth': you get motion over a range of frequencies, but less and less motion as you get further from the resonant pitch on either side. Usually this mode centers around 350 Hz or so (F on the high E string, second fret), and the band width will be less than a semitone, so it's not really effective at driving the top below E or above F#.

The exact configuration of this top mode depends on the bracing and top stiffness, and also the mass of the bridge. Concentrations of mass and stiffness tend to 'pin' modes in place: you often get either an innactive 'node' line or a very active 'antinode' where there is a lot of mass or stiffness. The bridge often weighs as much as all of the other top bracing put together, and it's pretty stiff, too, so the innactive node line, the fulcrum for the rocking motion, tends to run along the bridge. Just where it will be is hard to predict, but fairly easy to find by experiment.

In short, there's no general answer to your question: different tops move in different ways. How effective the rocking motion of the bridge will be in producing sound depends on a lot of factors, including the way the air moves inside the box (another whole can of worms!). The tension change that rocks the bridge occurs twice for every full vibration cycle of the string, so the sound it produces will be an octave higher than the normal sounding pitch of the string. From what I can figure out, bridge rocking contributes to the 'timbre' of the guitar, but not a lot to the power.

Al, thanks so much for your response.......I think I'm learning something.



Good question. Good or bad, I concentrated on the bridge rocking because:

First, I read Roger Siminoff's book, "The Luthier's Handbook". Roger attached an aluminum bracket to the bridge with 2 screws and attached a rod to the bracket that could rotate and either be attached vertically to a fixture, preventing the soundboard from moving up and down, or attached horizontally to a fixture at the rear of the guitar that prevented the bridge from rocking. He measured the db loss with a meter with different tensions on the rod and concluded there was more db loss when the bridge was prevented from rocking (horizontal tension in the rod) than when the soundboard was prevented from bouncing (vertical tension in the rod).

Second, I bought Kent Everett's voicing video and he emphasized the rocking motion of the bridge. His thought was the string termination was the center of the rocking rotation so he centered the pin holes in the bridge and preferred not to align the holes in the bridge with the saddle fearing it would affect the rocking motion of the bridge.

So rightly or wrongly, that's why I've been pondering the rocking motion of the bridge.

However, you bring up some good points Al. And again, I appreciate your input as I highly respect your opinions and observations. If you don't mind, I have a couple of questions to clear up a few things in my mind after reading your post.

When you state, ".......for most strings the 'transverse' force is much greater than the 'tension change', and it's the tension change that rocks the bridge", are you saying that the change in the transverse force is greater than the change in tension? I'm assuming the change in force or change in tension is what drives motion either rocking or bouncing.

Essentially all modes will have part of the top moving one direction and another part of the top moving the opposite direction with the node line between wouldn't they? Is there a node where the entire top moves like a loudspeaker with no node lines? If so, is the rim of the guitar essentially the node line? Seems this would be for a very low frequency only......though it could be a very powerful frequency. I like to hear those old bluegrass Martins with the great cut so this intrigues me.

Al thank you again for taking time to teach a guy like me you haven't even met. I'm sure you get tired of answering these "how does this work" type questions.......but don't think it goes unappreciated.

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Formerly known as Adaboy.......

The transverse wave in a string exerts a perpendicular force. The change in tension exerts a parallel, or longitudinal force (this is often confused with a longitudinal wave, which is actually independent of tension and diameter, and insignificant for our purposes). It is the change in tension / longitudinal force which exerts torque on the bridge system, in effect rocking it.

On nylon strings the longitudinal forces are much more insignificant than steel strings. Since Young's modulus of elasticity is approx 40-50 times greater in steel strings than nylon (this is from memory, so don't quote me here), longitudinal forces can be significantly greater in steel strings. The longitudinal forces increase quadratically in relation to the perpendicular forces as a string is driven harder (again, recollection, so reference this yourself if really interested), so when a steel string is driven very hard the forces exerted can reach near equal value. This high relative torque however is very short lived, and will only play a significant roll on an initial heavy attack, decaying in to insignificance very quickly.

More importantly, the string is more efficiently coupled to drive the top by transverse waves, which lessens the influence of the longitudinal forces even further. Much like a speaker, a top will deliver the energy in to sound waves much more effectively when driven in and out, rather than to and fro. Of course there is the long dipole Alan mentioned (the 1,0 mode?), but that's prominent only at pretty limited frequencies.

Then again, there's little dispute that a steep neck angle and tall saddle will affect changes in timbre, and seemingly volume as well, though I've neither seen nor done any controlled testing here. Is this a change in static forces or "loading" of the top, or by influence of dynamic forces, indicating tension change may carry more influence than I credit it for? Is it more due to a change in boundary conditions by the increased break angle? I dunno. This may segue from the original question, but I'd be interested to hear Alan's views on this.

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Eschew obfuscation, espouse elucidation.

For the record, Siminoff's testing was on a steel string, drednaught sized guitar. I will say after re-reading the test in the book that it is difficult to make a comparison as he did. The shape of teh aluminum bracket he used created a 2" (roughly) moment arm amplifying the tension in the rod and this moment arm didn't exist when the rod was connected vertically to prevent the bridge/sounboard from bouncing. So how does one make an apples-to-apples comparison? Also, in the horizontal position (that prevented the bridge from rocking) the tension in the rod was not only pulling against the stiffness of the soundboard and bracing, but also pulling against teh tension of the strings which isn't teh case when the rod was rotated to the vertical position. Roger didn't mention the frequencies he used for the test. So maybe this wasn't the ideal test.

David, interesting point about the neck angle and the saddle height.

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Formerly known as Adaboy.......

Daryl Young asked:
"are you saying that the change in the transverse force is greater than the change in tension? I'm assuming the change in force or change in tension is what drives motion either rocking or bouncing."

Right; I should have said the 'transverse signal has much higher amplitude than the tension change signal', or something like that.

"Essentially all modes will have part of the top moving one direction and another part of the top moving the opposite direction with the node line between wouldn't they? Is there a node where the entire top moves like a loudspeaker with no node lines? If so, is the rim of the guitar essentially the node line? Seems this would be for a very low frequency only......"

The 'main top' resonant mode is the one that's moving like a loudspeaker cone, with the edge of the top and the waist bar as the node (more or less). It usually comes in around the pitch of your open G string, so it's mid-range at best. It's actually the higher frequency part of the 'bass reflex couple', fabled in song and story.... Many researchers feel that most of the actual power output of the guitar is developed by the bass reflex couple.

There are lots of higher order modes that move multiple areas of the top. Some of them, like the 'cross tripole' mode, are fairly effective radiators of sound by themselves. Others, particularly the top 'long dipole' can couple effectively with an air resonant mode in the body to produce a fair amount of sound at some pitch. The back, and even the sides and the neck, can get into the act.

David Collins brings up some interesting points. I did not test the transverse/tension signal ratio for different amplitudes: I used a 'wire break' technique to pluck the strings with a reproducible force at a known location and direction, but only used one size of wire. I did try the same strings at different tensions, and found that the tighter a given string was, the higher the transverse/tensin signal ratio. For steel strings the ratio ranged from about 1:1, for a plain steel string tuned the G=196, to about 6:1 for the same string tuned about an octave higher. With a plain nylon string the ratios ran from about 3:1 to almost 9:1 for roughly the same conditions. Plucking at a different location on the string also gave different Tr/Te ratios.

He wrote:
"Then again, there's little dispute that a steep neck angle and tall saddle will affect changes in timbre, and seemingly volume as well, though I've neither seen nor done any controlled testing here."

I looked into that one. It has been claimed that a high neck angle, approaching 5* upward, will work in much the same way as a harp, with the tension change pulling the soundboard and driving the 'main top' mode directly. This certainly does happen on harps: I was able to measure the effect, again using a wire pull pluck, and looking at the content of odd and even partials when the string was plucked exactly in the center. When you do that, there should be only odd-order partials in the transverse signal, and even order ones in the tension change. On a small harp I saw both sets of partials in the radiated sound, and the odd- and even-order partials decayed at different rates, indicating that they were coupled differently with the soundboard. Tilting the neck of one of my 'test mule' guitars up, so that the strings pulled upward on the top by 5*, and repeating the same sort of wire pull, there was no appreciable content of even-order partials in the signal. At such a low angle the tension change could not drive the top effecively.

A tall saddle does alter the proportion of the even- and odd-order partials: the higher the saddle, the more even order partial energy in the tone. The reason seems straightforward: more leverage.

I have read about Siminoff's test. On the face of it, it makes little sense. I've done a similar test, using an electromagnetic driver to force the string into motion in one plane. When the string vibrates 'parallel' to the plane of the top the output is much less (iirc, about 10 dB) than when the string is vibrating 'vertically'. This is directly counter to his results, or so it seems.

It has occured to me, though, that he states in the run-up, as a fact, that 'the strings move parallel to the soundboard'. For strings moving in that way, his results would be exactly what I'd expect. It's possible that when he carefully plucked the strings he made sure that they were only moving parallel to the soundboard, and that's why he got the results he did.

Why does he think they move that way? Perhaps it's because that's the direction the pick moves. I'd suggest that that is a faulty conclusion: I have a cam in my car that goes 'round and 'round, but the valves it is connected to go up and down. The pick is a sort of cam, that converts at least some (and often, a lot) of the horizontal motion of the arm into vertical force on the strings. String normallt start off with sme component of motion in both directions, and the plane of motion rotates over time, probably due to motion of the top. Strings on a rigid rig keep going in the same direction a the signal decays.