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A few recent threads have got me thinking - the one on ebony, and Lance's pinless bridge one.

What are the main elements of the energy transfer from strings to the top in the saddle/bridge area in a steel string guitar with fixed bridge and how does this follow on into how bridges should be designed?

For example is the transfer one of vibration from the strings into saddle/bridge vibration then into top vibration and then air movement in the box - in which case I can see that a bridge whose wood "dampens" this vibration transfer through type/weight would be a "bad thing"? Or is it through a rocking/pumping action of the bridge - in which case the "damping" issue might not be the big thing and ebony "could" have advantages. Or is it a combination?

Leaving aside the pratical structural considerations (but bringing them back in later) should the bridge have a small footprint on the top side to side and front to back to aid the transfer (leaving more of the top free to vibrate) or is a bridge with long wings more efficient?

Does pinless vrs pinned impact the transfer?

Also is a better shape for the bridge in cross section an aeroplane wing type with more gentle parabolic type curves or thich were the saddle is scalloping down to the wings?

Apologies if these are lurking in the archives in which case point me in the right direction.

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Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

I just _know_ I'm gonna get flak for this, but I can't help but post a reply: it's a disease, really....;)

To cut to the chase: as far as I can tell the _main_ 'job' of the bridge is to tell the string how long it is, so it will 'know' what pitch to make. All of the math that predicts what a string does is built on the notion that the ends don't move at all, and as soon as they _do_ start to move you've got problems with intonation, wolf' notes, and so on. Of course, if the bridge was heavy/stiff enough so that it didn't move at all, you'd never hear the guitar, so in practice it's all a compromise.

In that light you could look at the bridge as being the biggest brace on the top. It weighs about as much as all of the other bracing put together, but, because of the way it's designed it (usually) doesn't add as much stiffness as it does mass. If you find the 'main tap tone' of the top before you glue on the bridge and then check it afterward you'll usually find that the pitch has dropped some. On my guitars it's normally about 1/2 semitone.

I'm still mulling over some measurements of the string forces I made back around the end of last year. Almost all of the physics books that talk about the forces the string exerts on the bridge start out with a simple model, like a big nut slung between two rubber bands. They show that pushing the nut aside causes a sideways (transverse) force that is proportional to the displacement and also a pull from incresed tension that is much smaller than the transverse force, and non-linear (there's a 'squared' or 'cubed' term) . Since the tension change is 'small' and is hard to deal with mathematically they just toss it out. The only book I have that treats the tension change at all is Fletcher and Rossing. "The Physics of Musical Instruments". They actually calculate that tension change at around 10% of the transverse force, or a bit less, iirc.

I set up a test rig to measure the two forces last winter, using piezo sensors. Unfortuneately, piezos don't measure force, they measure the change in force, and I've had to play around with ways to convert one to the other (yes, that's an integration...). So far it looks as though F&R were about right, with a couple of 'interesting' little twists that have had me scratching my head.

As further preliminary: most of the 'tech' folks I know who have thought much about it seem to be of the opinion that the break angle of the strings over the saddle is not too important in sound production, provided it's big enough to keep the string in good contact with the saddle top. There's a discussion in Dave Hurd's book about this, and I'm sure we could go 'round and 'round all week (hi Mario!). One of the big issues is that it's difficult on a given instrument to change the break angle and saddle height off the top indepedantly, so if the tone changes it's impossible to assign the blame, so to speak.

So most of the acoustic force exerted by the string on the bridge saddle is 'transverse': that is, it's across the line of the strings' axis. If the string is moving 'up and down', directly toward and away from the soundboard, then that force is pushing the top in and out like a loudspeaker cone, and that seems to be the most effective way to produce sound. If the string is moving at some angle the effective force on the top is less, of course. In the real world the string seems to 'orbit' or 'precess' over time, no matter what angle it started with, so the sound tends to 'come and go' a bit.   

There is a 'small' tension change force that pulls the top of the bridge toward the neck twice for every cycle of vibration of the string (and at multiples of that, of course): for the low A string that's 110 'downward' pushes and 220 'torquewise' pulls per second. The bridge blocks most of that torquewise energy from getting into the top below the pitch of the 'top long dipole' resonance, which is usually around 350 Hz (F, first fret on the high E). Becuase there is significant 'phase cancellation' involved with this sort of dipole mode the torquewise driving doesn't add much power to the output at low frequencies, but it certainly can make a difference in the overtones. That's probably why raising the saddle changes the tone: more leverage.

In 'The New Science of Strong Materials' (cussed if I can remember the author's name) he points out that the strength of a glue line in shear depends on the highest stress level that is reached at the leading and trailing edges. This depends critically on the length of the joint along the direction of pull. Martin went to belly bridges when the straight ones started to pull up too often (partly, I'm sure, becuase they 'toothed' them on the bottom, but that's another story). Martin's belly bridges have a smaller total 'footprint' area than a lot of classical guitar bridges, but you would not have much luck putting steel strings on a classical guitar owing to the narrower width. The 'belly' reduces the max stress at the back of the bridge to well below the peel strength of the glue, and it holds (mostly).

In acoustics we tend to use the term 'damping' to mean the energy that gets 'wasted': dissipated in friction and so forth. A heavy bridge doesn't so much 'damp' the sound as it keeps the energy in the string. You tend to end up with a lower level and longer sustain, but the total in horsepower/hours is the same. We're in deep danger of seeing the word 'impedance' used in a sentance here, and that's usually a good time to bow out of one of these posts.

The bottom line for me is that the bridge has to be wide enough (deep along the line of pull) to stay glued down. That's going to depend on a lot of stuff like how good you are at using whatever glue you use, and how well the wood of the top holds up against peeling stress. The length (across the top), mass, stiffness, and so forth, all influence the tone in ways that will be hard to predict in any detail for a specifc design, since they often have to do with the way _this_ bridge ties in with _that_ top and bracing to drive the air around _this_ body. You can get a roungh feel for this stuff pretty quickly, and guys like Mario who build a lot of guitars and swap out bridges frequently can develop a pretty refined sesibility, but I find that sort of thing has to be learned, and can't be taught very well. Physics can give you some broad general rules about the direction a particular change might take you in a given case, but can't tell you what that will 'mean' in terms of tone quality beyond some rough guidlines, owing to the subjective nature of tone perception. And now this post has definetly gotten too long....

Al,

You'll get no flak from me, and make the post as long as you like - as usual it is full of relevant and interesting stuff!!

A few follow-on/clarifying questions if I may (feel free to ignore):

You say that a heavier bridge keeps the energy in the string more(lower level but longer sustain) but the horsepower/hours stays the same. Does this mean the same energy gets transfered eventually but over a longer period (more sustain)?

How do you think this effect would alter as you go from a flat top to a heavy cylindrical arched top such as in a Sobell?

If the main purpose is to tell the strings how long they are, then is it best to have most of the bridge mass concentrated where the strings are (the saddle) and then "sculpt" away from there in ways that minimise sheer stresses on the glued bridge?

Does having the strings anchored downwards through the top (pinned) rather than at more of an angle at the back of the bridge (pinless) do a better or worse job of telling the strings how long they are?

Thanks again for your responses - as you say putting ots of different bridges on a test guitar is the way to go and what I will do.

_________________
Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

Dave White asked:
"You say that a heavier bridge keeps the energy in the string more(lower level but longer sustain) but the horsepower/hours stays the same. Does this mean the same energy gets transfered eventually but over a longer period (more sustain)? "

Yes, all else equal. Note that there are losses directly from the string, such as viscous damping in the air and the loss within the string material itself (which is much greater for nylon than steel strings, iirc), so in fact the longer sustain gained from a heavier bridge does come at the expense of a little overall output.

"How do you think this effect would alter as you go from a flat top to a heavy cylindrical arched top such as in a Sobell?"

Generally it would be the same, but the details will vary a lot from one guitar to another. This is where we really do need to talk about impedance.

Acoustic impedance is the ratio of Force/Velocity at a given frequency at a certain point. It's just a measure of how hard it is to move something at a given frequency. If you are looking at something simple, like a mass glued to the end of a stiff stick that has the other end fixed, the impedance is determined by the mass, the stiffness and the intrinsic 'losses'. 'Losses', friction and such, add to the impedance at all frequencies. Mass has little effect on the impedance at low frequencies, but that increases as the frequency goes up. Stiffness adds a lot of impedance at low frequencies, and the effect falls off as the frequency goes up. In fact, the 'reactance' of stiffness can become a _negative_ number as you go to higher frequencies. Resonance occurs when the mass and stiffness reactances cancel out, so that all you have to do to keep the thing going is replace any energy that was lost to friction and such. Adding stiffness to a given system raises the impedance, particularly at low frequencies, and pushes the minimum (the resonant frequency) up, while adding mass adds more impedance, particularly at high frequencies, and drops the resonant pitch.

Strings have a 'characteristic impedance' that is determined by their mass per unit length (pounds per inch, whatever) and tension, and has nothing to do with the length. Iirc the impedance you 'feel' when you push on a real string will always be higher than the 'characteristic impedance', but drops to nearly the 'ideal' value at all of the resonances of the string.

Complicated things like guitar tops with bridges glued onto them have complicated impedances. You can't really predict them, all you can do is measure. In general, though, you can say that since the guitar top is more massive than the string and pretty stiff it's likely to have a higer impedance than the strings do most of the time.

That Sobell, or any archtop, gets a lot of stiffness from the arching, so it's likely to have higher impedance at low frequencies than a flat top of the 'same' construction but without the arching.

Of course, if the bridge is sitting on a spot on the top that is moving for a particular resonance, then the impedance of the bridge can be quite low at the frequency of that resonance. For example, the 'main top' resonance, which is roughly like a loudspeaker moving, moves a lot where the bridge sits, so the impedance is relatively low at that pitch, which is often around the open G string. If the G string has the right weight and tension so that it's 'characteristic impedance' is close to that of the top at that pitch the energy can get out of the string in a hurry, and you'll end up with a note that as no sustain to speak of. Anything you can do to increase the mismatch in impedance between the bridge and string, such as using a different string gauge, or adding weight to the bridge, will help.

Now, adding weight to the bridge will also change the pitch of the top resonance. Adding stiffness will raise it. Swapping a rosewood bridge for an ebony one of the same size and shape will usually increase the weight more than the stiffness, so the resonance pitch will drop and the impedance will be higher. You might experience a more 'bass balanced' sound with more sustain (or maybe not). Changing the shape of the bridge can change the stiffness, and the way it's distributed around the top, so that the 'brace' function changes. This can shift many of the top resonances around, depending on all the usual variables.

"If the main purpose is to tell the strings how long they are, then is it best to have most of the bridge mass concentrated where the strings are (the saddle) and then "sculpt" away from there in ways that minimise sheer stresses on the glued bridge?"

Good question: cussed if I know the answer. A _hard_ saddle seems to make more difference than a _massive_ one, but then, you can't really pick and choose among, for instance, saddle materials of the same density but different hardnesses. That's one reason I don't know the answer.

"Does having the strings anchored downwards through the top (pinned) rather than at more of an angle at the back of the bridge (pinless) do a better or worse job of telling the strings how long they are?"

I don't think there should be any difference, but I know there are people who will disagree. My own feeling is that once you've set the breakover angle it shouldn't matter what goes on 'in the back room' so to speak, at least in terms of the way the strings vibrate.

Finally, you _can't_ think of the bridge as something seperate from the top. It's not even that they 'work together': the bridge is a main top brace, and a big lump of mass on the top. A bridge shape that might be 'perfect' for a given top might not work well on another top. Understanding the priciples of wat the bridge's 'job' is and how it works as part of the top should help to home in on what's 'best' in a given circumstance.

That wind-like sound you're hearing is everything Alan just said going WAY over my head.


Al, it's a good thing you're around or I wouldn't learn anything beyond the basics!

_________________
"I want to know what kind of pickups Vince Gill uses in his Tele, because if I had those, as good of a player as I am, I'm sure I could make it sound like that.
Only badly."

Alan,

Many, many thanks. I get the gist but am going away to digest the details more fully. In particular the impedance. I build guitars whose tops have big arches in them (similar but not as extreme as in Stefan Sobell's) and use Macassar ebony bridges that generaly weigh in at between 25-30g. Having read the usual stuff about ebony damping I tried a Braz Rosewood one that was much lighter and the G and D strings became very "honky" like a resonator guitar and this only went away when I added more mass to the bridge (using Blu-Tac). This may be something to do with the impedance you mention around the top resonant frequency. The arching of the top and the large soundhole I used that is shifted up in the upper bout raise the pitch and the heavier bridge I suspect works well with this combination.

Anyway - thanks again.

_________________
Dave White
De Faoite Stringed Instruments
". . . the one thing a machine just can't do is give you character and personalities and sometimes that comes with flaws, but it always comes with humanity" Monty Don talking about hand weaving, "Mastercrafts", Weaving, BBC March 2010

[QUOTE=Don Williams] That wind-like sound you're hearing is everything Alan just said going WAY over my head.


Al, it's a good thing you're around or I wouldn't learn anything beyond the basics![/QUOTE]

I'm with you Don....whoosh! However, the more times I read Al's posts the more I am starting to understand the physics involved in construction. Keep the posts coming Al!

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Don Atwood
Arlington, VA

You wouldn't beleive how long it took me to start to get a handle on the concept of impedance, and I'm still trying to figure out how to explain it without going right off the deep end. What did it for me was actually doing some demo experiments, in the process of writing the plate tuning articles for American Lutherie. Once you get the feel for it, it all makes sense, even though it can be hard to explain. I'll keep trying, though...