Bridges - Materials and energy losses

[Paco Jimenez]

I tend to prefer single piece bridges over mutiple part ones. Of course there's always exceptions. But I've never thought too much about it or the causes for it in other terms than overall weight/mass, stiffness (floating bridges on arched tops are still braces somehow, aren't they?), impedance (when I happen to remember about it) and assuming that different materials behave and sound different due to their inherent physical and mechanical properties.

Last night I had a happy accident. I just remembered that every time a wave propagates into a different medium both reflection and refraction happen. Too bad for a guy who studied optics at college, relating waves physics to guitar bridges twenty some years late...

I don't know if refraction would be worthwhile to consider or would have any noticeable impact in overall sound, but I guess reflection actually does. Simplifying it, every portion of energy that doesn't make it through, from the strings to the bridge, or through the bridge to the top is an energy loss. Every reflection is a loss.

The bridge has two or three main functions (three if we consider it as a brace): One is (as Alan Carruth uses to say) telling the strings how long they are, and second, being the link between the strings and the top.

Consider a typical bridge. Let's say a bone saddle, a wooden upper part, two metal adjustable height posts and a wooden foot. We are adding three medium boundaries or interfaces between the strings and the top to the two unavoidable ones; strings-to-bridge and bridge-to-top. All them five will introduce their own reflections, thus three additional energy loss spots. I guess impedance and refractive index must be related somehow.

Subjective preferences and tonal "coloring" aside, it seems that this worths some consideration for multi part bridges. In the case of bridges made of pieces of the same hardwood like those with a height adjustable wedge, my wild guess is that shouldn't be too different from an equivalent single piece bridge of the same material, all else equal, since their refractive indexes should be really close, or almost identical besides there's not two exactly matching pieces of wood.

What do you think, guys? Any insights?

[Alan Carruth]

When thinking about the wave nature of sound you have to keep wave length in mind. That, of course, is a function of the frequency and the speed of sound in the material. We're dealing here with compression waves, not the bending waves we work with in plates, or strings for the most part, so the speed of sound will depend on the density and Young's modulus. For most materials it turns out that the speed of sound is pretty high, and not all that much different from one material to another. That makes the wavelengths for acoustic frequencies very long; much longer than the dimensions of the bridge, for example. In that case there is no appreciable phase difference between, say, the string force at the top of the bridge and the force the foot puts on the top. We're not really dealing with a 'wave' phenomenon here, just a varying force, IMO.

Now, if the bridge flexes to any extent then it can have resonant frequencies of those bending waves in the acoustic range, and those can alter the forces on the bridge feet. This is certainly the case with violin bridges, which act as filters between the string signal and the top, and can be tuned to help shape the sound. Most arch top bridges are much stiffer than that, and their resonances are almost certainly not a factor at most acoustic frequencies most of the time. I do remember working on an arch top guitar that belonged to a friend of mine that had an unpleasant sound. The bridge was a home made version of the usual two-wheel adjustable setup, and the top was very light, to the point where it had sagged a bit in the middle from the down pressure. I made a heavier top, and the sound improved a lot.

Now, obviously, energy will be reflected at a boundary where there is an impedance mismatch. The transverse bending waves of the string reflect off the bridge to maintain the wave in the string, but the 'zip tone' a compression wave within the string material, probably is transmitted into the guitar more efficiently, since, once again, there's not such a large impedance mismatch between the string material and the bridge. OTOH, on arch tops the zip tone can't really drive the top strongly, so it doesn't seem to produce sound the way it dos on a flat top,where the leverage of the bridge rotation causes top motion.

The bottom line, IMO, is that for most arch top bridges you can treat them as a 'lump' of a certain mass without too much danger of leaving anything out. The mass adds to that of the top, determining resonant frequencies and impedance, but I don't think either reflection or refraction is much of an issue in terms of sound transmission to the top unless the bride is notably flexible,as said.

[Brian Evans]

I have virtually no science behind any of my bridge musings, not least because the hours I've spent trying to research how vibration moves through materials and joints between materials has come up no trumps. Nada useful at my level of math. So my personal experiments are purely anectodal. I find that the lighter the bridge, the better it seems to transfer energy. I find that a large footprint on the top dampens transfer and that the smaller the footprint, the better the transfer. Ditto a narrow saddle top and string interface. Ken Parker has made bridges (his are non-adjustable since he has that adjustable neck deal) from softwood, very light, hollow inside, so they appear somewhat large and substantial, are very stiff, but the actual footprint on the top is small, only the perimiter of the base is actually touching the top. I had what for me is an epiphany (but I am easily amused...) when I touched the ball end of a tuning fork to the top of my guitar one day, as you do when you can't find your Snark. The tiniest touch of the ball, light light pressure, and the theoretical surface area of a ball touching a plane surface is zero (a dimensionless point), yet the vibration transfered just as well as when I pressed down quite hard. So I transfered that concept to the threaded posts of a typical adjustable bridge and realized that there is, if the tuning fork analogy persists, all the reason in the world for that to be a completely acceptable "joint" to transfer the minute vibrations from the string to the top - it's a very small surface area, it's very stiff and hard material. So my bridges are now derived from cheap imported ebony blanks that I get from Amazon (I started buying them just to get the adjusters, the whole bridge was cheaper than I could buy the post and thumb wheel). I tweak the top radius and finesse the intonation, I marry the bridge base to the top as normal, but more for appearance, for longevity of the top (so the base doesn't mar the top from physical stress, and I'm quite pleased. I've stopped making non-adjustable bridges, and retired the ones that were on the guitars. Not saying I'm right about this, but it works for me.

[Alan Carruth]

Brian Evans wrote:
" I find that the lighter the bridge, the better it seems to transfer energy. "

I would say that the lighter the bridge the less it loads the top, so it's easier for the top to move. Added mass on the top cuts down on the output more in the treble than the bass, and that might tend to make the thing sound 'louder' since we're more sensitive to highs than lows. The energy in a plucked string is limited, so if you get more sound power out it's likely at the expense of sustain, although there are various ways to look at that.

[Paco Jimenez]

We're not really dealing with a 'wave' phenomenon here, just a varying force, IMO.

The bottom line, IMO, is that for most arch top bridges you can treat them as a 'lump' of a certain mass without too much danger of leaving anything out. The mass adds to that of the top, determining resonant frequencies and impedance, but I don't think either reflection or refraction is much of an issue in terms of sound transmission to the top unless the bride is notably flexible,as said.

Makes sense. I've never had a clear preference about single vs two-feet bridges. I guess the two-feet ones I've used were still too stiff to tell an evident difference. Or at least too stiff compared with the common violin types. I only remember a single case. A guitar had an original two-feet bridge made of plastic and aluminum. I thought that some rosewood would improve the sound for sure and made an IRW one with the typical single feet. The guitar went dead. Choked somehow. I wouldn't believe it. The bridge was lighter than the stock one and had a nice ringing when taped. Went back and forth a few times without any improvement. Then in a hurry got one of those pre-made thingys of some sort of rosewood with two flexible feet intended to fit any arching without much need of fitting, and the change was drastic once again but in the opposite direction. That guitar started to actually sing. I don't know the reasons why this happened but got me thinking that flexible bridges might deserve some testing. Though I never made it so far.

Ken Parker has made bridges (his are non-adjustable since he has that adjustable neck deal) from softwood

I don't remember softwood bridges on Parkers. He used pernambuco and some other stuff, but hardwoods as far as I can remember.

I agree about the contact surface. There's not a lot needed for sound transmission. A good (or enough) contact area is needed to avoid the bridge shifting around and to avoid it dipping into the top.

I find that a large footprint on the top dampens transfer and that the smaller the footprint

This is another area that sould worth some testing. There's quite a disagreement here amongst makers. For one, Jimmy D'Aquisto favored big ones and also Michael McCarthy says:

"The feet are a bit wider (in the direction of the strings) than is typical for a bridge from the classic era, to enhance the long dipole movements."

McCarthy also favors flexible two-feet bridges and uses different wood spices for saddle and feet.

[Alan Carruth]

"... to enhance the long dipole movements."

The problem is that bridge rocking of that sort is, at best, unimportant on an arch top. There are two string 'signals' that can drive the top through that sort of bridge rocking. The main one is a product of the twice-per-cycle tension change of the strings. This is a relatively small signal; about 1/7 the amplitude of the 'transverse' string force on average. On flat tops this can enhance the proportion of sound output of the even numbered partials, particularly the second and fourth, if the strings are high off the top. On an arch top, where the tension is actually taken up by the tailpiece it doesn't seem to make any contribution. I did an experiment on that once.

If you pluck a string exactly in the middle the 'transverse' wave form will have no energy in the even order partials. The reason is that, in order to produce those, the string has to have a stationary 'node' at that point, and by plucking it there you've forced it to be moving. On the other hand, since the 'tension' signal is frequency doubled as compared with the 'transverse' signal, it will only have energy at those frequencies that are even-order partials of the pitch the string is tuned to.

I used a mechanical 'plucker' that provides a known amount of force at a specified location along the string, and drives it in a known direction. Plucking the string just at the 12th fret, in such a way that it starts out moving 'vertically' with respect to the plane of the soundboard, gives driving forces that are as pure' as possible at the top of the saddle.

When you drive a flat top guitar this way the sound output has both odd and even order partials, although there is much less power in the even ones. Flat tops are built to resist this sort of bridge rocking, so there is very little motion for a given force, especially below the 'long dipole' resonant pitch, which is typically around 350 Hz. Since this activates a dipole motion of the top there is a lot of 'phase cancellation' of the sound coming off the areas in front of and behind the bridge, so it's inefficient. And, of course, the forces involved are unbalanced, with the vertical 'transverse' force being much stronger.

On an arch top, there was essentially no output of the even-order partials under the same conditions. The tension change simply was not driving the top in any way to produce sound.

The other string signal that drives the 'rocking' mode of the bridge is the 'zip tone'; a longitudinal compression wave within the string. It's usually up around the 7th or 8th partial, and since it has no direct relationship to the tension of the string it is often dissonant. Again, on a flat top this can drive the top to some effect, depending on the height of the strings off the top, but it doesn't seem to be a factor in arch top sound.

None of which is to say that the long dipole of the top has no effect on the sound; just that on archtops it's not directly driven by the string tension change or 'zip tone' as it can be on a flat top.

One of my customers is of the opinion that the larger and heavier the bridge on an arch top, the better. It certainly should help to emphasize the fundamental, and to produce good sustain. It also drops the 'main top' pitch.

Speaking of which; that's one effect of a high break angle on an arch top. Vertical loading on the top via down pressure on the bridge drops the 'main top' pitch. This possibility was pointed out to me years ago by Joshua Gordis of the Naval Post Graduate Research School. It's related to column loading.

If you have a column that is fixed at the top and bottom it will have a fundamental bending mode resonance at a particular frequency depending on it's stiffness and mass. However, if you put it in compression with a load on the top that pitch drops. In a sense it's the opposite of the pitch rise that happens when you put the column under tension. What's interesting is that the drop in pitch is linearly related to load the column can withstand before it buckles. The fundamental mode pitch drops to zero at the buckling stress, and at half that stress it's down an octave from the unloaded pitch. This has proven to be a useful non-destructive test of truss structures, such as helicopter tail assemblies: you find the unloaded pitches of all the elements, then load it up to 50% and see which ones dropped too much. It's an elegant way of optimizing a structure.

At any rate, the 'main top' pitch on arch top guitars does drop when you tighten up the strings, and the more download the greater the drop. This doesn't happen on flat tops. What's interesting is that the back pitch rises on all guitars, as you'd expect when you think about it. After all the back is under tension. Getting the 'tap tones' right before you string it up may not be as straightforward as you'd like..

[Paco Jimenez]

The problem is that bridge rocking of that sort is, at best, unimportant on an arch top.

That's how I understand it too. Floating bridges don't rock that much, if any. So I still don't get the reasonings behind using transversally wide bridge feet other than adding mass. Some other guys talk about impedance matching or balancing which I don't understand either as vibrations propagate equally in all directions at about the same speeds throughout the bridge for all relevant frequencies and impedance at specific frequencies don't seem to vary that much either. I don't understand how that sort of impedance balance is achieved. Maybe I'm missing something.

One of my customers is of the opinion that the larger and heavier the bridge on an arch top, the better. It certainly should help to emphasize the fundamental, and to produce good sustain. It also drops the 'main top' pitch.

Absolutely. I tend to favor just the opposite to get fast, responsive and dynamic guitars. But my ideal bridge on a specific guitar might be a no go for the next guy and viceversa. Our two different bridges would be getting "the best possible response" from that guitar for our subjective preferences. Even that emphasis on the fundamentals perception is quite subjective. A lighter weight bridge with lower inertia will react faster and will do transients better than a heavy mass slow one. How we like it one or the other is a different story. Back to materials, the guys after that "slow" response tend to favor ebony, which also filters the upper jangle somehow. I guess those guys would love maple too besides the politically incorrect light color for a guitar bridge. I tend to prefer more ringing materials (rosewoods, walnut, pearwood... Well, pearwood doesn't ring that much, but it's light and yields a nice tone). As they say, horses for courses.