Bridge and waist - guitar design theory

[Mark Hammer]

One day, while staring at pictures of a bunch of gorgeous guitars, it struck me how different they could be in the location of the bridge. In particular, I was struck by the variation in how close the bridge was to the waist of the guitar (the narrowest part of the body), as opposed to the centre of the rear half of the body (and please note we are dealing with the more conventional rounded bodies here, not the weird and wonderful).

In part, this is a function of where the neck joins the body, but it is also a function of deliberate changes to body shape. For example, the SG neck joins the body at the last fret. As a consequence of that neck/body joint and the scale of the neck, the bridge is situated very close to the waist of the body. This is in contrast to the Les Paul, which, through its use of a deeper cutaway, joins the neck top the body higher up and thus sets the bridge farther back from the waist; not quite AT the widest part of the body, but fairly close to it. In stark contrast, many of the Rickenbacker guitars, while they too join the neck to the body very high up (if not every bit as high up as the SG), use a compressed body style that situates the waist further forward than one might find on a Gibson, allowing the bridge to be situated even closer to the widest part of the body than on a Les Paul.

So, while the point where the neck meets the body can be a driver of the bridge location, relative to the waist (as illustrated by the SG), one can alter the body shape to effectively situate the bridge wherever you want.

Why should this make a difference? If you think of it, the width of the body, at the point where the bridge is installed, presents a critical mass which defines what frequencies will resonate more and less. We like to think of the SG as having a kind of alto voicing compared to the more tenor qualities of a Les Paul, and tend to attribute it to the different thickness of the body and lack of maple top, but there is also that big difference in how much mass is sitting adjacent to the bridge. You have to ask yourself "Just what is surrounding the bridge, and what is it damping?".

The ES-335 and its derivatives may all look the same, but they can be very different in this respect. I'm looking at a picture of a 335 and its Guild copycat cousin, the Starfire. Where the 335 joins the body at the 20th fret, the Starfire joins at the 17th and sets the bridge further back from the waist of the guitar than the 335 does. Naturally, the two sound a little different.

In general, Fenders tend to have the bridges set further back from the waist than Gibsons, and similar-styled instruments. I suspect that as a result of this, they actually sound warmer than one might expect, given the differential nature of the humbucking and single-coil pickups.

Now, all of this may be no great revelation for many here, but it was for me, and started me to thinking about whether there is any sort of algorithm to describe or predict the behaviour of a solid-body guitar, based on the location of the bridge, relative to the waist vs the "haunches" (widest point of the body). I'd always looked at the instrument from the aesthetic point of view, and ease of upper access point of view, rarely considering that the birdge was situated somewhere different as a result of those design choices.

[Brock Little]

I've often wondered the same thing. There is merit in having the bridge of an acoustic in the centre of the soundboard, but in an electric? Good question.

Somehow I found myself at Minarik's website http://www.minarikguitars.com
This isn't really very helpful to the above question, but they suggest that by having more timber on the heavy string side allows them to resonate more. I'm obviously not getting it. Why would my heavy E string only resonate on one side of the instrument? They then talk about tone chambers inside the body that further the effect. So they add, all important, mass on the upper bout and then go and chop a bunch out for tone chambers...
I think I would sooner just believe in "tonally engineered" hollow sections.

I didn't stay on their site long after reading "The Minarik Inferno is the most scientifically advanced electric guitar ever built." And here I was thinking it was just another wanky looking, queer shaped guitar.

[David Schwab]

I think electric guitars just followed the acoustic counterparts. You can see that a Les Paul is made a lot like an arch top.

Then you take something like a headless Steinberger, and it doesn't follow that design, and it works just fine.

Basses also have the bridge located closer to the back of the body to keep he neck from sticking too far out.

[bbsailor]

One day, while staring at pictures of a bunch of gorgeous guitars, it struck me how different they could be in the location of the bridge. In particular, I was struck by the variation in how close the bridge was to the waist of the guitar (the narrowest part of the body), as opposed to the centre of the rear half of the body (and please note we are dealing with the more conventional rounded bodies here, not the weird and wonderful).

In part, this is a function of where the neck joins the body, but it is also a function of deliberate changes to body shape. For example, the SG neck joins the body at the last fret. As a consequence of that neck/body joint and the scale of the neck, the bridge is situated very close to the waist of the body. This is in contrast to the Les Paul, which, through its use of a deeper cutaway, joins the neck top the body higher up and thus sets the bridge farther back from the waist; not quite AT the widest part of the body, but fairly close to it. In stark contrast, many of the Rickenbacker guitars, while they too join the neck to the body very high up (if not every bit as high up as the SG), use a compressed body style that situates the waist further forward than one might find on a Gibson, allowing the bridge to be situated even closer to the widest part of the body than on a Les Paul.

So, while the point where the neck meets the body can be a driver of the bridge location, relative to the waist (as illustrated by the SG), one can alter the body shape to effectively situate the bridge wherever you want.

Why should this make a difference? If you think of it, the width of the body, at the point where the bridge is installed, presents a critical mass which defines what frequencies will resonate more and less. We like to think of the SG as having a kind of alto voicing compared to the more tenor qualities of a Les Paul, and tend to attribute it to the different thickness of the body and lack of maple top, but there is also that big difference in how much mass is sitting adjacent to the bridge. You have to ask yourself "Just what is surrounding the bridge, and what is it damping?".

The ES-335 and its derivatives may all look the same, but they can be very different in this respect. I'm looking at a picture of a 335 and its Guild copycat cousin, the Starfire. Where the 335 joins the body at the 20th fret, the Starfire joins at the 17th and sets the bridge further back from the waist of the guitar than the 335 does. Naturally, the two sound a little different.

In general, Fenders tend to have the bridges set further back from the waist than Gibsons, and similar-styled instruments. I suspect that as a result of this, they actually sound warmer than one might expect, given the differential nature of the humbucking and single-coil pickups.

Now, all of this may be no great revelation for many here, but it was for me, and started me to thinking about whether there is any sort of algorithm to describe or predict the behaviour of a solid-body guitar, based on the location of the bridge, relative to the waist vs the "haunches" (widest point of the body). I'd always looked at the instrument from the aesthetic point of view, and ease of upper access point of view, rarely considering that the birdge was situated somewhere different as a result of those design choices.

Mark,

Many years ago I acquired a Travis Bean-like aluminum neck from Kramer Guitars in Neptune NJ. I decided to make a custom Tele body to use it. I made the body out of butcher block laminated mahogony .75" strips but did something unusual in the center 4.5" wide block that held the neck and bridge. I cut a .375" thick slit horizontally to implant a hardened alumium .375" thick X 4.5" wide X 12" long, just deep enough for the aluminum neck to mount against. The bridge studs were press-fit fully into the aluminum plate at a machine shop.

This guitar, when fully assembled with all the parts, weighed in at over 11 lbs. It had little string dynamics, meaning all the notes played at about the same level and sustained for a very long time as the body did not absorb very much energy.

Other than the energy that is absorbed from the string through the body, most string damping comes from air friction and heat at the nut and bridge through metal flex friction. Most of the string decay is due to the friction of the string against the air; faster vibrations equal more friction like the difference in air pressure when sticking your hand out of a car window when going slow or fast. That is why thinner strings, that vibrate at a higher frequency, decay faster than strings that vibrate at a lower frequency.

One thing I have not seen or even heard talked about is the following. Extend the neck truss rod to the end of the guitar body with a tension adjustment screw to pull the heel of the neck into the guitar body with a tension adjustment located where the strap pin is normallly located. This could minimize any variations introduced by body shape relative to where the bridge is located. A variation on this could be made with two rods that span the width of the neck to allow traditional pickups to still fit.

This is just a design thought for those who might want to experiment.

Also, this allows the truss rod extension to become a ground return for some creative ways to make the strings an active part of a ribbon-like microphone. A metal nut would need to be electrically connected to the truss for this to work.

Joseph Rogowski

[Sweetfinger]

That is why thinner strings, that vibrate at a higher frequency, decay faster than strings that vibrate at a lower frequency.

Joseph Rogowski

That isn't quite true. You could then infer that lowering the pitches of the strings would increase sustain. If so, a guitar strung with two plain .012's with one tuned to E and the second tuned to an octave down, when strummed, would have the lower tuned E sustain longer than the higher. One could also counter with the argument that the thicker strings have more wind resistance, and therefore should decay FASTER than the thin strings. Its probably a wash. The sustain has more to do with to do with the mass of the string. Your picking hand is able to supply the maximum amount of retainable kinetic energy to every string, but the smaller strings with less mass cannot absorb as much energy as the thicker ones. This energy is then siphoned off primarily by the body of the guitar. I'm not saying that the air has no effect, but that in this case, it is not the cause for differing decay rates.

[bbsailor]

That isn't quite true. You could then infer that lowering the pitches of the strings would increase sustain. If so, a guitar strung with two plain .012's with one tuned to E and the second tuned to an octave down, when strummed, would have the lower tuned E sustain longer than the higher. One could also counter with the argument that the thicker strings have more wind resistance, and therefore should decay FASTER than the thin strings. Its probably a wash. The sustain has more to do with to do with the mass of the string. Your picking hand is able to supply the maximum amount of retainable kinetic energy to every string, but the smaller strings with less mass cannot absorb as much energy as the thicker ones. This energy is then siphoned off primarily by the body of the guitar. I'm not saying that the air has no effect, but that in this case, it is not the cause for differing decay rates.

Sweetfinger,

Check out the following reference. http://www.ee.washington.edu/researc...s/physics.html
Here is a quote from that web page. "Higher frequencies are damped much faster than lower frequencies". In another study, when strings were mechanically vibrated and placed into a vacuum the differences between high and low frequency string vibration durations diminished as the vacuum was increased. This experiment controlled the variable of air friction.

Joseph Rogowski

[Sweetfinger]

Sweetfinger,

Check out the following reference. http://www.ee.washington.edu/researc...s/physics.html
Here is a quote from that web page. "Higher frequencies are damped much faster than lower frequencies". In another study, when strings were mechanically vibrated and placed into a vacuum the differences between high and low frequency string vibration durations diminished as the vacuum was increased. This experiment controlled the variable of air friction.

Joseph Rogowski

In that study linked to above, I think you mis-understand. The high frequency components of the complex waveform are gradually converted to the lower frequencies as the note decays. This frequency shift isn't the same as a drop in sustain time. This study doesn't actually pertain to the differences in decay time between different sized strings at different pitches.

Here the study basically says that it isn't really addressing anything close to the complexities of real-life "on the guitar" string vibration:

"Damped Oscillation

A rigourous analysis of a non-conservative vibration will not be undertaken here. The mathematics are extremely complicated, and were not really vital to the goals of this project. However, there are a couple points of note."

And here, addresses my very point:
"The general effects of friction on the guitar string are not large."

In the other study, did they test different sizes of strings specifically for amplitude decay? I looked for info on that, or anything resembling it, but came up empty. I think that they probably used the same string, but at different tensions, just to show that the effect of air on a vibrating string is a measurable and mathematically predictable effect.
It is true that the effects of air friction on a vibrating string will diminish as you get to near vacuum, and on two equal sized strings of equal mass and length there will be a difference in the effect of air friction on the vibration at different frequencies, but just because it occurs and is measurable or predictable, doesn't mean that it is a significant factor in explaining the differences in sustain for strings of very different masses.

Here's a neat little text which describes the natural damping of higher frequencies in a complex waveform, and also provides the basis for understanding how mass determines how much energy a vibrating object such as a string contains:

http://www.soundlablearning.com/PDF3/chapt2.pdf

[bbsailor]

Your picking hand is able to supply the maximum amount of retainable kinetic energy to every string, but the smaller strings with less mass cannot absorb as much energy as the thicker ones. This energy is then siphoned off primarily by the body of the guitar. I'm not saying that the air has no effect, but that in this case, it is not the cause for differing decay rates.

Sweetfinger,

I am not trying to defend mathematical models that attempt to account for all the variables and constants involved in the conservation of energy, which ultimately must account for the total dissipation of energy in any vibrating string. I was taking a practical approach to relaying my observations about what happens to the energy in a string where I attempted to constrain the density of the aluminum neck with an aluminum plate through the body connecting to the bridge to minimize the energy absorbed by the body in line with the topic of this discussion.

The following article, while not a definitive work, is a good summary of the things involved in string decay. http://www.musemath.com/miscellany/mathModelString.pdf

The author cites three main mechanisms of string decay as:
"1. Resistance to bending of the string
2. Air resistance breaking the movement of the string
3. Transfer of energy from the string to the body of the guitar."

You are right that strings with more mass will vibrate longer but this has to do with the energy and mass they have while moving to overcome the friction with the air when vibrating. The other two mechanisms are still present to a greater or lesser degree on solid body guitars or acoustic guitars or guitars where attempts are made to minimize body energy absorbtion.

Take a coat hanger and bend it back and forth to break the wire through metal fatigue. Then immediately check the temperature of the ends that were previously connected and you might burn your fingers with the heat generated. This is the same thing that happens to lesser degree between the stationary part of the string on the nut or bridge and the freely vibrating sections that are a few mm away. Some heat is generated at these two points and at vaious harmonic nodes where the greatest string flexing occurs.

Anyone who has observed a string vibrating on an oscilloscope can verify that the higher harmonics decay at a faster rate than the primary frequency and lower harmonics. Strings decay in two phases. The attack phase has higher harmonics along with the primary frequency,then the decay phase has the lower harmonics along with the primary frequency. This is because it take more energy to sustain the higher harmonics against the 3 things above that want to damp it or convet its energy.

The guitar low E string on a solid body guitar will continue to vibrate long after you can no longer hear it. Just pick the low E string and place your finger on the body near the bridge or most places on the body and you can feel the string vibrate and even see it vibrate for a few seconds after you no longer hear it. Now try this with the high E string. Some decay measurements that I have reviewed look for the time it takes for the string to decay 25db from its initial level.

So, I'll end this discussion and say you are right!

Joseph Rogowski

[Mark Hammer]

For my part, I look at the body as if it were a speaker cabinet of entirely unknown (or only minimally understood) properties, or properties too complex to boil down to studies of string decay in simple systems. Energy from the string is partially propogated via the bridge into the body, but as a resonant body, whether it has chambers, a centre bock, a thru-body neck, or whatever, that energy distributed into the body does not always exist "in-phase" so to speak. Isn't it at least a teensy bit like a bathtub where ripples of energy travel out to the perimeter and bounce back, cancelling with other oncoming waves? The part of the overall discussion that makes me tilt my head like the RCA Victor dog is whether the tonal properties to expect depend on where in relation to the "middle of the tub" you happen to drop the soap. In other words, the point at which the energy from the strings is transferred to the body to begin its propogation journey.

Seems to me that if you start that journey where the distance between the bridge and the perimeter of the body is short (as in an SG or comparable instrument) you get a different sound than if you start the journey where the distance is somewhat longer. Obviously the nature and composition of the bridge matters, as does the wood's resonant properties.

The "acoustically inert" guitar was somewhat fashionable for a little while. The most well-known exemplar is the Dan Armstrong. It strikes me, though, that the intent of inert body design was to sidestep the challenge of designing around inherent cancellations by ignoring any and all energy transfer to the body. A more conventional resonant body functions to reinforce vibrations in the string, by transferring some reflected energy from the body back into the string. Sort of like a passive Fernandes Sustainer pickup. or at least that's what it seems to me. Much like sex, the two bodies involved - string and body - have to move in concert rather than against each other, and the resulting tone is partly a function of the frequencies at which that happens more rather than less. Those frequencies, in turn, result partly from where the bridge is situated relative to the widest and narrowest parts of the body.

Or at least that's how it seems from my rather modest understanding. I will happily defer to those with more plausible physics explanations at their disposal.

EDIT: Incidentally, thanks for the very interesting discussion and erudite discourse! Enjoying it a great deal.