MIMF

A Bridge might look simple but analysis is not
One other problem with the way you are looking at it Louie, is that the string is not attached to the top of the saddle, so you cannot just treat the saddle as a "lever arm". Depending on the break angle and other aspects of geometry including saddle width and shape, there will be some lateral force exerted but it will not be string tension times the height of the saddle.

Alan, very interesting work! Were you able to discern from your test subjects, aside from what they sensed audibly, as to what sounds they might have found more pleasurable to the ear?

Jeff I realize that on a traditional bridge (that's not worn) the strings are not restricted to move (or possibly roll) laterally on the saddle, other than by sheer pressure. This is seen to the extreme in the case of Mark Swanson's client described above. I would propose that this problem is multiplied, in that case, by the fact that since the saddle is radiused to some extent, the high E is laying on a downward slope laterally, and would be susceptible to move in that direction. Mark explained how 'slotting' the string seemed to cause a loss in volume and brightness. I would wonder if 'reversing' the curve at the saddle at that point, so it starts sloping UP past that E string, would help counteract any tendance for the string to slide or roll in that direction, without making a noticeable change in sound (loss of brightness...) In fact, thinking about this now, I wonder if that would make a difference on the B string as well?

On my saddle design, my intent was to create the saddle in such a way that it DOES act as a lever of sorts. That a traditional bridge does not work in this manner is entirely my point. This is why it's slotted along its entire spine, to restrict it's movement relative to the saddle as much I can. I know that this analysis is a bit simpleton, until I can afford the time or equipment to do more "scientific" tests.

Louis Atienza asked:
"Were you able to discern from your test subjects, aside from what they sensed audibly, as to what sounds they might have found more pleasurable to the ear?"

We deliberately did not ask that question, since it would have complicated the analysis a lot, and required a much larger sample to sort out. Some people did volonteer that, but I didn't note it down. As it was, we got about 100 samples of each comparison (A to A, A to B, A to C, and so on), and that took a fair amount of time, and arm twisting of my students.

"On my saddle design, my intent was to create the saddle in such a way that it DOES act as a lever of sorts."

But the saddle is a lever: it can't help but being one, since it's above the neutral axis of the top structure. I looked at the top deflection under load on my test mule, and with the strings higher off the top it was greater: the taller saddle had more leverage with the same strings. That looks to be the main reason why the guitar sounded different with the taller saddle: the different force components of the vibrating string had their effectiveness altered, and that changed the sound.

The thing is that there's a lot to sort out in this. The taller saddle gave greater static deflection, which means a different pre-stress on the top. One thing this changed was the actual resonant mode frequencies of the top, so the relationships between the string modes and those of the top were changed. It also seems to have effected how much amplitude you got from a given mode for a given input of force; some pitches were easier to drive and some harder with a taller saddle. All of this got to be very confusing at times. All I checked in this test was the open string pithes; to sort out some of the effect of the resonant pitch changes, for example, would require testing a lot more notes, probably everything up the fourth fret. One controlled pluck takes a few minutes to set up and record; doing all of them would take more than a week, since you need multiple examples of each one. Then there's the listening tests (with five times as many notes, you might need five times as many of those, too), all the other data gathering, and the statistical anlaysis. Now that we know what to look for, my statistics guru and I could probably get through much of this relatively fast compared with last time, but it would still be a lot of work.

"I know that this analysis is a bit simpleton, until I can afford the time or equipment to do more "scientific" tests."

The equipment you'd need is probably fairly simple. The worst part is the time; not just the time to do the experiments, but the time to do them enough times so that you get good at it. You'd be surprised at how much your error rate drops with some practice. The big time waster for me is just trying to figure out what the heck I'm looking at, and how to ask the questions so that I can get answers. It's like a lot of riddles: you can stew on it for weeks, and then, when you see the answer, it's so simple you spend another day or two kicking yourself for not seeing it sooner. That's the stuff that doesn't get into the scientific papers, but it's the part that takes the most time. Gabby Weinrich said that the problem with science is that you're always doing something you're not good at, and that's so true...

Alan Carruth / Luthier

Alan Carruth wrote:
But the saddle is a lever: it can't help but being one, since it's above the neutral axis of the top structure. I looked at the top deflection under load on my test mule, and with the strings higher off the top it was greater: the taller saddle had more leverage with the same strings. That looks to be the main reason why the guitar sounded different with the taller saddle: the different force components of the vibrating string had their effectiveness altered, and that changed the sound.



Alan Carruth / Luthier

I would not see the SADDLE as a lever in itself since the string is not fixed to it. It acts primarily as a strut between the string and the bridge(with some lateral forces depending on the break angle and other aspects of the bridge geometry)

The Bridge/saddle combination however does exert leverage on the soundboard and this is roughly proportional to the height of the strings above the soundboard

Alan Carruth wrote: But the saddle is a lever: it can't help but being one, since it's above the neutral axis of the top structure. I looked at the top deflection under load on my test mule, and with the strings higher off the top it was greater: the taller saddle had more leverage with the same strings. That looks to be the main reason why the guitar sounded different with the taller saddle: the different force components of the vibrating string had their effectiveness altered, and that changed the sound.

The thing is that there's a lot to sort out in this. The taller saddle gave greater static deflection, which means a different pre-stress on the top. One thing this changed was the actual resonant mode frequencies of the top, so the relationships between the string modes and those of the top were changed. It also seems to have effected how much amplitude you got from a given mode for a given input of force; some pitches were easier to drive and some harder with a taller saddle. All of this got to be very confusing at times. All I checked in this test was the open string pithes; to sort out some of the effect of the resonant pitch changes, for example, would require testing a lot more notes, probably everything up the fourth fret. One controlled pluck takes a few minutes to set up and record; doing all of them would take more than a week, since you need multiple examples of each one. Then there's the listening tests (with five times as many notes, you might need five times as many of those, too), all the other data gathering, and the statistical anlaysis. Now that we know what to look for, my statistics guru and I could probably get through much of this relatively fast compared with last time, but it would still be a lot of work.

Jeff Highland wrote:I would not see the SADDLE as a lever in itself since the string is not fixed to it. It acts primarily as a strut between the string and the bridge(with some lateral forces depending on the break angle and other aspects of the bridge geometry)

The Bridge/saddle combination however does exert leverage on the soundboard and this is roughly proportional to the height of the strings above the soundboard

Jeff, I think I agree with you on this point, at least on the direction of string pull. Since the string "pushes" down on the saddle, it's actually the bridge itself that 'levers' against the soundboard, along the point of the front edge of the bridge. One could affect this by either making the saddle taller, thus effectively making the string pull more tangental to the rotation of the bridge, or putting the string holes as close to the saddle as possible.

Alan I believe I could set up a test to accurate record and pluck a string as many times as possible, using my CNC as the guitarist. It wouldn't be hard to write a subroutine that "plucks" a string while simultaneously triggering a relay that turns a recorder on/off. The hard part is actually having the time and desire to do this! In this way, though, I could make hundreds of samples autonomously, in a way that would be difficult to do consistantly by manual means. Having volunteers listen to the same notes over and over for an hour may bring me to my death!

Louie Atienza wrote:
Jeff, I think I agree with you on this point, at least on the direction of string pull. Since the string "pushes" down on the saddle, it's actually the bridge itself that 'levers' against the soundboard, along the point of the front edge of the bridge. One could affect this by either making the saddle taller, thus effectively making the string pull more tangental to the rotation of the bridge, or putting the string holes as close to the saddle as possible.

Louie, the amount of saddle protusion is not relevant to bridge torque, it is the combined bridge /saddle height that matters. Likewise the position of bridge holes does not change the bridge torque.
I looked at this a few years ago,It's not simple and one guy on a forum tried testing it and confirmed that hole position did not affect torque but many still did not believe it,
It is the sort of problem you would give to a class of second year structural engineering students to analyse and expect half of them to get it wrong.

Jeff Highland wrote: Louie, the amount of saddle protusion is not relevant to bridge torque, it is the combined bridge /saddle height that matters. Likewise the position of bridge holes does not change the bridge torque.
I looked at this a few years ago,It's not simple and one guy on a forum tried testing it and confirmed that hole position did not affect torque but many still did not believe it,
It is the sort of problem you would give to a class of second year structural engineering students to analyse and expect half of them to get it wrong.

I agree that the whole system has to be taken into consideration. But the strings still exert a component of both downward and pull on the saddle, in addition to the combined unit of saddle/bridge/string acting on the top. So, the way I see it, going by the way things are attached, the string exerts both a downward and 'nutward" force on the saddle. The bridge/saddle system will 'torque' the top as well, but that is a separate but related analysis to the saddle/bridge.

If you don't believe that there is no correlation between string hole location and 'saddle torque', consider the extreme example with a high saddle of regular thickness, and the string holes right next to the saddle so that the strings rest against the saddle. I predict it wouldn't be long before string tension causes the saddle or bridge to snap. Now consider the other extreme, where the bridge extends all the way to the butt of the guitar, with the string holes all the way by the neck block, and strings resting on top of same saddle. There is almost no 'nutward' pull on the saddle, almost all force of the string is pushing down on the saddle.

Now as far as the hole locations affeting torque at the BRIDGE, I agree it doesn't make a difference, because it's actually the width of the bridge and height of the strings off the soundboard (and to an extent how far past the saddle the bridge extends toward the soundhole) that would affect the torque of the bridge on the soundboard. It's obvious to me that moving the string holes ouldn't significantly affect this, aside from any flex in the bridge. But it DOES affect how much downward and forward force is placed on the saddle itself.

Gotta bow out, this discussion is making no sense

Jeff sorry to hear, I value your input and it helps keep me thinking, for better or worse I guess.

I'm sorry I don't have an engineering degree to explain my thoughts in a way that's understandable. But the plainest way I can describe is that most analysis of the bridge treats it as one piece. And in it's purest form, it could well be. But it's not. But it seems every analysis of the bridge treats it as one piece. So I have to ask why? And to extend that thought, why not build a bridge with that in mind?

I apologize for "sucking you in" to this conversation...

Louis:
The easiest way to get a uniform and reproducible pluck that I know of is to loop a length of fine magnet wire under the string and pull upward until it breaks. I've been using this for some time now, and made a little solenoid operated plucker so that I can trigger it from my computer desk. I just hit 'record' on Cool Wave, push the button, and hit 'stop' a couple of seconds later. Then it takes a few minutes to set the plucker up again. The nice thing about this is that you can pluck with the same force, in the same place, and the same direction, every time. All the mechanical picks I tried were not nearly as uniform or controllable.

I recently took the time to measure the breaking strength of the wire I've been using, which came from an old (WW II) relay. In eight trials I got an average of 160.2 gm., with no trial being off that by more than 2%. Not bad for a jury-rigged test setup.That wire is darned uniform.

Start with a string that is parallel to the soundboard, supported on the top of the saddle. All of the string pull (call that 'T') toward the saddle will be acting on the top of the saddle: it has to, or you would not get the right note from the string. If the string is assumed to have no friction over the saddle top (which is the usual convention to simplify the math) then the back string as it goes down to the string hole will be under the same tension as the vibrating part. The resultant force acts along the bisector of the break angle (call that 'A'), so it poins forward from the saddle toward the nut. You can resolve that into two vectors: a 'tipping force' equal to T*(1-cosA). The downward force perpendicular to the soundboard will be T(sinA), and there will be an upward force equal to that on the back of the bridge. The glue line between the bridge and the top will feel a force equal to the tension. As the break angle increases, the tipping force rises, but the actual leverage on the bridge itself (which is normally taken to be 'rigid') will not increase if the string height off the top is unchanged.That is, if the break angle is 90 degrees over the saddle top, sand the saddle is perpendicular to the top, it will feel the entire tension of the sytring trying to tip it over, but, so long as the front of the slot holds, it will simply transmit all of that force to the bridge, to act as a torque on the top. What does change with a change in break angle is the apparent center around which the torque of the down and up forces acts: as the angle increases this 'centroid' moves towad the saddle, so, in that 90 degree case, it would probably be right behind the saddle. Finally, if the saddle is actually tilted back at the bisector of the break angle, there is no net tipping force at the saddle top. This is how violins can get away with such tall skinny bridges.

To reiterate: all of this assumes a 'rigid' bridge, and, I suppose, a 'short' length of back string. In that case once you know the height of the strings off the top, and the break angle, you're there, and what the string does behind the saddle top doesn't matter. Of those two things, the one that really seems to matter is the height of the string off the top. In my tests poeple couldn't do much better than guesswork in trying to tell the sound apart when the break angle was changed without changing the string height off the top, but they were well able to pick out the difference when the string height was changed without altering the break angle.

Alan,

Thanks for the info. I plan (one day) to make a fixture for the guitar on the CNC. I can very accurately control the velocity the string is plucked and even the approach and escape angles, in 3D. It would be just a matter of telling the controller program to activate a relay to start and end record. The axis would have to start a distance away so that at string attack the velocity woll be exactly the same. Even with the magnet wire I can do this with CNC...

I guess the questions I have for you are: Does the "torque" the string imparts on the saddle have anything to do with the sound produced? In the bisected angle example, would there be a perceptible difference in sound? And then in the extreme condition with the sings at 90 degrees to the bridge out of the string hole, would that tipping force be a benefit or detriment to the sound?

Louis Atienza asked:
"I guess the questions I have for you are: Does the "torque" the string imparts on the saddle have anything to do with the sound produced? "

This gets complicated. The static torque by itself does not alter the dynamic forces the string exterts on the top of the saddle. However, changing the static torque, either by changing the string height off the top or, to a much lesser extent, by moving the 'centroid' of the rotation, could well change things like the resonant pitchs of various top modes, or the mobility of the top. We saw some of that in our experiements. Since a string will be more effective at driving the top near a resonance, altering those pitchs can change the sound. Ditto if the top becomes easier or harder to move.

Also, the tension on the string rises twice per cycle, and this rocks the bridge toward the nut. Again, depending on the pitch of the sound produced, and the mobility of the top, and the effectivness in producing sounde of the resulting motion, the sound can change.

Finally, there is a high frequency longitudinal compression wave generated in the string when it's plucked off center in it's length, usually up around the 7th or 8th partial of the transverse fundamental (the pitch you tuned the string to). This acts like the tension force on the top of the saddle, and should also produce some sound subject to the same constraints.

We saw evidence of all of these things, but don't have enough data to be able to sort it all out fully.

"In the bisected angle example, would there be a perceptible difference in sound? "

Not having done that particular experiment, I can't say for sure. I do use a 9 degree back angle on the saddle on my guitars these days, to cut down on the splitting out force on the front of the saddle slot, and also to minimise intonation adjustments when the action is raised or lowered. I can't say there's been any change in the sound of my guitars since I started doing that, and I don't see how it could effect the acoustic sound. It does make USTs work better, since it increases the down force on them.

"And then in the extreme condition with the sings at 90 degrees to the bridge out of the string hole, would that tipping force be a benefit or detriment to the sound?"

I don't think it would be a benfit, and if it splits out the front of the saddle slot, that would certainly hurt the tone.... ;o)

Alan Carruth / Luthier

Alan, could you spell out what "USTs" are for those of us unfamiliar with the acronym? Thanks.

Under Saddle Transducer, piezo pickup

Hi Louie,
If you do pursue testing this bridge design can I make a suggestion? Try limiting the scope of your testing.
The tests that Alan described have a very general scope, like the affect of string height or break angle on ANY guitar. Fact is, you're dealing with a guitar that has (if I remember right) 1. new bracing pattern, 2. phenolic sides, 3. multi-scale, 4. new bridge design, 5. taller than normal saddle,.... Picking out what did what at this point is just a guess.
If you want to test just a bridge design change, how about making the change a single removable feature? If you could make the string guide you're discussing a removable feature, with everything else constant, you can listen to what that one feature adds to your guitars.
Good luck...

Dick, thanks for the comments...

At this point, it would be tough for me to do a "one thing at a time" test to see what works/doesn't. Though it would be relatively easy to say, compare lateral and longitudal top/bracing stiffness at the bridge between a typical and my design, for example. Or compare teh volume of my guitar at a certain point on a certain string, compared to another.

The other thing I stuggle with is that, even though I think of analyzing different parts of the guitar "system" I do realize that the sound is a culmination of all parts, regardless of construction or materials. Admittedly, the phenolc was used since it was free and kept the cost of the guitar down! The body was also tapered in two directions, which made me come up with an alternative approach to doing that without making things too complicated or taking too much time (I invested avout 20 hours in the complete construction!) Also the top is very slightly arched, and actually has a slight recarve at the edges.

Much of what I did on this particular guitar came about from my questions as to why a certain part was made this way, why is this braced like that, why is this necessary, what considerations were made in the original guitar designs, etc. There are a couple general thoughts I've concluded about this whole exercise. First, if all these design 'changes' have no apparant affect on sound versus the standard 'sound' I'm happy with that, because that would mean that the aesthetic and mechanical designs could still produce a familiar sound. Second, if the sound pleases those who play and listen to the guitar, who cares if this string is louder or the plate vibrates differently or the frets are fanned? Certainly not the listener (unless they're a MIMF member!)

The only thing that would be detrimental to the design is if the construction led to it's certain demise (as the side construction may indicate) or the sound wasn't pleasing at all. I will say, that as lightly as the lower bout is braced, the top still hasn't budged, and that's with 12-56 strings tuned standard. My band is currently recording, so we hope to feature the guitar on a couple songs. I 've sadly succumbed to the electronic 'guitar-by-wire' revolution and play mainly a piezo-equipped electric through a Roland GR-55, but will be combining those sounds with 'naturally-aspirated' instruments!

Alan, quick question:

I've heard that break angle's important, but never made it a top-shelf priority.

However you mention that string height effects the centroid of rotation. Would installing the ball of the string below the soundboard, and closer to the saddle, as Mario relates, have the same effect?

If so, is this what's behind the talk of break angles and string displacement?

I'm looking forward to your paper.

Tom

Tom Sommerville asked:
"I've heard that break angle's important, but never made it a top-shelf priority."

That's what I wanted to find out in my project. Usually people alter the break angle by changing the saddle height, so there are actually two variables involved, and I tried to isolate them as best I could.

"However you mention that string height effects the centroid of rotation."

My data says that it's the break angle that changes the centroid of rotation. Two setups with the same guitar and break angle, but different saddle heights, had the center of rotation of the bridge in the same place. Changing the break angle but keeping the string height off the top the same changed the center of rotation.

" Would installing the ball of the string below the soundboard, and closer to the saddle, as Mario relates, have the same effect? "

I don't have any data on that. There's some discussion about whether you need to look at the angle between the top of the saddle and the ball, rather than simply citing the angle the string makes over the top of the saddle as the 'break angle'. I used a classical guitar in my experiments, changing the way the strings were tied off to change the break angle while preserving the saddle height. I can't see any reason why a pin bridge would be different; why the simple angle of the string over the saddle top would not be the operative factor, but without data on a pin bridge I can't be sure.

"If so, is this what's behind the talk of break angles and string displacement?"

As the string vibrates up and down it makes an angle that can tend to lift the string off the saddle top. So long as the break angle exceeds this the string will stay in contact. Whether it needs to do more than just stay in touch is a point of discussion: I can't entirely rule out the notion that a greater break angle will transmit more signal to the top, but I'm not entirely convinced that it does, either. As always, more data...

Alan Carruth / Luthier

Al,
Many thanks for your response.

Mario's observations are reasonable: notching the bridge rather than the pin would result in a sharper break angle, shifting
the centroid and obtain generally positive results.

It all depends on what kind of instrument you're trying to build of course.

Again, I'm looking forward to your paper, and grateful as hell to you for sharing a lot of hard work.

Tom

Tom Sommerville wrote:
"Mario's observations are reasonable: notching the bridge rather than the pin would result in a sharper break angle, shifting
the centroid and obtain generally positive results. "

Notching the bridge rather than the pins might indeed make a difference in the break angle, and thus alter the centroid. It's a long way from saying that happens to positing a universal benefit from it. Argument from authority is a logical fallacy, which is why I try to get data.

Alan Carruth / Luthier