Trem bridges - 2 vs. 6

[Prometheus]

I’ve seen the discussion of friction in tremolo bridges many times before, and in my opinion, they’re often just a little off the mark. So let me put my understanding of it forward, and you can tell me what you think.

Let’s look at the 6-screw trem, and so long as it’s a floatable trem based in essence on Leo’s design, a lot of makers’ offerings can be included here. There’s the bridge itself, with 6 holes. And the screws, which are columns arising vertically from the body, nominally in a straight line. And the surface of the guitar top. There are other factors at play as well, and it’s actually more complicated than it looks. But for right now let’s leave it at that, the simplest model.

When the strings are brought to tension, a considerable force is developed, somewhere around 100 pounds. The mounting screws resist this, at the point where they contact the bridge. So these metal components are pressed together, and attempts to moving them perpendicularly to that force will be resisted by friction.

At first there’s static friction, characterized by the force necessary to begin sliding. And then there’s sliding friction, which is the force necessary to keep the movement going. Sliding friction is at most equal to static friction, and practically always less. Think of moving your kitchen table. You first have to give it a bit of oomph to get it “un-stuck”, but once it’s in motion, the required force is less. This is not because the floor was dirty. It's because there's an extra force holding objects together that's not in play while they're moving. But for both these types of friction, the force required to overcome them is determined by the characteristics of the materials. In the simplest of terms, the harder and smoother the materials are, the less the friction. But of course it always varies with the force between the objects. Have someone sit on that table before trying to slide it, and it’ll take a bigger push.

Luckily, with the mechanical advantage granted by the trem arm, and the fact that we have to overcome spring tension anyway, and the hardness of the materials, the difference between static and sliding friction is imperceptible. But it was worth mentioning. So from here on we're really concerned just with sliding friction.

In addition to the amount of force holding the objects together, the force needed to overcome friction also depends upon the surface area of the contact between the items. In general, the greater the surface area, the less force require to overcome friction. This is because there’s less force per unit of surface area that’s pressing the two objects together. So there’s less friction to overcome. So decreasing the pressing force or increasing the surface area will have roughly the same effect. Here’s an extreme example for you. If there was a nail sticking up out of the floor, and you stepped on it, it would go right through your foot (don’t ask me how I know this). A large force (your weight) in a small area (the point of the nail). But if you had several hundreds of nails sticking up, you could lie down on them and have a nap. Swamis used to amaze people with this trick. Even though each individual point of contact is small, they sum up. Yeah, OK, that's not sliding though, is it? Well, for those of you who’ve moved furniture, you know that a big dresser doesn’t slide across carpet very easily on those pointy little feet. But lie it down on its side and away you go. That’s because those little feet were digging in, because the entire weight was distributed across a couple square inches of contact. Increase that contact surface area to several square feet, and friction plummets.

So, I wonder why people claim that 6-point bridges are bad because they have all those friction points. When in fact, they’re GOOD because of that. If you have only two points, then each of them carries 3 times the force that any of the 6-screws does!! So static friction and sliding friction will be GREATER with a two-point system than a 6-point system. You don’t have to agree with me. Go argue with a physicist or an engineer. Good luck. The laws of physics don’t care what you think, what you think you know, what you’ve heard, or anything else.

Here’s a related note about round and “knife” edges. First, a sharp edge is just a round edge with a small radius. Magnify any sharp edge and eventually it ain’t sharp no more. Secondly, a rounder object (larger radius of curvature) will slide EASIER than a sharp object. This is because it’s not as bothered by all the little surface imperfections. Didja ever wonder why the first bicycles had such big bloody wheels? Because the roads and streets they were riding on were awfully rough, and those things had no shocks. A bigger wheel smoothed out the bumps. A smaller (steel!) wheel would have been murder. Wheels got smaller as rubber technology improved. Now, those are wheels, and they’re turning, and we’re here talking about sliding - but the same principle applies. A sharp edge “feels the bumps” more than a larger radius. A knife edge, given the same downwards force, will slider HARDER than a round edge.
Remember that in all this we have largely been educated by what we’ve been told, what we’ve read, or what we found on the net. But a lot of the information regarding how guitars work and what needs to be improved originated from ... the people selling them. And a lot of that has been geared to people who really don’t have an in-depth knowledge of how all the parts of a guitar work, and how they work together. So if an authoritative voice pipes up and says “Well, there’s a problem with yer widget, ‘cuz it’s flim-flam is all wonky, and that’s really bad fer yer tone! But we’ve got just the thing to fix ya up!”... then millions will believe you. And they’ll all tell everyone the same thing. Eventually, because "everybody knows that", it becomes “the truth”. Except that often, it’s not.

Now, if you’re going to design your bridge so that there’s no sliding, well, then pretty much all of this is moot. All you need then is a good pivot axis. This could be a line, or two points, or two or more aligned points. And sure, a knife edge would be fine. But it’s not going to do much good if you seat it in a rounded support. In other words, a knife edge in a cupped recess is still bad, because that knife edge will want to slide around the bottom of the recess. You’d be much better off with a knife edge in a sharp recess, or a rounded edge in a rounded recess. Incidentally, both of these will have about the same (negligible) friction, but the rounded version will be stronger, and less prone to damage and wear, because again the force is distributed over a greater surface contact area.

So then why does it seem that people are gradually gravitating towards the two-point system? A couple of reasons. First, fewer parts. Always a good thing. Secondly, easier to set up. An even better thing. I know that a good-quality 6-point trem bridge can be installed and set up to be strong and stable. But it’s not easy or simple to do. If or when adjustments are necessary or desired, it’s just as easy (easier) for the average non-luthier player to make it worse rather than better. While the two-point system is not foolproof, it is at least easier to get right.

So, using Occam’s razor (everything else being equal, the simpler solution is the better one), the two-point system has the advantage. But other than its complexity, I maintain that there’s nothing “wrong” with the 6-point system either.

 

[stratamania]

I think your Occam's razor answered the point.

Other than that a lot of the six screw trems are not exactly marvels of engineering perhaps if they were it may be different.

The point about overcoming inertia to push an inate object I understand but does it really apply practically because with a tremelo you are causing something to pivot by applying more force than the equilibrium of the springs opposing the spring tension. When released you want to be sure it returns to the point where it started, with six screw trems there are four more possibilities that may not happen.

The Supervee Bladerunner is interesting in that nothing pivots against screws or posts but it's spring steel.

I have tremolos with six screws, more with two posts and a Bladerunner that replaced a poor six screw bridge. Practically I'd rather go with the ones that are more reliable to stay in tune.

And it does depend on what you are going to do with those trems etc.

I don't think it's a gradual move to two point trems either. It happened quite quickly for many looking for a better mouse trap back in the eighties.

 

[Cagey]

You're correct in that spreading the force over a larger area reduces the amount of force per unit. For instance, 100lbs on a 1" square would be 100lbs/sq". 100lbs on a 4" square would be 25lbs/sq". But, you'd have 4 times the area, so you have 4 times the friction. Friction and force are two different things. If things worked the way you present them, then drag racers wouldn't put wider, larger diameter tires on the rear drive wheels. Also, you could theoretically improve the performance of a 6 point bridge by increasing the number of screws to 18.

In reality, trying to use six pivot points instead of two, assuming they're identical pivots, is that you've increased your friction by a factor of 3. In the case of a balance such as the Fender vibrato bridge, this results in an inconsistent return to neutral. It's not that the bridge won't tune, as is usually presented, it's that it won't stay that way, which is arguably just as bad.

 

[swarfrat]

Show me the area term in friction again? The advantage of 2 point is that its Repeatable. 6 point is statically indeterminate. It can't be analyzed statically but it also means that as things wear, the wear is not likely to be distributed evenly. Its like having a 6 legges chair. If the legs are perfectly rigid I can pretty much guarantee it will rock at least some tiny amount. A 3 legged chair is minimally constrained (its sufficiently constrained, minimal just means that if it had any less lega it would fall over)

 

[Prometheus]

I have to agree about the "engineering" seen in a lot of the 6-screw trems. They are some truly crappy pieces out there, and more being made all the time. Of course, on the other hand, there are a few makers who really do turn out precision components.

And now that I think about it, you are right. Two-pivot systems did make a pretty big splash. Not so gradual. It'll be interesting to see what proportion of 6- vs 2- are being manufactured ten years from now.

I've looked at the Bladerunner and almost got one for my current build. Now, that's the most truly original thing to come along in a long time. And it quite elegantly negates the whole friction issue. I've heard a lot of good user reports about it. And a couple that stated a loss of sustain or fullness. Naturally, it's impossible to find a component where somebody hasn't said that at some point, so a big grain of salt there. But as you've tried several designs, and you've stuck with the Bladerunner, I'd like to hear your review of it.

The static friction force (or force necessary to overcome it) is not the same as inertia. Of course accelerating an object, whether at rest or already in motion, requires some force. That can be seen in having to push a suspended object. But the static friction is different. You do have a good point though, which I acknowledged, in that the mechanical advantage of the trem arm, and the springs at play, pretty much make the static friction a non-issue. The main reason that I bothered to bring it up, and then dismissed it, is so that I could avoid the "yeah, well you forgot about...".

But please help me out here. I'm trying to picture what you're getting at with your statement that "with six screw trems there are four more possibilities that may not happen". I see six holes and six support points. I appreciate that moving the arm will slide the holes along the supports. And I know that the springs attempt to return it (slide back) to its original position. But what I don't see is why six points makes that any less likely. I've already made my case for the fact that (in a sliding system) the six-point has lower frictional resistance, and therefore should be easier to return. So please, so that I can understand your point, could you draw the picture for me, and explain the process by which it's less likely to return home?

BTW - I'm a pretty gentle trem user. Mostly just actual tremolo. A bit of up and down, nothing fierce. If anything, more often up than down. And not a lot of the time either. It's the spice, not the main course.

 

[Prometheus]

Hmmm. Posts came in while I was posting.

OK, Cagey first. Thanks for chiming in. Yes, friction and force are two different things. Friction boils down to the resistance to forces. It is a mechanical interaction, quantified by the amount of force required to overcome it. The mechanical interaction is governed by the material properties, the surface area, and the force between the objects. So that's two forces now. When talking about sliding a kitchen table, the force between the objects (the table and the floor) is gravity. And the push you must give to move it is the force required to overcome the friction between the table and the floor.

In the case of dragsters, they're actually trying to create the reverse of what we're doing here. First they use the natural no-so-slippery nature of the tires (very high friction) to burn in their tires. The heat accumulated by the friction makes the tires hot and even stickier. And since they want to stick, and are counting on getting as much stick as they can, they actually have an advantage in getting more rubber on the road. And there's a very complicated system in getting the right rubber compound, width, and diameter, to get the right stickiness, weight per sq in, and rotational speed at the ground.

But now, back to guitars.

Interesting point about 18 screws being less sliding resistance than 6. Yes, I'd agree with that - but not that I've increased my frictional factor by 3. I've increased the surface area by three, which has dropped the amount of force borne by each point of contact, and thus reduced the frictional resistance at each of them. And yeah, 36 points would be better than 18. Keep going until you have one long continuous sharp-ish surface, sliding across a flat-ish surface. Now the string force is maximally distributed, which means it's at its minimum at any point, which means that its sliding resistance is at a minimum as well.

Let’s consider sanding wood. That’s one rough surface sliding across another rough surface. If you were to magnify metal enough, you’d see the same sort of thing. Now, if you have a flat sanding block on a flat surface, you can push down on it a fair bit. The down-force, the “together force” is distributed across the entire contact area. The rough surfaces resist sliding, which is friction. Keeping the materials constant, the resistance varies with the size of the block and the amount you bear down. But it can still be slid across the surface fairly easily. This horizontal force is the force required to overcome the friction.  Now if you tilt that sanding block up on one edge, and bear down with the same pressure, the resistance increases. Because the same weight is now distributed across a much smaller contact area. You can still slide it easily, but only if you lighten up on the pressure. Now put the block flat again, say on a painted flat surface, bear down normally, and now run off the flat surface and down across the edge. An instant of feeling the “bite”, and a guaranteed burn-through. Why? Because you didn’t have time to lighten up the pressure. The bite was the friction increase as the contact area plummeted. If you’re going to sand an edge, you have to really really lighten up, because it cuts so fast. Why? Because what “feels light”, compared to normal sanding pressure, is still actually much more contact pressure per square inch when the contact is just a thin edge. So again, back on the flat surface, a greater contact area with a given amount of “together” force, will require less horizontal force to overcome the friction.

Given constant materials, with a constant force between them (down-force, together-force, or for bridges, string tension), an increase in contact area results in a reduction of the force required to overcome frictional resistance.

Swarfrat, good point about alignment. I knew that'd come up, because that's an aspect of the 6-point that's pretty darned weak. Getting the screw holes perfectly straight, finding six identical screws, getting them all in perfectly straight - good luck. What's going to happen then? Well, some will be bearing more pressure and others less, and some maybe even none. But over time, this will wear in. I agree with your comment about it's wear not likely to be distributed evenly. But that's a good thing. It's a naturally correcting system. It will eventually settle to where everything's evenly distributed. Sort of like your six-legged chair being vibrated in one spot long enough until it eventually has equal contact all around. Now, I must admit, as self-correcting systems go, this is pretty crappy. And as soon as you change a screw, it's got to go through the "breaking in" period again. A guy could get old. Wait, I'm already old...

This is a fun discussion. Yikes, I guess I have to get out more. Please don't get me wrong, I'm not some radical advocate of the 6-screw system. I like the 2-point system a lot, and admit that it is superior from an engineering standpoint. And my next build will probably have one. Or a Bladerunner. But I started this because I just heard so many time that a 6-screw system increases friction, and that's just plain wrong.

 

[line6man]

I don't have time to read the whole discussion right now, so I'll just make a quick point. Saying that the force distributed over each of the six screws of a six-point bridge is one-third of that of each screw in a two-point bridge assumes that all of your screws have equal contact with the bridge. On most of the six-point bridges I have owned, the screws all bent, and then when I went to adjust them, they had uneven contact with the bridge. You could easily have most of the force distributed over whichever two screws happen to be closest to the bridge, so the point is moot. Of course, I may have had cheap screws, but even if the screws are straight, there are other variables, such as compression of the wood, or dimensional variations in the drilling of the mounting holes, the bridge holes, the screw diameter, and plating thicknesses.

 

[stratamania]

The four more ways it may not return to tune, was one of alignment already mentioned. I initially had planned on giving an example of try hanging a door with six hinges rather than two.

It's also how it returns to the point where the thing started or it's ability to stay in tune. Any point introduced where the bridge doesn't return to a zero point of where it started or somewhere a string can bind itself is an additional possibility of pitch stability being lost.

With the six screw trems an often used method is to screw in till the plate just lifts from the body and back off a little on the outer two screws. The inner four are raised a little more so that you only have in effect two pivot points again. But then the plate can slide up and down four points it doesn't need to and possibly bind in some manner. 

Then if you take a look at the bottom of a Fender plate the angle is a bit out for it to pivot correctly. Then the saddles the holes behind give places the strings can bind before going over the saddle.

The Supervee I have I used as a replacement on a Mexican Strat, not a bad guitar but hampered by its tremolo. Sustain and tuning stability was most definitely improved. It does feel stiffer than a six screw tremolo, but that's just a case of getting used to a different feel. It's a well made device.

Anyway that's a brief overview. I'm always a proponent of use what you want in your guitar. But it's good if the user does so from an informed angle as it were. Sometimes I think choices get made due to its "vintage" or so and so has one. I think we are all influenced in some shape or form to a greater or lesser degree. When I was a youngster I had a Les Paul copy because i loved Led Zeppelin. I now don't own one at all as Strat based guitars suited me better. Actually the Les Paul copy was traded in when I got my first Strat, which would now be vintage if I still had it ;-) 

When I was progressing from the 70s and into the 80s we were looking for things like Floyd Roses, gizmos and other stuff that could make things efficient and more playable. Now there is a trend toward vintage and making reissues of old guitar models, plus ca change, plus ce le meme chose...

Nowadays there is such a choice compared to the 70s and the quality in general is better.

By the way which six screw tremolo or vibrato did you decide on ?

 

[Prometheus]

Thanks for the input, guys. This discussion has expanded beyond my initial address of “six screws increase the friction”, but that’s fine with me. If everyone’s input turns this into a resource from which  everyone can learn about trems (including me!), that’s a good thing. I’ve evolved in this thread to the role of an advocate for the six-screw design, which I’m not really. But sort of like being assigned a random side in a high school debate, I’m willing to run with it.

The issue with getting all the ducks in a row, or in this case, six screws, is a major one.  In my opinion, it’s the actual weak point of the design. Because it’s practically impossible. The wood of the body is organic, so even if the holes are CNC’d, then with temperature and humidity they’re gonna change a little. And the wood may be of different strength across the six locations too, which means that the pressure is going to compress it differently. And the screws aren’t machined, so they may be of slightly different diameters, or not perfectly straight, or slightly out-of-round (all this was mentioned by line6man). And the bridge plate’s holes may not be in perfect alignment either. What all this boils down to is that when you screw in a six-screw trem for the first time, there will inevitably be some small deviation from the perfect case of six straight and equal contact points. These imperfections may be pretty small, but we know that small things can make for big differences, and the devil’s in the details. Of course, if you have five perfectly straight contacts and one set back out-of-contact, no biggie. But if you have five perfect and one set forward, well, now you gots yerself a rocking chair bridge. No fun.

I earlier mentioned how I think that maybe these small (if indeed they are small) non-linearities are self-correcting to a degree. If one screw has more pressure, due to it’s being in contact while its neighbor is not, then it will wear due to friction, whereas its neighbor will not. Eventually, it’ll even out and they’ll both bear an equal load. But that is really not what I’d call a saving grace. Who knows how long that’d take to happen? It could take a really, really long time. And when I set up a bridge, I want it to be right, and right now, not a month or a year or more from now. And as soon as you turn a screw, you’re back to imperfect again. Nah. Interesting point, but not what I’d call a benefit.

Stratamania mentioned the angle at the bottom of the bridge plate, which is a very good point. There, near the front, the plane of the plate breaks upward at an angle, sort of in the way a knife’s shaft breaks from flat towards a point. The profile changes from what would have been a long thin rectangle into a bit more triangular shape at the front. The angle there becomes a pivoting point of contact between the bottom of the base plate and the surface of the guitar body. When the plate is in contact with the body, that is.

One would think that the correct placement of this pivot line would be about as far forward as the holes for the mounting screws. But the original design, and most since, have it poorly located, significantly further back. So the action of rotation of the bridge around the mounting screw contact point describes one motion. But the rotation of the bridge around the body contact point describes another motion. They’re both movements in a circle (well, a small part of a circle), but those circles have different center points in space. A full-floating bridge, when first pulled up, pivots in one arc around the mounting screws. As the base comes in contact with the body top, it then changes its motion to begin pivoting around the break angle on the bottom. Or some weird combination of trying to pivot on both at the same time. An additional negative consequence is that this metal-to-wood/lacquer contact is not very smooth, and can bind. For those who keep their bridge full-floating, the release of the bar will allow the bridge base plate to come up off the top’s surface, and again be supported at the mounting screws. But for those who want the bridge in contact with the body, particularly in a “dive-only” or spring-decked manner, the bridge base plate remains in contact with the body, and there’s no guarantee that the pivot angle on the bottom is going to grind its way back to the desired position. The two points of contact (mounting screw line and body contact line) fight each other, and the winner is a coin toss. And the loser is tuning instability. I think this can be one of the most significant contributing factors to trem bridge tuning instability.

As I understand it, Leo designed his tremolo bridge for creating vibrato. But he mis-named it - Leo wasn’t a playa, he was more of an industrialist. Anyway, it was intended to be wiggled up and down, to slightly vary the pitch up and down. As time went by, players wanted to do more with it, things it was never intended to do. And the original design is inappropriate for these demands. It was never intended to do dive-bombs. And not decked, but floating. Decking it creates problems like the above, by actually clamping it between the mounting screws and the base plate’s bottom facet and the body. All this is made worse by screwing the screws in too far. Sums up to pretty much guaranteed grinding and binding.

Yes, Leo was an innovator. Pretty good idea for the time. But times, they are a’changin’. It’s a testament to the original design that the improvements we’ve seen can for the most part be considered incremental rather than revolutionary. But these days we do have choices better than the original. And while I’m a fan of the vintage sound, I’m also all in favor of the better mousetrap. And I feel there’s no particular good reason to stick with a solution because that’s what worked yesterday. If today brings a better solution, then I’m all for it.

As far as tuning stability goes, or lack thereof, there are several factors present other than the friction at the mounting point of the bridge. I figure I may as well bring them up because somebody will eventually. And it'll made more fodder for discussion. There are several points at which the string can move when the trem is used, and may not reliably return to its original state when the trem is released. One such point is at the tuner, if such is a vintage-style many-wrap type. The string can stretch and/or compress against the underlying wraps, and bind. This can be addressed with locking tuners (or a locking nut). Another point is the string tree, which is a friction point (aka possible sticking point). Addressed with roller trees, slippery trees, or just no trees! Then there’s the nut – probably the most common point of string binding. Addressed with a proper nut setup and maintenance, and/or a slippery nut, or a locking bridge, or a roller bridge. And then there are the saddles themselves, which can become corroded or rough. Addressed with harder materials, good dressing, and cleaning (these things apply to ALL related parts). There’s also the break point behind the saddles where the string passes down into the bridge (Stratamania mentioned this too). This should be smooth, rounded, and clean. And finally there’s the seat for the string in the block, wherein a down-bending trem action can remove enough tension from the string that the ball loosens and later re-seats in a different location. Oh yeah, nice clean strings help too. And of course we all know that a little bit of lube goes a long way, and that applies to all points of string movement too.

 

[Prometheus]

Yikes, my posts are all so bloody long. So here's one that's really short.    :toothy10:

 

[stratamania]

The ball reseating in a different location is a point lots of trems have not addressed. A Floyd does of course. The Guthrie Govan Charvel is using a none fine tuner Floyd Rose, most likely for that reason.

So here's another discussion point. Will a broader spacing for a two point tremolo provide better stability. E.g. floyd Rose spacing is wider. I feel it possibly does with a broader base but interested in anyone else's view.

 

[drewfx]

If you are asserting that both parts can do the job required equally well in practice (if set up properly), then all of the armchair physics is unnecessary.

 

[bagman67]

I'm somewhat with drewfx here - as long as your pinhead is big enough for all the angels you need, there's no need to figure out how many angels CAN dance on said pinhead.


In other words, a part of sufficient quality from either camp, coupled with competent installation and setup, should result in a generally quite usable configuration.  In my experience, the two-pointer is easier to get set up correctly, and I lack the finesse as a craftsman to do harder things, so - my reasoning is at an end.


But this is not to pooh-pooh your inquiry, Prometheus - it's just not a line of argument I find profitable myself.  But then, I enjoy reading decisions of the US Supreme Court and providing critical analysis, so maybe I just don't drink the same flavor of nerd Kool-Aid as you do.

 

[Rob]

Pretty intense discussion. My mind is much simpler. I find the 2 point superior over the 6 point. From a carpentry standpoint, if you had a prybar under 6 screw points, pulling up and down on the prybar, something's going to get loose. Expansion and contraction, woooden screw threads get worn out and loosening. That to me causes instability.and impacts reliability. The movement of the 2 point relies more on a fulcrum point on the pins that are firmly anchored in the recessed threaded insert. I just find that stronger and a more stable action. Just my opinion.

 

[Prometheus]

Thanks everyone for chipping in. The consensus is that the 2-point system is more desirable, given its greater stability via its mechanical simplicity, and its easier setup and maintenance. I agree. Although a 6-point trem may be able to operate just as well if properly set up, that’s something that’s much more difficult to achieve and maintain. I’d originally wanted to address the fallacy that 6 mounting points have greater friction, which I’ve done to death and will leave alone now.

Stratamania, your question about mount spacing is pretty interesting. Sure, I’ll drink that Kool-Aid.  It might be worth doing a real analysis of, but I’d have to refresh my Statics and Dynamics, because it’s been too long since I’ve had to deal with a system this complex. But maybe we can just look at it conceptually. First, the load is created by 6 strings, each of a different tension. So the forces on the two posts will be different. And the line of that force is offset vertically from the mounting post pivot points (saddle height), countered by spring tension. And the trem arm mounting point is offset rightwards from the middle of the post span, and downwards toward the tail.

The differences being addressed between the Floyd (2-point) and Fender (6-point) designs are the width of the mounting point spacing and the amount of left-right offset of the trem arm mount point. I think that they could both theoretically make a difference. Looking at the trem arm horizontal location, the best point for it would be at a horizontal (left-right) location that coincides with the middle-point of the total string tension. Because the lower strings have greater tension than the treble strings, this location will be left of center, let’s just arbitrarily say right at the D string. If the arm were there, it would minimize the tendency for trem arm actuation to produce a rotational torque on the mounting points. But that trem mounting location is not very practical – it really has to be off to one side.

So what happens when the trem arm is relocated horizontally? The further it’s offset, the more that trem arm action wants to not just rotate the trem around the left-right axis of the bridge mounts (tilting forward and back), but also torque it around a head-tail axis (like the strings). Of course the mounting points will resist this, and it won’t actually rotate. But when the arm is pressed down, the torque will apply (if the arm is mounted on the right/bass side) a greater down-force on the right post than on the left post. If the arm were to be mounted out to the right, one whole mounting point spacing towards the lower (right) side of the body, then the effect would become a downforce on the right post and an upforce on the left post. A lovely little teeter-totter. Very bad. Some of this effect would be seen at any point beyond the treble mounting post.

So if you’re interested in keeping the forces on the posts as equal as possible, and minimize the unwanted rotational torque, the thing would be to keep the trem arm mount as close to the middle (or the D) as possible. Better to at least be somewhere inside of the mounting posts. Is it necessary? Well, I’m not sure that there’s too much of a practical advantage in the case of the two-point system, because the posts provide plenty of strength and stability, and when combined with the considerable string tension, so that the bridge will stay securely seated in the "socketed" grooves, no matter the small torque from an off-center arm. But I suspect it would matter more in a floating vintage 6-point system, in which both sides of the bridge can slide up and down the screws a little.

And so finally about the mount spacing – well, for what difference it makes, wider-spaced posts will allow the trem arm mounting location to be relatively further inward, so that adds mechanical soundness. But practically speaking? Well (as Bagman alluded), a difference that makes no difference is not a difference. In other words, I think the system is robust enough that it doesn’t really matter.

Interesting that the 6-point Fender design, in which longitudinal rotation is possible, has a narrow mounting span and has the trem arm mount outside of it. While the Floyd has a wider post spacing and the arm mounted further in, but whose other features minimize or negate rotation anyway, and therefore such features provide little additional benefit. Overall, again, the 2-point system wins.

More Kool-Aid anyone?