Myth/science In Lutherie

[fryovanni]

Since the subject of research and theory/myth/science of building seems to appear a lot around here. I thought this could be a good topic. Things such as the effect of neck break angles and percieved string tension (trying to re-focus a discussion from another topic). The seperation of the bass/treble side of a guitar, and the effect of shape on body vibration. and so on....

This is a nice page with info that can be discussed/debated-Click

Feel free to add more pages with research or information that may add refernce.

Peace,Rich

[erikbojerik]

This always kills me when I hear people talk about increases in nut/saddle break angles increasing "string tension"...meaning the string tension the player feels between the nut and bridge.

If you know that specific musical pitches correspond to specific frequencies (Hz), and are able to recall enough elementary physics & trig to calculate 2D force vectors, it quickly becomes apparent what nonsense this is.

If you're tuned to pitch, increasing the break angle (leaving everything else constant) will increase only the downward pressure on the nut/saddle. The tension between nut & tuning pegs, and between saddles & tailpiece WILL increase, but not the player's tension (between nut & saddle). Otherwise, you'd be out of tune.

[NamelessOne]

The tension between nut & tuning pegs, and between saddles & tailpiece WILL increase

Negative. the tension remains the same over the entire string, no matter what. the only exception is when there is a locking device, such as a floyd rose nut (or any tuning peg), that achors the string. however, the entire portion on the string between the bridge anchor (tie block, trem, string-through holes, etc) and the tuner is the same tension.

now, to toss another can of worms in there, the compliance (not tension. compliance in this case means the force required to strech a string a certain distance) of a string will increase as the unused length increases, for example by having a longer distance between nut and tuner. This is likely one of the main differences between top-loaded and string-through-body bridges, the other being longitudal (not measured by pickups) vibrations in the string, which can vibrate the body more on a string-through, making the pickups move slightly relative to the strings.

[Robert Irizarry]

now, to toss another can of worms in there, the compliance (not tension. compliance in this case means the force required to strech a string a certain distance) of a string will increase as the unused length increases, for example by having a longer distance between nut and tuner. This is likely one of the main differences between top-loaded and string-through-body bridges, the other being longitudal (not measured by pickups) vibrations in the string, which can vibrate the body more on a string-through, making the pickups move slightly relative to the strings.

So this means a headless guitar (Steinberger type) has a lower compliance, all other factors (scale length, string gauges) being equal, than a conventional guitar with a headstock? Just trying to make sure I understand...

[fryovanni]

So, I would hope we could agree that physics tells us the actual string tension will remain constant throughout the entire length of the string (I believe the article in the link above makes that clear, and I believe pretty hard to deny).

Compliance or "percieved string tension while bending". It makes sense to me that the longer a string will allow for slightly easier bend (given that it is moving a given distance). It seems to me the string will have to be bent slightly further to bring the string to its higher pitch if it has a longer overall length. I can see how there could be a different feel, but I can't imagine it would be easy to percieve. After reading Bendetto's findings I believe it is really going to be a very slight difference. That is my take on it.

Hey Mick (if you read this), What are your thoughts. I know you are working on your headstock design.

Peace,Rich

Edit: You know this is something that could be put to the test. Place two identical gauge strings in the high and low E positions and bend them at the same fret position one full step up in pitch. Then measure the distance required to reach the pitch. If in fact the distance is greater for the longer string (full length) than we have info that would support the theory. I have a little scale I could use to measure tension required to pull the strings a given distance also. I will see if I can put it to the test.

[erikbojerik]

Negative. the tension remains the same over the entire string, no matter what....the entire portion on the string between the bridge anchor (tie block, trem, string-through holes, etc) and the tuner is the same tension.

Sorry, no. This is pure fiction. I will prove it mathematically using the assumption of no friction across the nut/saddle....but right now I have to head out and run some errands. I should have it up in a few hours.

Think of it this way (you can actually try this with twine): say you have to pull the string to 20 lbs tension over 25 inches to tune to E, and you are pulling across your chest with both hands. Now stretch the string across the backs of 2 chair backs (nut & saddle) that are 25" apart and break them over by 15 degrees. You'll have to exert more than 20 lbs of tension between your hands in order to get 20 lbs of tension between the chairs.......this is because now some of your pulling force is being partitioned into a downward force on the chair backs, it is no longer all going to pull on the string. The greater the break angle, the more force you'll need to get 20 lbs.

[Daniel Sorbera]

I don't know about all the theory etc. But what I do know is this.

My wenge guitar (24" scale , ebony board) has an 11 degree headstock angle.

My bubinga/mahognay semihollow (24" scale, ebony board, the same tuners/nut that the wenge has) has a 18 degree headstock angle.

BTW both have the same fretwire and the neck is the same size/carve.

The wenge guitar has -very- floppy strings and the action has to be set pretty high. The semi hollow has -very- tight strings compared to the wenge guitar. The action can be set much lower and string bends are much easier.

It's not a small diffrence between the guitars, It's a huge, very noticiable, diffrence.

Now is this caused by the headstock angle? Or something else? I don't know the answer to that question. I just know the facts about how each guitar plays.

Feel free to call me a liar and tell me the results I'm getting are not physicly possiable

Edited June 30, 2006 by Godin SD

[Ben]

Are they both in standard tuning and do they both use the same gauge of strings?

[Daniel Sorbera]

Are they both in standard tuning and do they both use the same gauge of strings?

Kinda obvious

but yes.

and not only the same gauge, but the same strings. And I've changed strings multiple times with the same results (so It's not just a weird set of strings)

Edited July 1, 2006 by Godin SD

[AlGeeEater]

Edit: Nevermind.

Edited July 1, 2006 by AlGeeEater

[Ben]

What about the distance from bridge to tailpiece / nut to tuners in each case then?

Are they similar or significantly different?

Does either have a vibrato? On my guitar with a floyd rose the bridge actually gets pulled forward when you do big bends, making you have to bend further to reach the same pitch- making the strings seem loser.

EDIT: Just checked your site... if I'm looking at the right 2 guitars looks like theyre both strat style hardtails and 3x3 headstocks....

EDIT#2: OK, so my new theory is that you are a liar. Those results are not physicaly possible

Edited July 1, 2006 by Ben

[NamelessOne]

Godin- is one of them string-through? that would explain a bit...

edit-

looked at website.

Wenge guitar looks thicker. perhaps the added length in the string-through holes? I would think that it wouldn't be enough to increase the compliance that much, though... hmmm...

/edit

Erik- the tension remains the same. get a spring scale or two. (the little ones that work under tension). put one at one end of a string, anchored on something. put the other at the other end of the string, and pull until it registers a certain amount. the other scale will register the same amount, if they're both accurate. now, place an object like the aforementioned chair back in between. bring it up to tension, and they'll still both the the same.

In ANY object under tension, the tension remains the same over the whole object (unless there are other objects adding or releiving tension). the same guitar string, tuned to pitch on the same scale length, will always have the same tension. Ergo, the string between the nut and tuner will always be at the same tension, if the scale length is the same.

However, I am awaiting your proof. I am... confident that I am correct, but have been wrong in the past.

Edited July 1, 2006 by NamelessOne

[Daniel Sorbera]

Both guitars are the same thickness.

The only diffrences are what they are made out of, the shape (the semi hollow is bigger), and the fact that one is semihollow. and the pickups but I don't see how that could make a diffrence.

and I told you everyone would call me a liar and tell me it's not possiable

I still can't figure out why on earth this is happening

Edited July 1, 2006 by Godin SD

[GregP]

Negative. the tension remains the same over the entire string, no matter what....the entire portion on the string between the bridge anchor (tie block, trem, string-through holes, etc) and the tuner is the same tension.

Sorry, no. This is pure fiction. I will prove it mathematically using the assumption of no friction across the nut/saddle....but right now I have to head out and run some errands. I should have it up in a few hours.

Think of it this way (you can actually try this with twine): say you have to pull the string to 20 lbs tension over 25 inches to tune to E, and you are pulling across your chest with both hands. Now stretch the string across the backs of 2 chair backs (nut & saddle) that are 25" apart and break them over by 15 degrees. You'll have to exert more than 20 lbs of tension between your hands in order to get 20 lbs of tension between the chairs.......this is because now some of your pulling force is being partitioned into a downward force on the chair backs, it is no longer all going to pull on the string. The greater the break angle, the more force you'll need to get 20 lbs.

*boogidy boogidy*

With the SAME distance between the "nut" (or surrogate nut in your example) and "bridge" (ie. we're not talking about different scale length), and the same string guage, you will ALWAYS have the same string tension in order to get the same pitch. PERIOD. It's physics. After the nut and after the bridge, anything at all can happen. You can have an extra mile of string. You can break it at 5 degrees or 90 degrees. But the string tension will be the same.

You first say, "proving...using the assumption of no friction", but then your example demonstrates ONLY the effect of friction. With zero friction, the string tension must be the same no matter the angle.

I had a thread about 2 years ago in which I explained it all with a very long example... wonder if I could still track it down... but I was referring in the example to the length of the string rather than the angle, so not an identical argument, but the basic premise is the same-- on the same scale, with the same guage of string, the tension is identical no matter what happens before and after the nut and bridge.

Greg

[sumphead]

My only theory about Godin's same scale oddity would be the neck material. If it varied enough to show differences regardless of truss then a neck with enough back bow would actually have a physical distance (strait line) between the nut and bridge shorter than a more rigid neck. Thus changing the total tension to the same tuning....

Maybe...hmmm

Or we could all agree not to try to reinvent the wheel and go have a beer. :0)

R-

[erikbojerik]

The wenge guitar has -very- floppy strings and the action has to be set pretty high. The semi hollow has -very- tight strings compared to the wenge guitar. The action can be set much lower and string bends are much easier.

It's not a small diffrence between the guitars, It's a huge, very noticiable, diffrence.

This is not the same thing as string tension. This is what is meant by string compliance (as defined in the article that was linked in the first post), which is the resistance to stretch.

In the case of strings, tension is force/area. I think compliance is more like a bulk modulus (resistance to elastic deformation).

What Greg said is correct. All else (gauge, scale length & materials) being equal, if the guitars are tuned to the exact same pitch, they have the EXACT same string tension between nut and bridge.

To address Greg's comment on my twine-chair analogy....no, this is not friction at all. It is simply the fact that, by introducing a non-zero break angle, a fraction of the force exerted on the string will be diverted into pushing down on the bridge (vertical force) rather than pulling the string (horizontal force). The partitioning of force in these two directions changes with the break angle. With a non-zero break angle, more force is required to tune the guitar to pitch than if you just had a tailpiece and a tuner stuck into wood 25" apart.

It really is a no-brainer. But I've had a few beers tonight, and its late, so I'll have to prove it tomorrow.

[NamelessOne]

force is exerted on the nut, and bridge, but this does not increase the amount of force required to bring the string to pitch. if a string is under 20n of tension, it takes 20n to keep it there. it does not matter how many 100s of n it is exerting on another object, as long as it does not do any work on that object. think of multi-pulley systems, that's like grade 8 physics. In a simple two-pulley system, you apply 50n of force to the rope, through 1m, and it applys 100n to the load, through 0.5m. the rope is never under more that 50n of tension, but applies 100n of force.

In a guitar, the string never actually does any work (the lazy b*stards!). the only work done in tuning a guitar is in storing the mechanical energy used to turn the peg as elastic potential in the string. the bridge, or headstock angle, makes ZERO difference.

I repeat, it always takes the same amount of force to bring a string to the same amount to tension, no matter what. it takes the same amount of force to put a 1cm string under 20n of tension as it does to put a 1000m string under 20n of tension. in fact, that's why they use the same unit. it takes 1n to put something under 1n of tension, just like (for you americans) it takes 1lb to put something under 1lb of tension.

[fryovanni]

Godin- Why on earth would you think anyone would call you a liar . Obviously something is making the guitars feel different, and in this case enough to force you to raise the action. You have been building long enough and have the guitars at your disposal (you built em' you know them better than us). Put your mind to figuring out the "mystery". Try some testing. Personally I would not be able to just shrug my shoulders and say I dunno.

Two strings of the same mass and length from nut to bridge will have equal tension. I think the guys are still debating nut to tuner and after the bridge, but nut to bridge is not really in dispute(I believe ). How much force is required to move the strings a fixed distance is still quite likely to vary with actual total string length and of course this effect will most likely be effected by friction at the break angles. To quantify the effect is the challenge. Well that and after you can quantify it on a given break angle/nut/length of string. To compair the effects to other combinations of these factors (seemingly an overwelming task). However if we want to actually get somewhere that is our challenge. We are not going to find the one perfect combination for all situation, but it would be handy to have at least an understanding. maybe a better idea as to how these factors play on each other, and what to expect as we design.

I would propose we get over calling things "Voodoo" or just speculating, and spend a bit of effort trying to collect some data. If we can come up with a viable method (must be simple of course) to test our guitars and we all do a bit of testing we can post our findings and compair notes. Then it is time to debate the heck out of that data. Anyone game? Suggestions for a good test (I had posted a couple ideas for tests I wanted to try(fairly simple), but that as off the cuff and I am open to better methods.

Peace,Rich

[Mickguard]

Hey Mick (if you read this), What are your thoughts. I know you are working on your headstock design.

I read everything.

There are two bits of Science that I'm looking for:

1. A calculation, for a given string guage and scale length, providing the exact distance from nut to saddle for each string. You'd think this would be an easy one to whip up in java --and essential information. So why can't I find it? It's basic physics, right? Sure, you might still want a tuner to fine tune things, but it seems to me you should be able to get things pretty accurate from the get-go.

2. The exact drop from nut slot to tuner hole for each string needed to provide the necessary downward force to keep a string in its slot. I'm thinking specifically of drop-down headstocks, since that's what I'm working with (I consider the drop down to be superior in design--at least in terms of strength).

My thoughts are that it makes a lot of sense to keep as much of the headstock wood as possible--that is, a continuation of the line of neck wood. It just makes sense to me, and that's what attracted me to the Zachary headstock. But his execution is flawed.

But the more of a drop, the less wood remains. So it makes sense to me to try to keep as much of the wood as possible and drop the tuner holes instead.

More importantly, it makes sense to eliminate the need for string trees.

The way I intend to achieve this is by performing an EZ-Lok mod on the set of Gotohs I have --I can 'drop' the string by nearly 5 mm, which is pretty significant. The string hole ends up being about 2 mm above the surface of the wood. (I could go further, and recess the washer into the wood, which would look cool too)

So if I know the exact amount of drop necessary to keep the string in the slot, then I know how much of the headstock wood to take away. Because my 'feeling' is that Fender's drop down is excessive--it was governed by the tuners that were available in the day, not by any other reason.

For example, just for argument's sake, let's say the optimum 'drop' happens to be 7 mm for the High E string (taking this measurement from my Strat).

Since I know that my nut (actually a string guide, since I'm using a zero fret) will stand 5 mm above the surface of the wood --then I know that I only need take away 4 millimeters (2 for the drop, 2 to accommodate the hole for the tuner).

Which means that on a neck that's 15 mm thick (not including the fretboard), a full 11 mm of the headstock thickness represents a continuation of the wood.

Of course, my Fender headstock drops by 8 mm --and obviously it's holding up just fine in terms of strength. But it requires two sets of string trees.

But suppose that the optimum drop turns out to be just 5 mm instead of 7 mm? That's 2 mm more of headstock wood you can keep.

Staggered tuners set out to achieve the same thing as the Ez-Lok mod. But those seem to be meant more a as retrofit --since we're building from scratch here, then it should be possible to incorporate these ideas into the design itself.

Now, I wouldn't know how one should go about measuring this...I'll leave that up to you science-oriented fellows...

So I agree, there's a need for science --not just in the less quantifiable voodoo parts, but in this type of calculation (for the builder who wants to break away from the traditional headstocks, at any rate).

About Godin's Conundrum :

One thing I do know is that there's a pretty dramatic difference in 'compliance' between a 25.5" scale neck and a 24.625" scale neck --that it's more difficult to bend with the longer scale. And obviously the thicker the string, the less 'compliant' it will be. Just a couple more parts of the equation.

So it seems to me if Godin's necks are really 24", then they ought both be floppy. My vote is the difference in neck woods--perhaps one is less rigid than the other. Seems like it doesn't take much to change everything.

Also this:

Perry suggested in another thread that the length of the "dead" string (after the nut and saddle) can have an effect on intonation --but I still haven't figured out what he means by that. He's a pretty cryptic fellow...

[rhoads56]

Also this:

Perry suggested in another thread that the length of the "dead" string (after the nut and saddle) can have an effect on intonation --but I still haven't figured out what he means by that. He's a pretty cryptic fellow...

No, just giving you enough info to go make your own tests, which will in the end, reveal a lot more than words on a screen ever can. someone once forced me to "do the required work" as they called it. I didnt, and got nowhere.

One day it dawned on me, that i had a heap of answers in front of me, but not the questions. I did the "required work" and ever since, i take no-ones 'expert advice' for anything other than an 'opinion', until ive done the required work to prove it to myself.

Length of "dead" string (dead string = from nut to tuner, and saddle to pin/stoptail/ferrule/tremblack) has a huge effect on PLAYABILITY, but definately NOT string tension at a given pitch. String tension is CONSTANT for a given pitch, over a given LENGTH, using a given STRING GUAGE.

Make up a neck with a nut, and a "12th" fret only. Add one tuner a couple inches from the nut. Add a second tuner 12 inches back. Tune both strings to the same pitch. They will be the same tension (absolutely, this is FACT, you get that one for free ).

NOW, fret the note at the "12th" fret for each string individually. Which one "feels" easier to fret?? Intonate both strings, WOW, they will both require different saddle positions, OMG *** WOW BBQ, what is going on??

Now do the entire thing over again, but add a tension guage into the mix. Report back with the your findings...

Now, go one step further and contact a string manufacturer to obtain a specially made string which can be used with a "regular" scale length, but with a tuner 6' (yes feet! to take the theory to an extreme) behind the nut. Convert the nut to a floyd style locking nut. Try intonating the string at the "twelth" both locked and unlocked. Not the difference (if any) in saddle positions. Use a compression gauge to measure the difference in "fretting pressure" between the SAME STRING, tuned to the SAME PITCH, both locked and unlocked (the nut). Note the differences.

Theres a full days worth of research. Go for it fellas, report back with your findings, then i'll give you another "myth busting" project to do. If you can do one a week, we might be finished by the end of next year... but by then i'll have heaps more tasks for you.

Now, some of you will sit back and PROVE that im some sort of lying idiot, out to cause trouble. Some will "do the required work". I dont really care which one you are (any of you). If you dont want to do the work, and dont think i have a clue, fine, move on, i could care less. Ive done the work that brings me to the conclusions i have. I dont base my advice, ideas, or constructional methods on anything less than methods that have proven themselves to me. Furthermore, if you're looking to argue the subject, thats fine, but find someone else to do it with, i aint interested

[GregP]

The length of "dead string" will have an effect on fretted intonation. Seems self-evident.

This whole "being given a task to do the work" is for the birds, though. I agree that some things are better learned by practice, but there are also such things as different learning styles. Doing your project will only be an effective teaching method for about 20% of the population. Some of the rest are fine with:

With a longer amount of "dead string," the increased tension of fretting is distributed through more 'material', i.e., string. Therefore when fretting, you won't pull quite as sharp, resulting in better intonation. Put on a locking nut and all bets are off.

Greg

[Mickguard]

Make up a neck with a nut, and a "12th" fret only. Add one tuner a couple inches from the nut. Add a second tuner 12 inches back.

Okay, I got ya...and I love to experiment...

But I have a thought --it's easy enough to test the idea behind this with a six in line guitar, since that gives the more usual difference in dead string length.

Just string the Low E tuner with a high E string (although there's a slight difference in nut slot depth/height I suppose).

The length of "dead string" will have an effect on fretted intonation. Seems self-evident.

Ah, see, it's not so evident to me. Or at any rate, it's not so obvious in which direction it effects things.

[GregP]

I think I added more information while you were typing your reply.

At any rate, a 6-in-line guitar is a much quicker way of testing than building a prototype neck, for sure.

Greg

[fryovanni]

I am not sure if I have enough time this weekend to pull off the tests you suggest Perry (babysitting). I believe I can sneek in some testing. I will grab a spare neck and set it up on a test board (give me some room to work). If I get a chance I will work up a test neck with a fb and nut I will leave the HS undrilled for the moment. Honestly I don't know if I need to do this, but I am game if we can share the info.

Peace,Rich

P.S. Bear with me I am definately not a lazy man, but a very busy one.

[NamelessOne]

I've been trying to say what perry just said, though I was getting sidetracked with erik's little argument. I know what perry's getting at, and totally agree with him.

so, to rephrase that (since I seem to be having trouble explaining physics with words), +3 to Perry.