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Myth/science In Lutherie


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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.

http://www.pacificsites.net/~dog/StringTensionApplet.html

There you go :D

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The proof is in the pudding. :D

Definitions:

string tension = tension between nut & saddle

pulling force = tension between tuning peg and opposite pinned end of string

nut pressure = force pushing down on the nut

There are two pages. Make sure you understand each step before moving on to the next.

Starting with trigonometry (assuming you've had it...).

Break Angles P. 1

Break Angles P. 2

Let me know if you don't understand something, and I'll try to explain it better.

This makes it easy to understand Godin's observations....with a larger headstock angle, he's bending against a larger total pulling force....but this pulling force is NOT the same as string tension. :D

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Okay, it is true (I did state it in an above post) that a higher break angle at the nut means that the string is exerting more force on the neck, which is what you just proved above.

However, the tuner is still exerting the same force on the string, no matter what the angle is.

While a higher break angle does increase the forces acting between the string and the nut, and causes more of a bending moment on the neck, the tuner is still applying an equal force to the string.

I understand your argument about greater downward force on archtops, and in fact, a few weeks ago on TB (which I know you frequent), there was a thread asking about exactly that, which was replied to with pretty much exactly the same claculations you used above. however, this force is only between the bridge and the string, and while it is affected by string tension, it does not have any effect on string tension.

Rule One of engineering: Don't push on a string :D

Edited by NamelessOne
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As for using a 6-inline headstock to try my "project", thats cool, but remember..... the nut action, and 12th fret action must be identical, AND there will be a slight difference in nut break angle from E to E with most headstocks. Also take note on how much string you put around the tuning post.

For my tests, i tuned the string, and we had a clamp system that locked the string (imagine a floyd nut right next to the tuner, but well away from the nut). This stops the string "settling" on the tuning post as you fret at the twelth, as all strings do over time.

Remember, if you are going to do experiments and tests, you need to avoid discrepancies in the tests by avoiding issues which may effect the outcome (other than the one thing you're testing for).

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Erik,

Can you show how your equation works with the full string length (assume a 15 deg. string angle at the bridge). What I am trying to resolve in my head is what the whole picture would look like. If I understand your equation, and it was correct across the full length of the string. You should have high tension/ low tension/ high tensionsituation. Assuming a min. friction method (say roller saddles and nut are used). Your saying the downward pressure used at the nut will decrease the tension past the nut. Then use more tension at the saddle, but increase tension again. I am Just trying to understand why the tension on the string itself would change.

P.S. You said to let you know if I didn't understand something. You should have saw this one coming (I am not the brightest fella :D )

Peace,Rich

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As for using a 6-inline headstock to try my "project", thats cool, but remember..... the nut action, and 12th fret action must be identical, AND there will be a slight difference in nut break angle from E to E with most headstocks. Also take note on how much string you put around the tuning post.

For my tests, i tuned the string, and we had a clamp system that locked the string (imagine a floyd nut right next to the tuner, but well away from the nut). This stops the string "settling" on the tuning post as you fret at the twelth, as all strings do over time.

Remember, if you are going to do experiments and tests, you need to avoid discrepancies in the tests by avoiding issues which may effect the outcome (other than the one thing you're testing for).

Noted: I am thinking I will just use a raised fretboard, 0 fret/12th fret, tuners,bridge config. all placed on a workboard. That should cut it down to the most basic configurationas well as allow for longer tuner positions. I will be able to swap and interchange the configuration a bit later for more testing. Plus that takes the sloppy Fry guy neck work variable out of the equation. :D

Peace,Rich

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Well, this doesn't exactly give me what I'm looking for--but maybe it's possible to reconfigure it. Because the applet depends on a predetermined string length --what I'd want would be take the information --tension/note/pitch/guage/string type etc. and inverse it to provide the string length.

I know nothing about java--is that possible with this applet?

Perry--I only use locking tuners, so that helps!

I have an extra (trashed) fretboard here, it shouldn't be difficult to rig something up. Gonna have to wait though, no time right now.

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The discussion of what's written on the site that RIch posted has been very fact driven so far. I'd like to take a philosophical turn, if you'll bear with me.

When discussing the results of the various tests - particularly when it comes to perceived quality of sound of instruments, Mottola mentions many times the seemingly unavoidable limitation of having blinded studies. What that means is that the fact that the players know which are the instruments that have the theoretically desirable qualities (older, more frequently played etc.) makes them play it differently. This can have so much of an effect that the perception of the instrument being "better" may have more of an objectiive effect than the actual variable being tested. In medicine this is called the placebo effect.

What this means is that the player's relationship with the instrument may have more to do with improved sound than anything objective about the instrument.

I think that the players subjective relationship with his instrument is one of the most influential "variables" affecting the objective sound of the played instrument. Is that controversial?

So when Mickguard suggests that a certain builder "starts building guitars and calls them the coolest thing on earth and jacks up the price so those same dorks who need a price tag and a fancy brand name will feel comfortable buying his guitars.", or Chris (TIC) opines that "Semi-nudity and increased skin-to-wood contact enhances the connection between the player and the instrument and makes the guitar playing a more sensual experience- resulting in a more organic tone and a 16% increase in sustain" maybe that does make the guitars sound better because the players play them with true faith.

Same with any number of innovations that major guitar companies market. (Fender's Highway series comes to mind)

On some metaphysical level, maybe there is some reflection of the builder's soul in an instrument that a particular player relates to that improves the sound of the playing in addition to the objective variables.

Maybe all the things that we refer to as voodoo really do work, if only because the player thinks they do. :D

Cheers,

Brian.

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However, the tuner is still exerting the same force on the string, no matter what the angle is.

The table of numbers at the end of P. 2 show this is not true. If you want to tune to pitch, the tuners will pull harder on the string at higher break angles.

While a higher break angle does increase the forces acting between the string and the nut, and causes more of a bending moment on the neck, the tuner is still applying an equal force to the string.

This sentence contradicts itself (and the one above). If the forces applied between tuner post and nut increase with break angle, the tuner is applying a higher force to the string (assuming you're still in tune between nut and saddle).

Rich, the equations given are just trig definitions, which are used to break down any simple Newtonian physical vector quantity (force, velocity, momentum, etc) into horizontal and vertical components. Because the example assumes the string is horizontal, and that the elasticity of the string is assumed constant, the horizontal component of the force is constant along the string. The same set of equations work for the bridge.

So yes, if you had a tailpiece-TOM setup, the forces would be high (tail to TOM), then low (TOM to nut), then high again (nut to tuner peg). Just make another calculation for your break angle at the bridge, and add the tailpiece-TOM force to the string tension and nut-tuner peg force to calculate the total force on the string (tailpiece to peg).

For something like a Strat string-thru situation, you have 2 break angles around the bridge (across the bridge string-thru holes, and across the saddles), and so you have to add a third term.

There is a very simple test one can do to see the effects of these forces. Just make a split headstock with two fairly different break angles (say 5° and 15°) and drill for one tuner on each side such that the length of string is EXACTLY the same between nut edge and tuner post. String it up with identical strings, tune to whatever pitch you want (but exactly the same for both strings). Now, pluck the strings between nut and tuner post. I predict the 15° string will ring a higher pitch than the 5° string because of the higher force on it.

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Alright, erik, One thing about your argument I don't get... you say the force is higher on the headstock that it is on the working portion of the string. but, what if we, say, put frets, pickups, etc. on the headstock, made it 25 inches long, and said it was at a 11 degree angle while the working portion, now only a few inches long and sporting tuners, is flat. whould there still be more force on the (now longer) headstock? less on the (now shortened) working portion of the string? All I'm doing here is rescaling the example, so nothing should change.

I'd work on showing this graphically, but I have to leave soon and won't be able to reply for several days, and I am not sure what program would be useful for this.

and, trying to quantify my statement above that you say contradicts itself: At one end of the string, there is an anchor, that applys a force exactly equal to the tension on the string. At the other end, there is another anchor, but this one has the ability to apply a greater or lesser force, when a person make it to do so. these forces balance each other out, as if the tuner applys 10n of force, the anchor at the bridge applies 10n of force. when the string must deflect around something, like a nut, it applies a force to the nut. The magnitude of this force is dependant on, but does not change, the angle at which it deflects, and the tension on the string. the force here is ONLY between the string and the nut, but does not change the tension on the string. no matter how many nuts, pulleys, or saddles there are between the anchors, the amount of force they apply to bring the string to a given amount of tension will remain the same. While the force acting on the nut depends on the force the tuner applies, the force that the tuner applies does not depend on the force acting on the nut. It's the same as "While the volume coming from the amp depends, in part, on the position of the volume potentiometer on the guitar, the position of the volume potentiometer on the guitar does not depend on the volume from the amp".

I like the idea of an experiment, though I would suggest that they use a single headstock on a hinge, rather than two, to remove inaccuracies. For this to work, though, the nut would have to be placed on the rotational axis of the hinge, so that the length doesn't change. to hold the headstock at the angle, a board with well-place nails in it should suffice.

Edited by NamelessOne
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Erik, the proof is NOT in the pudding just yet. I don't see how any of that shows that a higher angle = a higher force. A higher force would generate more tension and therefore change the pitch. You don't have to "pull harder" just because you're changing the angle. That doesn't hold up to science at all.

The ONLY time the angle will make things trickier is in the presence of friction, which makes for a very complex calculation indeed, since even different materials will produce varying amounts of friction. Since we're talking about theory in the absence of friction, that's irrelevant for the moment.

Another experiment, which you don't actually have to perform if you're feeling lazy: take a length of string, or even a spare guitar string. Using your hands, place it over a surrogate nut and bridge... anything that won't move when you put downward pressure.... the backs of 2 chairs if you want, as long as they're heavy enough to not fall. Press downward and get someone to "play" the string. Change the angle without changing the pitch... you won't have to pull harder, and in fact you CAN'T pull harder because then you'll change the pitch.

Greg

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"I like the idea of an experiment, though I would suggest that they use a single headstock on a hinge, rather than two, to remove inaccuracies. For this to work, though, the nut would have to be placed on the rotational axis of the hinge, so that the length doesn't change. to hold the headstock at the angle, a board with well-place nails in it should suffice."

This is basically my plan. However, my plan is to keep it simple with a zero fret as instead of confusing things with different types of nuts (at least for this test). I will also try to set it up so that we can switch up our scale length for comparison. I am sure at some point Pickup location may be investigated also. So I will try to set the pickup on a sliding system(should be pretty simple). I am also figuring I will need to be able to take snap shots of some results with my recording system. All that will be down the road. My wife gets back later today, and I hope to build something up tonight.

Peace,Rich

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Alright, but make sure that the fret is in a position where the tilting of the headstock will not change the length of the string. The only way to do that is to have to string break over a point that lies exactly on the axis of rotation of the string.

I will not be able to see or reply to this thread for several days, but it's good to see others who support my opinion to carry on the argument in my absence.

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Erik,

In the absence of friction, the string tension is the same on both sides of the saddle is the same.

I think the part you're missing is that the force between the string and the nut/saddle (NP in your diagram) isn't perpendicular to the nut-to-saddle string force (ST in your diagram). The force on the nut/saddle bisects the angle formed by the strings as it goes over the nut/saddle.

If there's a break angle of the string over the nut/saddle, the string is trying to pull the nut toward the saddle. The nut/saddle reacts this with a load component opposite to the direction ST. Think about how your method would handle a 90° break angle.

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Alright, erik, One thing about your argument I don't get... you say the force is higher on the headstock that it is on the working portion of the string. but, what if we, say, put frets, pickups, etc. on the headstock, made it 25 inches long, and said it was at a 11 degree angle while the working portion, now only a few inches long and sporting tuners, is flat. whould there still be more force on the (now longer) headstock? less on the (now shortened) working portion of the string? All I'm doing here is rescaling the example, so nothing should change.

Correct. There is no variable in the equations for the length of string on either side of the nut. It is a simple force balance, there is no dependence on string length.

and, trying to quantify my statement above that you say contradicts itself: At one end of the string, there is an anchor, that applys a force exactly equal to the tension on the string.

This is true only in my example, because I assume the string is pinned exactly at the end. If there is a bridge-saddle arrangement involved, then the horizontal component of the (bridge) force balances the string tension, while the vertical component of the (bridge) force is balanced by the support provided to the bridge by the body.

At the other end, there is another anchor, but this one has the ability to apply a greater or lesser force, when a person make it to do so. these forces balance each other out, as if the tuner applys 10n of force, the anchor at the bridge applies 10n of force.

The "adjustable" anchor is of course the tuning peg. What you are saying is true to a point, but you are thinking only in terms of forces parallel to the string (horizontal), so your example implicitly assumes a zero break angle. You are ignoring the fact that, when there is a finite break angle, the tuner not only pulls the string across the nut, it also pulls the string down on the nut. So the tuner needs to apply more force to achieve the same horizontal string tension.

when the string must deflect around something, like a nut, it applies a force to the nut. The magnitude of this force is dependant on, but does not change, the angle at which it deflects, and the tension on the string.

I don't understand what you're trying to say here...

the force here is ONLY between the string and the nut, but does not change the tension on the string. no matter how many nuts, pulleys, or saddles there are between the anchors, the amount of force they apply to bring the string to a given amount of tension will remain the same.

Not so. Make your headstock 2 feet long, and put a dozen roller string trees between the nut and tuning peg, thread the string through so it alternates up & down throug the string trees, then tell me the force applied by the tuning peg is the same as without 12 string trees.

I don't see how any of that shows that a higher angle = a higher force. A higher force would generate more tension and therefore change the pitch. You don't have to "pull harder" just because you're changing the angle. That doesn't hold up to science at all.

Greg, I'm actually a PhD scientist by day. :D I need lutherie to exercise the left side of my brain.

In the absence of friction, the string tension is the same on both sides of the saddle (meaning nut).

I think the part you're missing is that the force between the string and the nut/saddle (NP in your diagram) isn't perpendicular to the nut-to-saddle string force (ST in your diagram). The force on the nut/saddle bisects the angle formed by the strings as it goes over the nut/saddle.

If there's a break angle of the string over the nut/saddle, the string is trying to pull the nut toward the saddle. The nut/saddle reacts this with a load component opposite to the direction ST. Think about how your method would handle a 90° break angle.

Nameless and Greg and tirapop....what you guys are not quite getting is that you need to (first) decide on a common reference frame (horizontal = parallel to the string is the most logical) and then (second) do a regular vector decomposition into horizontal and vertical components.

Nameless and Greg, you are ignoring the fact that a tuning peg not only pulls the string across the nut, it also pulls the string down on the nut. Both forces must come from the tuning peg. This fact alone requires that the force on the tuning peg is higher than the string tension (when break angle is > 0).

Tirapop, you want to make the hypotenuse of an obtuse (scalene) triangle be the horizontal reference, with the other two sides being the "player's" string (between saddle and nut) and the "dead" string (between nut and tuner). Fine, you can do that, and still use trig to calculate the forces parallel to the two lengths of string (although the force will not bisect the break angle....). If you can bring the equations (more difficult than using a right triangle), I am certain you will come to the same conclusion that I did.

I'm trying to explain this as best I can with words. But if any of you guys can put your thoughts into mathematical equation form, I think you'll come to some interesting realizations....and I might be able to understand your points better. :D

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You're making it needlessly complex and missing some important points. And being a PhD scientist by day is a shaky qualification because I doubt that it relates to this point. My girlfriend is a PhD scientist by day, too, and she thinks you're wrong. So whose qualification takes precedence? :D

Look, it's simple. The tuner exerts no force in and of itself. The break angle means that there IS force downward on the nut, but in the absence of friction (as proposed by you yourself) this is meaningless. The angle at which the force gets distributed is completely irrelevant to string tension, which is what we're discussing. No matter what forces are exerted, in no matter what direction, by no matter what source (whether it's a tuner or 2 Russians, one named Yakov and one named Boris), the string tension MUST be the same in order to produce an identical pitch from a string of identical guage. That's it, that's all. No vectors, angles, or anything else change that fact.

And I don't need a PhD to know this. :D

Don't lose the forest for the trees... your mathematical equations might be calculating something irrelevant and you won't even know it. You need to decide which factors are important and what is being calculated before you even get that far, or your energy is wasted.

It's just as easy for me to turn around and say, "maybe if YOU sort out the logic in your findings we can get somewhere".

:D

PS, this is all fun for me... I like discussing logic and all that... so no hard feelings here at all. Yet. B)

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Ok guys, Darci got back and I had a few minutes so here is what I "slapped together".

testrig.jpg

Now I have tuned it up with a couple low E's (I will double check exact gauge). It tuned up. The intonation needs to be adjusted. I went for a wide string spread with same gauge for the first tests. The angle at the bridge and headstock are bare minimum (as you can see), and of course just a zero fret/ roller bridge. I will get back with findings.

Peace,Rich

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I can't help but think you'd find it easier to work on this experiment without all that crap spread all over the floor. Tell you what, box it all up, ship it to me, and I'll burn it for you. I'll even pay shipping - can't say fairer that that... right?

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Ok Dokey,

Well first round-

First of all. I have no down force to speak of. This would NOT be playable. I also felt shakey about my tests because the strings felt like they were floating.

Gauge on both strings- .042

Scale length 25"

Distance behind bridge approx 3.5" (slight variance because of intonation)

longer string nut to saddle-25.05", saddle to tuner- 34"

shorter strng nut to saddle -25.11", saddle to tuner-28.0625"

I also compaired distance required to bring the string up a full step at the 12th. fret.

longer string-.41"

shorter string-.325"

I tried to apply 500 grams of pull at the 12th.fret.

My findings shorter string moved slightly less distance. However my method was less than reliable. So I will rig it up in a better way and let you know what I find.

So thats what I got. Thoughts?

Perry is that sounding flawed to you? I am hoping I can count on you as a guide in case I am getting odd results (I would hate to have flawed info passed on to the board).

Peace,Rich

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I can't help but think you'd find it easier to work on this experiment without all that crap spread all over the floor. Tell you what, box it all up, ship it to me, and I'll burn it for you. I'll even pay shipping - can't say fairer that that... right?

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I can't help but think you'd find it easier to work on this experiment without all that crap spread all over the floor. Tell you what, box it all up, ship it to me, and I'll burn it for you. I'll even pay shipping - can't say fairer that that... right?

:D

Well your a heck of a guy Setch. I only wish someone would take my drum kit too. Then I would have a lot of room for experiments. :D

Peace,Rich

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Well your a heck of a guy Setch. I only wish someone would take my drum kit too. Then I would have a lot of room for experiments. :D

Well, my kid wants to play drums (yeah, right, this one's a born front man), so I'll take 'em.

Just to be clear:

longer string nut to saddle-25.05", saddle to tuner- 34"

shorter strng nut to saddle -25.11", saddle to tuner-28.0625"

These measurements come from the strings after they've been tuned and intonated, right?

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