String Tension verses Depression=Nut String angle , Calling Engineers & Mathematician

[AcousticDreams]

I am looking to understand how String angle from Nut to headstock effects:
* How hard it is to depress the string in the first few frets ,
* The Attack times & Sustain times.
Please note that angle of the string can be changed by just how many winds there are on a post, as more winds brings the string closer to the headstock. There are a few Adjustable Post height Tuners on the market as well now.

Here is what some people say:
+ “ A greater string angle helps the string to seat in the nut slot, which can increase sustain and resonance. “

+ “Increased string angle at the nut has it's most effect on the OPEN NOTES, and this is because the open note is the one that has endpoints ”

+“They only thing I have found to be absolutely true is the practicality of the strings holding on and not slipping when pulled and bent. “

+ "As you increase string angle, the overall length of the string thus increases. To achieve the same tension needed a slightly less number of turns is needed at the tuners."

Personally, I have been using Gotoh 510 MG Locking tuners for many years now on most all of my guitars. The post hole is already fairly low. Normally I try and have no winds on my post. I pull with as much tension as I can beforehand, and then lock the string in place. While only a theory, I guessed that the string could then vibrate a tiny bit more as there were no winds above and below impeding the strings vibrations. This of course is only a large guess, as I have done no experimentation to validate it.

In an experiment I did just the other day, I added a few winds to each string on my locking tuners. We are talking a very small difference, still it lowered the string coming off the post closer to the headstock,

I feel as if it is now slightly harder to depress the strings on the first few frets after the nut.

I have also been experimenting with the just Sixth string, in an extremely low drop tuning.
With no winds, the sixth string flopped around and bused quite a bit when hit hard. With just one more wind on my heavy .058 string, I got less bussing. Which could only mean that the strings wave pattern, vibration up and down is less?
I can not as of yet, note on differences in Sustain, as I did a few other modifications to the string and bridge at the same time. I did get more sustain with he High E., & B,(but again, I did a few other mods so have no idea which mod or combination of mods gave the higher sustain. Not sure what I got with the wound strings? There is a change, but I am not sure what that change is.

In reality impossible to tell as this experiment is nearly impossible to go back and forth between no winds and extra winds. Clipping the string short on Locking tuners for no winds leaves no room to experiment unless I sacrifice a new set each time for the winds verses no winds test.

Looking to understand what is the truth is in all this.
1. Is there an actual difference in how hard it to depress with greater string angle from the nut?
2. Is there a difference with Sustain & or Attack times?

[AcousticDreams]

A primitive Computer drawing to further show the difference in string angle with winds verses no winds.

in actuality with a locking post...the string will wrap around 3/4 of one turn before exiting the post. This diagram just easier to draw and demonstrate the differences.

[HodgdonExtreme]

I can't see how string angle over the nut could effect the amount of force required to fret a string anywhere along the neck.

That's because the tension of a string is equal along it's entire length, except for effects of friction. If you have enough friction between string and nut (or string/saddle) to result in different string tension on one side of the nut than the other - you would have wild tuning instability and hysteresis... Meaning that once string was tuned to, say, 440hz - if you bent the string, it would increase tension, pull some extra string over the nut, and when you unbend the string, it would end up at a lower pitch than you started. Then you could bend the string between tuning machine post and nut - pulling string back over the nut, increasing pitch of the open string.

For good tuning stability - the string/nut interaction must be essentially frictionless; again implying that string tension is equal along the entire length of the string.

Thus, the amount of force required to fret a note depends only upon:

initial string tension, string length, Youngs modulus of the string, fret distance from the nut and distance the string must be deflected downward to make contact with the fret.

[rick-slo]

In cases of simple fretting on a fret the static friction of the string at the nut is greater than the minute increase in tension the string
will have between the nut and saddle. If you bend a fretted string however the increase in tension of the string between nut and saddle
could be greater than the static friction at the nut. The angle of the string between the tuning peg and nut slot may affect string/slot
static friction (binding) and that could possibly be noticeable to the player in how much bend is needed to reach a certain pitch increase.

[MC5C]

The overall length of the string has no impact on tension needed to tune the string to a given pitch. The longer the effective overall length of the string, the lower the additional tension developed when fretting the string. This reduces the compensation needed, reduces the "stiffness" percieved when fretting the string, it's the theory behind the Epiphone Frequensator tailpiece and the Hofner Compensator tailpiece. It also makes bending less effective. It's one reason noted scientific luthier Ken Parker developed his unique Parker Fly headstock. So part of your thesis is correct - longer string length results in a lesser INCREASE in tension when fretting. It does not result in lower tension when tuning to pitch.

Increased break angle across the nut does nothing good and lots bad. It increases the friction across the nut, increases structural loads within the neck and headstock transition, results in more easily broken necks at the nut (ask any guitar tech or luthier about repairing Gibson headstock breaks). Again, Ken Parker studied it and determined that in his design, headstock break angle would be minimized to just enough to keep the strings in the slots. I recall that he used 4 degrees. I built a neck using that idea, and it works great. So I guess Ken Parker and I think that the right angle across the nut is just enough angle, and no more.

I'm going to opine that the increase in break angle and string length from adding a couple of winds down on your tuning pegs makes the next thing to no difference in either effect. The effective string length doesn't incude the winds around the post, only the free length. You'd increase the string angle a wee tad, a few minutes of degree, not enough to have a discernable effect.

My take, anyway, that and a dollar will get you a cup of coffee...

[tadol]

Originally Posted by MC5C

My take, anyway, that and a dollar will get you a cup of coffee...

I agree with that, except for this last part - I have no idea where a dollar will get you a cup of coffee -

[AcousticDreams]

Originally Posted by rick-slo

The angle of the string between the tuning peg and nut slot may affect string/slot
static friction (binding) and that could possibly be noticeable to the player in how much bend is needed to reach a certain pitch increase.

This is very close to what one of my Luthier friends said. A greater angle , may not allow the string to move as freely through the nut slot groove as a less steep angle.

Hard to imagine much movement at all in the nut groove. However when you think about it, this would make the most difference in the first few frets.

A brick is placed at the ends of a 15 foot long plank of wood. If you walk across that board, the board will be the stiffest at the ends. In the middle it will bend more.

[rick-slo]

Originally Posted by Knives&Guitars

This is very close to what one of my Luthier friends said. A greater angle , may not allow the string to move as freely through the nut slot groove as a less steep angle.

Hard to imagine much movement at all in the nut groove. However when you think about it, this would make the most difference in the first few frets.

A brick is placed at the ends of a 15 foot long plank of wood. If you walk across that board, the board will be the stiffest at the ends. In the middle it will bend more.

Normally due to static friction the string does not move back and forth across the nut at all when doing routine picking and fretting anywhere on the fretboard. If that was occurring the nut groove would deepen before very long at all. The exception would be with some string bending. Of course tuning up and re-tuning wears down the nut grooves but that takes a fair amount of time to become as issue unless you already set up the guitar with super low action at the nut.

[MC5C]

All of this reinforces the idea that if you're going to be bending strings and using a vibrato/whammy bar, a locking nut and bridge are a good thing to have - the effect will be greatly increased with the string locked down at the nut and at the bridge, and it might stay in tune... Other than that, the consensus is that it's really hard to tell by playing what the various angles are, unless they are outside the window of "works well". Almost no one (besides me) thinks that a Frequensator or Compensator bridge actually make any difference at all to the player...

[HodgdonExtreme]

Reading these comments - it seems everybody disagrees with my assessment that string tension is equal along the entire length of the string - and there must be essentially zero friction between string and nut.

Anybody that has dealt with a sticky nut slot (high friction) and has experienced the string "ping" associated with small adjustments to the tuning machine - or changing string pitch before/after bending a note, should be able to appreciate that friction in the nut is unacceptable.

A good indicator of a good low friction nut, is when you watch the tuned pitch of your string with a good tuner. The tiniest adjustment to the tuning machine results in a measurable change of string pitch. The reverse is totally true: If you can adjust the tuning machine and don't see a pitch change in the string - your nut has high friction.

Why else do "they" make nut lubricants and use graphite etc?? The whole point is to minimize friction there. (unless we're talking about a Floyd Rose style locking arrangement, that tries to absolutely capture the string between nut and saddle)

Please educate me if I'm incorrect in my assessment.

[David Eastwood]

Originally Posted by HodgdonExtreme

Reading these comments - it seems everybody disagrees with my assessment that string tension is equal along the entire length of the string - and there must be essentially zero friction between string and nut.

For what it’s worth, I agree with you. The only way the tension could be different behind the nut (or the saddle) is if something’s stuck - or something’s about to break.

[rick-slo]

Originally Posted by HodgdonExtreme

Reading these comments - it seems everybody disagrees with my assessment that string tension is equal along the entire length of the string - and there must be essentially zero friction between string and nut.

Anybody that has dealt with a sticky nut slot (high friction) and has experienced the string "ping" associated with small adjustments to the tuning machine - or changing string pitch before/after bending a note, should be able to appreciate that friction in the nut is unacceptable.

A good indicator of a good low friction nut, is when you watch the tuned pitch of your string with a good tuner. The tiniest adjustment to the tuning machine results in a measurable change of string pitch. The reverse is totally true: If you can adjust the tuning machine and don't see a pitch change in the string - your nut has high friction.

Why else do "they" make nut lubricants and use graphite etc?? The whole point is to minimize friction there. (unless we're talking about a Floyd Rose style locking arrangement, that tries to absolutely capture the string between nut and saddle)

Please educate me if I'm incorrect in my assessment.

There is always going to be friction (except with a Bose-Einstein condensate) with static friction being higher than kinetic friction. You can look up the formulas on the internet.

[Rudy4]

Originally Posted by HodgdonExtreme

Reading these comments - it seems everybody disagrees with my assessment that string tension is equal along the entire length of the string - and there must be essentially zero friction between string and nut.

Anybody that has dealt with a sticky nut slot (high friction) and has experienced the string "ping" associated with small adjustments to the tuning machine - or changing string pitch before/after bending a note, should be able to appreciate that friction in the nut is unacceptable.

A good indicator of a good low friction nut, is when you watch the tuned pitch of your string with a good tuner. The tiniest adjustment to the tuning machine results in a measurable change of string pitch. The reverse is totally true: If you can adjust the tuning machine and don't see a pitch change in the string - your nut has high friction.

Why else do "they" make nut lubricants and use graphite etc?? The whole point is to minimize friction there. (unless we're talking about a Floyd Rose style locking arrangement, that tries to absolutely capture the string between nut and saddle)

Please educate me if I'm incorrect in my assessment.

Longitudinal tension over the length of the string is, of course, equal. What matters is the tension that it takes to depress the string at various points along it's length.

The effects of after length as well as headstock angle (as well as the small amount of difference in break angle over the nut due to such physical relationships such as vertical string post or slot head design, where the string is much lower, is an often debated topic.

In the real world it's probably not worth putting a lot of effort into analyzing.

[robj144]

Originally Posted by HodgdonExtreme

Reading these comments - it seems everybody disagrees with my assessment that string tension is equal along the entire length of the string - and there must be essentially zero friction between string and nut.

Anybody that has dealt with a sticky nut slot (high friction) and has experienced the string "ping" associated with small adjustments to the tuning machine - or changing string pitch before/after bending a note, should be able to appreciate that friction in the nut is unacceptable.

A good indicator of a good low friction nut, is when you watch the tuned pitch of your string with a good tuner. The tiniest adjustment to the tuning machine results in a measurable change of string pitch. The reverse is totally true: If you can adjust the tuning machine and don't see a pitch change in the string - your nut has high friction.

Why else do "they" make nut lubricants and use graphite etc?? The whole point is to minimize friction there. (unless we're talking about a Floyd Rose style locking arrangement, that tries to absolutely capture the string between nut and saddle)

Please educate me if I'm incorrect in my assessment.

I'm not quite understanding why there would be no friction (static friction). In order to be there virtually none, there would need to be little normal force, and even if the tension is the same in the string, there is always a component of the tension that's perpendicular to the nut/surface which provides a normal force on the string at that point.

[HodgdonExtreme]

Originally Posted by robj144

I'm not quite understanding why there would be no friction (static friction). In order to be there virtually none, there would need to be little normal force, and even if the tension is the same in the string, there is always a component of the tension that's perpendicular to the nut/surface which provides a normal force on the string at that point.

Of course there is some friction - we don't live in magic physics 101 land with massless/frictionless ropes and pulleys.

But again, I've pointed out several highly undesirable side effects of friction between string and nut - the point of which is there very little in a well set-up guitar.

The larger point I'm making, is string angle over the nut is not going to substantially change string tension (which is only a function of scale length and string diameter for any given pitch) - which would be the only way it could alter how much force it takes to deflect a string down to the fret when playing a note. Which was, to my understanding, a key topic in this thread.

This is based on my understanding of physics, as an engineer.