String tension, and peghead design

[bob]

Once again, it has been suggested that you can increase string tension by running the string to a tuner that is farther away from the nut. Some people hope this will give them a less floppy low B on a bass, for instance. Others have argued that increasing the distance from nut to tuner allows for strings to be bent more easily (I sort of think that implies less tension, not more, but we can delve into that further here).
 
The bending ease issue is somewhat curious and perhaps arguable, but my personal position is that regarding string tension itself, the distance between nut and peghead is totally irrelevant. More generally, there seems to be a lot of myth and confusion about string tension, and I would like to encourage clarity in this area.
 
I crassly started to hijack this thread (and apologize again for that). Please back up to read the preceding posts by lbpseq and flaxattack, which prompted my comments.
 
Here are links to some of the previous discussions on this subject (there are probably more):
 
speaking length
formula (scroll down a couple of screens in this post - my very first one - to the paragraph that starts with String tension, and you'll find a link to an informative article)
Extended B peghead (and some more math)
 
It would of course be quite simple to set up a definitive experiment, but certainly easier and more fun to just talk about it - so let's try that instead :-)
 
The remainder of this post is what I originally said back in Jeff's FTC thread, without alteration.
-Bob
 
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No.  
 
Well, that's just my opinion, and of course I could be wrong, and maybe we should even move this to a separate thread - because if Jeff wants a longer pull, then he should have it. And I let it go earlier this afternoon for just that reason, but if we want to get into it, then so be it.  
 
Tension is based on the vibrating length of the string. That's the portion between the nut and the bridge, just to be clear. There is a mathematical formula for this, that seems to work very nicely.  
 
It doesn't matter whether you have a an extended peghead, or run the bridge end of the strings through the body, or whatever, because to get a given string to a particular pitch, it must be under a specific tension between the nut and the bridge. That is all.  
 
Yes, I have read some articles about Hendrix, including the argument that it made bending easier on the higher strings. I will even agree that, *provided you assume* that the string can freely slip through the nut slot, then it would be easier to bend a string that extended further beyond the nut. That is a different matter, and has nothing to do with what tension the playing length of the string is under. The playing portion is under the same tension, but as long as it can slip freely through the nut, then you have more to stretch. This is a different physical phenomenon.  
 
Bill's statement is correct, that shorter strings have less tension to reach the same pitch, assuming that we use exactly the same strings on two different instruments, that have different scale lengths. Not nut to tuner, but scale length. So yes, if you put the same strings on a Gibson and a Fender, they will be easier to bend on the Gibson. But it does not matter what the peghead/tuner configuration is on the instruments, it is simply the fact that they have different scale lengths.  
 
Sorry guys, but this is bad science. A few writers speculating on why Hendrix (whom I sorely miss) chose to continue playing upside down, does not prove that we can address a floppy low B by running the string to a tuner further away from the nut. The only way to do that is to increase the scale length, or use a larger gauge string (or one with more mass for the same gauge).

[bsee]

Thanks for starting the thread.
 
How could the extra string outside of the speaking length affect bending?  Well, for that to be the case, more string would have to pass through the nut as the note is bent.  I think I comprehend the physics of how this could be true.  For a string at a particular tension, bending increases that tension proportional to the amount of bend relative to the length of the bendable string.  The length of the bendable string is the entire length from machine to tailpiece if you assume minimal nut and bridge friction.  The longer the bendable length, the more you would have to bend to raise the tension by a unit.
 
Based upon this science, I wonder if a longer string length outside of the speaking zone might result in loss of sustain or other negative issues.  If bending really is easier, then what happens when you just play a note?  As the string deforms, would the added pressure pull more string through the nut, thereby extending the speaking length of the string?  (Is eliminating this stretch part of the value of locking nut tremolo and double ball end systems?)  
 
Now, if the above is true, wouldn't notes played on a stretchy string be less tight as they modulate with changes in string speaking length?  It would seem that they don't modulate much, if at all, since tuners would become pretty useless, at least for open strings.  On the other hand, I do believe that tuners do show some variation based on how hard you pluck a note.
 
Is any of this true?  If so, does it matter?

[bigredbass]

I'm utterly lost at this, but will shoot two associated anecdotes across the bow, just to keep your heads down. . . .
 
I understand that Fodera reverses the peghead order to string the B furthest from the nut on their fives and sixes, I imagine where the 'A' key would be on a 3+3 six string, to get the longer length, and they think it's worth doing . . .
 
D'Addario once told me that a .145(!) was the guage required to make my B FEEL like the other four in a typical 45-105 set . . .
 
I always think it's from my keyboard days:  You'd run across so many different feeling actions and number of keys from synths to grand pianos to pipe organs, that I really got used to feeling different actions.  While I'm really silly about action on my basses, I just seem to accept that the B is just gonna feel a bit different than the other strings, forget about it, and go on.
 
J o e y

[bob]

Joey: maybe Fodera thinks it's worth doing, but that doesn't say whether it's for marketing/sales purposes, or based on sound technical merit.
 
I don't believe it can affect the feel in the speaking length, as you suggested yourself a while back.
 
However, the stretch issue is a little less clear. It sounds like Jeff may be thinking of using a different tuner, in hopes of getting a slightly finer control over tuning. I suppose that's conceivable, though if it's on the order of 1-2 more over a 32-34 scale, we're talking a very small percentage, and I doubt it would be noticeable.
 
Bob: I agree with what you are saying. Extra string beyond the nut (or bridge) makes a difference only if it can freely slip. And I think this is generally undesirable, and why locking nut systems were invented. It probably only matters for the higher guitar strings, but even those won't slip freely enough to stay in tune, plus they would eventually cut through your nut.
 
For accurate pitch, sustain, and complete harmonics, you really want the string to stop vibrating at a single, specific point. You don't want it vibrating in the slot.
 
Of course, if you are bending a lot, and just possibly using a lot of overdrive or feedback, then those may not be major concerns.  
 
I don't know what the answer is here. I'm sure most of us have noticed that after tuning, it may take a short time of playing for the string to settle in, and perhaps need a further tuning, which I believe is a result of the tension gradually equalizing over the nut. But I am fairly skeptical that people are setting things up so that strings will deliberately slip through the nut while bending, at least not with anything much heavier than about an .010-.020 (and they would probably be replacing nuts fairly often).
 
-Bob

[jazzyvee]

This is all way above my head and not something I have thought about before but I have to say it's a interesting discussion . :-)
I'm learning all the time :-)
 
Jazzyvee