# On string length at headstock

Discussion in 'Luthier's Corner' started by azureblue, Jul 22, 2012.

1. ### azureblue

Jan 29, 2008
Winston Salem, NC
I gather that over all string length affects the tension of a string. IOW, a 35" B is "tighter" than a 34", and a through body 34" is supposed to be "tighter" than a regular top load, by way of overall string length..

So, assuming this to be true, I see that almost all basses at the headstock, have the low strings the shortest, overall, from tuner to ferrule. It would seem that, to have higher tension on the low strings, that the reverse would work, the tuners for the low strings should be further away from the nut.

Educate me?

2. ### bongomaniaSupporting MemberCommercial User

Oct 17, 2005
PDX, OR
owner, OVNIFX and OVNILabs
The fact is, nobody has done actual scientific testing to prove whether the length of the string past the witness points (the nut and the bridge saddles) has any effect, or what effect it might have.

As a result, there are three main camps on this subject (and yes we've had hundreds of pages about it):

1) "I took physics in college, and I KNOW that the tension of a string is determined ONLY by the length between the witness points."

2) "I have anecdotal, non-scientific experience that shows one result or another, and I trust my ears."

3) "I have a hypothesis, and since it supports what I believed already, it is probably a fact."

3. ### sharp8874

Jan 10, 2011
I don't have an answer for you but I think that is a very interesting and valid point. I might have to try and do an experiment to figure it out

4. ### azureblue

Jan 29, 2008
Winston Salem, NC
From what I am told, the whole purpose of a long than 34" scale bass is to increase string tension, primarily to benefit the low strings.. So, logic would follow that moving the low estrange tuners to the end of the head stock would do the same thing. But -----

5. ### JehuJavaBass Frequency Technician

Oct 15, 2002
Oakland, CA
You're probably right. If going from 34 to 35 increases the tension, then increasing the length of the string beyond the witness points would also increase tension.

We're talking tension here, not scale, not frequency, but tension in the string. Tension should be even across the length of the string regardless of the nut or bridge...unless it was clamped. I'd say the true witness points for tension is the tuner peg and the ferrule stop. Just my unscientific, no physics class experience, not rumor has it, opinion.

6. ### JehuJavaBass Frequency Technician

Oct 15, 2002
Oakland, CA
Maybe someone can build a reverse headstock and settle this question.

7. ### MusiclogicCommercial User

Aug 6, 2005
Southwest Michigan
Owner/Builder: HJC Customs USA, The Cool Lute, C G O
You can find plenty of tension measurements for strings on line. You can also find plenty of threads here about tension, and the fallacy of many perceptions dealing with the theory of longer string lengths past the witness points. People believe what they want to. The reality is that tension is different for each type of string and each gauge of string to bring it to tune, so an understanding of string specs and and perception based theory will help you further your query.

8. ### rickdogGold Supporting Member

Mar 27, 2010
Keep in mind that the idealized model of a vibrating string is based on fixed endpoints and a string with no stiffness.

In the real world, the string slips over the nut, and its stiffness vibrates the non-speaking length behind the nut. Could these effects make an audible difference? Perhaps a subtle one?

9. ### FBB CustomTalkBass ProCommercial User

Jan 26, 2002
Maryland
Owner: FBB Bass Works
Here is the formula for frequency on an ideal, taut string :
f = (1/2L)&#8730;(T/&#956

f is Freq, L is speaking length, T is tension, and &#956; is linear density. here is a resource for those who would like to learn more:

Note that D'Addario is not compelled to include non-speaking length in their charts. As Neil deGrasse Tyson said, "The good thing about science is that it's true whether or not you believe it."

There are those who argue that playability is improved by additional string beyond the speaking length. There may be effects - particularly near the nut on a headless instrument, for example - that have more to do with stiffness of a bass string than tension. There are also arguments made about the availability of string mass during bends (therefore making them easier) but again, there is not more or less tension on the string when tuned to pitch.

10. ### MusiclogicCommercial User

Aug 6, 2005
Southwest Michigan
Owner/Builder: HJC Customs USA, The Cool Lute, C G O
Well put Matt(FBB)

11. ### JehuJavaBass Frequency Technician

Oct 15, 2002
Oakland, CA
Interesting. The D'adarrio formula actually shows the tension going down by increasing the length to achieve the same frequency. Or the frequency increases when the length is increased but tension and density remain the same.

Assuming you use the same string in a 34 or 35, you'd have to reduce the tension to get the same frequency.

So where does this leave us with regards to string length beyond the speaking length and its tension?

12. ### pilotjones

Nov 8, 2001
US-NY-NYC
Matt (fbb), thanks. Except for the typo! There's / missing between the L and the square root sign.

Jehujava, this is why you are getting a counter intuitive result. In fact the L is in the numerator and T in the denominator, so as length goes up, so does tension, to the second degree.

Bongo, this is no a matter of "no one's done the experiment.". I measured response of resonant frequency to tension in PH101 lab, as did fifty years of people before me.

13. ### Markpotato

Jul 19, 2012
Eureka Springs, AR
Luthier, Sorrentino Guitars
I would have to agree on this. It still takes the same amount of tension to bring the string to pitch, otherwise a fancy invention like this bridge: http://www.evertune.com/what-is-evertune/ would not work.

14. ### JehuJavaBass Frequency Technician

Oct 15, 2002
Oakland, CA
No crap? That explains it!! I thought I was an idiot.

15. ### azureblue

Jan 29, 2008
Winston Salem, NC
so apparently there are no tests that simulate a "real world" bass string, from end to end, not just vibrating length?

16. ### JehuJavaBass Frequency Technician

Oct 15, 2002
Oakland, CA
I'm sure there is somewhere, but that data is under lock and key next to the Area 51 data.

I am truly curious to the answer though. There must be a reason for the standard headstock layout in its current arrangement.

17. ### bongomaniaSupporting MemberCommercial User

Oct 17, 2005
PDX, OR
owner, OVNIFX and OVNILabs
The whole "science works whether you believe in it or not" thing is a double-edged sword. On the one hand, the laws of mechanical physics are pretty well established and can be learned in a 101 lab. OTOH, it is wrong to assume that only one law applies, or that a system can be reduced to only one measurement.

Instrument strings change tension constantly while being plucked and then oscillating. They slip over the witness points--the bridge and nut are not clamps! And the entire system (remember the thin wooden neck) flexes and vibrates, so the witness points are not held in rigid positions. All of these vibrations are interactive, causing peaks and cancellations in each others' waves. And more to the point, tension per se is not the only parameter that affects how a string plays and sounds.

That is why I separated out the "I took physics in college" group. It's one thing to perform a 101 lab experiment to measure a single variable, and quite another to analyze a complex and interactive system.

To the best of my knowledge, this set of tests has not been done, using a controlled laboratory methodology, and published.

18. ### azureblue

Jan 29, 2008
Winston Salem, NC

19. ### Markpotato

Jul 19, 2012
Eureka Springs, AR
Luthier, Sorrentino Guitars
Depends on what you call standard (4 in line, 2x2, 3x2). I think for the most part the standard headstock layout(s) are the way they are so that (a) The strings stay in a perfect line to the bridge (usually) (b) The tuners are far enough from each other to not compromise the structural integrity of the headstock and as to be able to tune freely without bumping the other tuners.

True, tension will change due to all the variables above, but it clearly stays within a restricted range and comes back to roughly the same tension when it stops vibrating. Otherwise you'd have to retune your bass every time you play a note. This actually does happen with a new set of strings as I'm sure you're aware, which is why they need to be "broken in".

I think if there is a sound difference by changing the length of the string from the nut to the tuner, it probably has little to do with tension, which again should theoretically stay within a restricted range. I would assume having a longer spacing between nut and tuner would threaten losing tune a little easier, though I could be wrong.

All of that being said however I'd love to be proven wrong on this, because it's another piece of information I can use to my advantage as a builder, and I'm really interested in the notion, otherwise I wouldn't be posting here.

20. ### JehuJavaBass Frequency Technician

Oct 15, 2002
Oakland, CA
You pretty much boiled it down to the three biggies.

The question really is about reversing the 4 in line. E being the longest vs G being the shortest...beyond the nut. E generally is the shortest of all strings (or B for that matter). Why?