# String Tension Science

Discussion in 'Strings [DB]' started by Matthew Tucker, Apr 11, 2005.

1. ### Matthew TuckerCommercial User

Aug 21, 2002
Sydney, Australia
Owner: Bresque Basses, Sydney Basses and Cellos
I've read a lot of posts in these forums where people suggest changing string tension by raising or lowering saddles, lengthening tailpiece wires, different tailpieces etc, but the more I read these the more I think there's something wrong with that logic.

If by "tension" is meant the "longitudinal tightness" of the strings, and hence resistance to lateral movement - with a lower tension resulting in an easier string to press down, and consequently floppier when played - then to my way of thinking, no amount of change in string angle, neck angle, or string length after the bridge will make any difference to tension, whatsoever.

When we tune a string, to get a higher note we have to tighten the string OR use a thinner (less dense) string OR shorten the string. So, using my best schoolboy maths,
Code:
```		  Tension
Pitch = ___________________
Density * Length

or

Tension = Pitch * Density * Length
```
Therefore, pitch, string gauge and scale length seem to be the only parameters (apart from elasticity which is a property of the string itself) that will have an effect on the tension of a string. So changing strings, changing the scale, using solo tuning will have an effect on tension, yes.

But I can't see how the ANGLE of the string over the bridge can affect string tension.

What it DOES affect of course, is the downward pressure that the string puts on the belly, and this will affect the tone by controlling the movement of the top/bassbar. A longer tailpiece wire might change the amount of movement in the afterlength. Changing neck angle will change bridge height and consequently the pressure on the belly. But not the string tension.

Is my logic flawed? Or is all this just too bloomin' obvious?

I've come to this through a floppy E experience. If I tune the E up to F, or even F# , the tone is strong and the string feels the same as the others to play - tight (all Spirocores). So I've been trying other ways to increase the tension of that string, with no luck.

Since I can't change the scale or the pitch, I reckon I'm going to have to try a stark E.

2. ### anonymous0726Guest

Nov 4, 2001
This was gone over pretty in-depth a couple of years ago here. Probably old enough to be buried forever in the archives? Not sure -- you'd have to as the TB god (Paul).

I'm not sure how it all works, exactly, but I think you're pretty much on the idea, short of the equation which is overly simple. The proper equation is something that bridge builders use and is way over my head.

There is something to the breaking angle over the bridge, however. This is why a lot of EUB sound like Slabs, as the breaking angle over the bridge is way too flat.

Sorry to not be of more help, but mebbe a dredge through the TB vaults will find you that thread.

3. ### KSB - Ken SmithBannedCommercial User

Mar 1, 2002
Perkasie, PA USA
Owner: Ken Smith Basses, Ltd.
You can take all that science and put it in a bottle and throw it in the ocean to land on a deserted Island for all I care. Even the weather swelling or shrinking the Back from seasons changing changes the feel/tension.

If you have been playing long enough and playing different Bass you would see how much this actually applies. Different Basses feel different with the exact same strings... Throw out the Science and put in the Feel..

The same knowledge taught in School turns out a Genus and a moron in the same class.... It's not the science, it's the application!!

4. ### anonymous0726Guest

Nov 4, 2001
String-tension freaks are a Genus?

5. ### jneuman

Apr 17, 2004
You Sir, are correct. String angle over the bridge changes the downward pressure on the top only (in theory). However, making the break angle more shallow might make the strings feel looser since there is less friction at the bridge slots and you end up stretching more of the string when you play, although I would guess that effect to be negligable. Tension is dependent only on the linear mass of the string and tuning pitch. The feeling of flexibility is more complicated matter though and is affected by the rigidity of the string construction, string height, string clearance at the nut etc.
Jon

6. ### Matthew TuckerCommercial User

Aug 21, 2002
Sydney, Australia
Owner: Bresque Basses, Sydney Basses and Cellos
Ken I don't deny that different basses perform differently!

Of course I haven't taken into consideration the elasticity of the string or the movement of the bridge or the movement of the top or the tailpiece or the flex of the wood or etc etc ... and I agree none of it can be put into a simple formula.

I'm taking about one bass, mine, and my conclusion is that if its increased tension I'm after, no amount of fiddling (!) is really able to do that, I need to change string density.

By the way, I'm rather proud that I can still do school maths, since it was taught to me oh about 30 years ago - and I haven't used it much since

I don't know why luthiery and science are so immiscible to some people. Science after all comes from the human tendency to ask "why is it so?" and then try to find answers through experimentation and conjecture. I can't speak for you of course, but I'm sure most luthiers do this; they just don't necessarily express it in terms of numbers. Every luthier I've had anything to do with has his/her own tricks and theories and rules, and these are the result of observation and experimentation. Some luthiers write these down and share them - and open a can of worms by doing so. Others are more guarded and keep what they know to themselves. But in my book, its all science!

7. ### Silversorcerer

Aug 11, 2004
Atlanta, GA USA
Your tension/pitch equation is mostly correct. Here's a better equation below. The full explanation is found here: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html
another derivation of the relationship here:http://home.planet.nl/~d.v.ooijen/lgs/stringtension.html
- partial quote from the site. Note the date of the publication. It is a during Amati's lifetime and just a few decades before Stradivarius. They probably downloaded it right off of Mersenne's blog page.

Does anyone think Pirastro, D'addario, etc. just messed around until it "felt right". I'm thinking anyone designing a stringed instrument after about 1650 starts right here. And if you can calculate the string characteristics you can begin to manipulate tone predictably as well. By tap tones, air volume, graduation, f hole size. Helmholtz would be the next "breakthrough" explanation: http://www.phys.unsw.edu.au/~jw/Helmholtz.html

What people often incorrectly refer to is changing the downward component of the tension by altering the neck to body angle, the height of the tailpiece from the end block or the bridge height. The tension of the strings produces a downward static force on the bridge that is proportional to the angles of the strings to the bridge in front of and behind the bridge. As the angles decrease or become more acute, that component moves closer to the total tension via a trigonometric function that I haven't yet found a great illustration of. Perhaps I will get busy and draw one. There are some in my old college physics book, but they are not exactly what goes on with the bridge of a bass but illustrate the point. I could do a drawing that would show the specifics to the bridge situation. Just watch for it to wash up here on the beach any day now.

If you can use science to calculate the feel instead of getting there by hit and miss, why wouldn't you?

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8. ### jneuman

Apr 17, 2004
I think the force downward on the bridge is just the tension of the string times the COS of the angle in front of plus COS of the angle below the bridge. So if the angle were 90, there would be no downward component and if the angle were 0, all of the force would be directed down.

Jon

9. ### Silversorcerer

Aug 11, 2004
Atlanta, GA USA
Force on bridge = String Tension (cos Angle before + cos Angle after). If these two angles are not equal, then the downward component is not perfectly perpendicular to the bass belly. Usually it will be pushing the bridge at the top a little toward the fingerboard, so the bridge is set with a slope on the front side to resist this. The back side is close to perpendicular. If one designs a bass's tailpiece, neck set angle, and bridge height carefully and matches the two angles, the energy transfer to the belly will be maximized with no wasted force. The bridge can be made with equal slope on the front and back. It might be possible with such a strategy to use a bridge somewhat lower than when the angles are unequal and deliver more of the string vibration to the body. In light of this we should not judge a bass with less overstand or a decreased neck angle until we look at the angle before and after the bridge. I can't say it would be a "better" design, just a more efficient one.

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10. ### Rob Knight

Mar 3, 2005
Leamington Spa, UK
I think the feel argument has merit in the real world because the science is just so complicated. Granted the equations and analogies presented so far do represent strings, and the body in the case of helmholz resonators. But these forms are derived from much more complicated equations by making assumptions about the system.

For example that the string is rigidly fixed at both ends. Not so at the bridge, or really at the nut. That the string has a uniform distribution of mass, that it's stiffness does not impinge on it's motion, etc.

Science is after all, a study of the physical world, and is driven by observation. If it feels different, it probably is!

11. ### Silversorcerer

Aug 11, 2004
Atlanta, GA USA
Complicated for whom? The equations as presented are not beyond High School science and math courses, even though some might consider these "college preparatory". Obviously there was a time (over 400 years ago) when this was cutting edge stuff, but now it is remedial science and math if you are a college graduate. If I were going to carve up a bunch of high dollar wood, I would work out the equations first. If I were going to spend \$400 dollars on gut strings, I'd want to calculate what they were going to "feel like" first.
The string is fixed at both ends;- that would be the tailpiece and the tuner shaft. That the vibrational length is "stopped" at the nut, bridge, or for that matter at your finger, is inconsequential to the primary physical relationship.
By today's manufacturing standard, the small variances in uniformity would be negligible.
The degree of effect that this has can be observed on the bridge of a properly intonated EBG. It is why the moveable saddles leave the higher guage strings longer than the lower gauge strings. The higher gauge strings have more motion reducing stiffness. Again, the affect is quite small and can be ignored on unfretted instruments.
This is not the question. The question is why does it feel different and how can I (beyond trial and error) make changes to (predictably) make it feel more like I want it to.

12. ### Rob Knight

Mar 3, 2005
Leamington Spa, UK
Silversorcerer,
I ought to lay out my table. I'm a big fan of Science. Every aspect of the behaviour of the instrument can be described mathematicaly. Essentially I agree with your standpoint, though I still maintain it is a lot more complicated than the fixed string equation.

The first line of the original post alludes to modifications that shouldn't affect tension but are claimed or perceived to.

The point I was trying to make, although it was slightly off topic, was similar to Ken's, at least the way I interpret what he said (... and I hope he wont mind the association). If you, or the weather, make a physical change to the instrument or any part of it and it 'feels' different afterwards there is a fair chance that it is. It could be a biomechanical difference but it feels different. If an equation says it's not different then we need to make sure we are using the right equation or that we are applying the correct boundary conditions.

Press gently on your bass' tailpiece where the strings are attached. Mine moves. That is not a rigid fixing point.

13. ### Silversorcerer

Aug 11, 2004
Atlanta, GA USA
Rob, I'm just trying to make sure that we don't lose sight of the fairly limited nature of the original topic and that we get the best understanding of it available. Sure if we change what we are talking about, then the answers are bound to be different.

To the credit of the original post, Matthew points out that our discussion of "string tension" which is fixed for a given pitch, string length, and string mass, is often being confused with the downward component of force on the bridge, which can be altered by adjusting the angles that control this static force component, even if everything about the strings remains constant.

If anything has become complicated, it is because some are confused about what we are talking about, not because these issues are beyond our understanding. Don't add to the confusion by maintaining it is still more complex than Mercenne's equation and static vectors. It isn't. If it is, please demonstrate how and why and also to what degree. Come on, I was born in Missouri, let's get on with the show me part of this opinion you maitain.

When we interject the ability/disability of human perception into the discussion, we are completely off topic. Since we are off topic anyway:

My studies in perceptual psychology (that is what I have a degree in) would generally support that human sensation, visual, auditory, olfactory, or tactile, is capable of very discrete comparative measures, within the range that is positively adaptive to our living conditions. When we see two different brightnesses we can adjust them to match within very close tolerances. This ability is confined to a limited section of the electromagnetic spectrum that we call light. Venture out of the range and the same type of energy is "completely invisible". If our strings become higher, we will know this immediately within our tactile range, which is finest in our fingertips. If we hear two pitches, we can within just a few cents, tell which is the flat pitch and the sharp. Ultrasonic and Subsonic waves we are clueless about without science.

I only use the electronic tuner for the first reference, because it is based on equal temperament and I want my instrument to be tuned in perfect 5ths. By the grace of Nature, I can do that by ear.

However, if I want to create an instrument with a specific subsonic Helmholtz frequency, I'm going to need an equation. My ear will not be able to hear that. It will, however be able to notice a distinct difference in how that instrument supports the audible harmonics of that subsonic frequency.

I would ammend that and say that there is better than 99% chance that any felt difference does indicate an actual difference. I just don't think that is what Matthew is talking about.

14. ### Silversorcerer

Aug 11, 2004
Atlanta, GA USA
Take a hammer and whack away at your endpin, when it finally breaks off, that can be judged to not be a rigid fixing point either. The tailpiece just transfers the tension to that relatively fixed point.

May 6, 2003
Columbus Ohio
Proprietor Fifth Avenue Fret Shop. Technical Editor Bass Gear Magazine
LOL. Now wiping my lunch off the screen.
Note to self, do not read and eat at the same time.

16. ### Chris FitzgeraldStudent of LifeStaff MemberAdministrator

Oct 19, 2000
Louisville, KY

Your honor, I'm just a caveman.

Seriously, and not to hijack the thread, but I'd like to encourage replies from any and all luthiers who may happen upon this. I'm wondering how much of this kind of thing real-life luthiers think about while building real life basses.

Sorry for the interrupt!

17. ### ChasarmsCasual Observer

May 24, 2001
Bettendorf, IA USA
To point to the original topic, there is a way to improve the the E string without changing the neck angle and/or TP angle. I replaced my tailpiece with a Pecanic compensated TP. This increases the afterlength of the E string and to a lesser extent the A and thus makes for a little stiffer feel and a fuller sound.

This, combined with a Flatchromesteel E, and I have a really strong E on the Shen now.

18. ### shwashwa

Aug 30, 2003
NJ
i just couldnt read every word of every post above, so i apologize if its been mentioned, but dont forget string length... the same set of strings will completely different on 2 basses if the string length is different... if a string is too tight for my 42" bass it's usually just right on my 40.5" bass...

19. ### Silversorcerer

Aug 11, 2004
Atlanta, GA USA
shwashwa, your observations are in complete agreement (how could they be otherwise?) with the Mersenne's equation. When the length of a given string becomes longer, it must be pulled tighter to produce the same frequency or pitch.
Looking at the plans I have of George Borun's 4/4 four string bass design, it appears that he set the string angles before and behind the bridge to be equal, thus maximizing the efficiency of the downward force on the bridge, and enabling a N-S symmetrical bridge. Of course George was a chemical engineer before turning to bass and violin construction.

If one wants to check the US Patent Office web site, under musical instruments you will find a patent application for a device to elevate the saddle (retrofit) on violins to achieve just this same purpose. The patent was applied for by a violin shop owner and his son. The USPTO has since changed it's search capabilities and I have unfortunately been unable to find the application, or perhaps it has been withdrawn. If I am able to locate it, I will post it, but it was for what we commonly refer to now as an elevated or high saddle. I think the design was for a retrofit adjustable variety for violins.

20. ### ChasarmsCasual Observer

May 24, 2001
Bettendorf, IA USA
There are at least a couple strings here at TB discussing the raised saddle concept on a bass, and it's use to lower string tension.