# Varying String Thickness Along Its Length

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Branched fromanother thread, we began a small chat about what would happen if you fiddled about with different thicknesses (mass) of string winding in different places along the same string.

It was suggested to start a new topic to elaborate.

One could easily affect the mass in different parts of the string by winding something (tape, wire) around the string or even soldering something on in a few places.

As we have previously stated, there may not be any real reason why this would be helpful but I thought that I may be possible to compensate for intonation or to change the impedance match with the bridge/nut. I was asked to elaborate on those two ideas so here we go (bear in mind that I am not claiming to speak with any great authority here so feel free to correct any mistakes I make):

Intonation:

We know that, as strings age, the rust and other deposits on the string cause the intonation to change. Would it be possible to take a virgin string and add mass to certain parts of it in order to compensate for the nomal intonation problems that you get with guitars? This would be instead of moving the bridge saddles.

How would this work? I'm not even sure that it would but I'll attempt to provide an argument in order to stimulate the debate.

If a small amount of mass were added (or removed) from the part of the string over the pickups (ie so it's not in the fretted part), this mass would have an increasingly significant effect on the vibrating part of the string it were fretted higher up the neck. This would be becasuse the added mass would be increasingly large relative to the vibrating part of the string. As such it might be able to compensate for the intonation.

Impedance:

A string/bridge interaction could be thought of as a string (of relatively small mass per unit length [MPUL]) joined to a string of very large MPUL. This provides a jump discontinuity in the impedance and waves are reflected back along the thin string with a small amount being transmitted to the thick string (bridge). The amound of energy transmitted is dependant on the impedance change and the wave frequency (lower pitches are transmitted better).

If one were to take a short section of the string before the bridge and continuously increase the MPUL up to the bridge, the impedance change would be less of a jump and hence the way the waves would be transmitted would be different. Perhaps it could be done in such a way as to transmit more energy to the bridge (and hence sound board) at the expence of sustain.

Sorry for the long and rambling post (you didn't have to read it if you didn't want to!)

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Just off the top of my head, and believe me this is only an itial though, I don't think it owuld be a good idea. Although the string as a whole vibrates there are loads of overtones which are where parts of the string vibrate around various nodes down the string length. If the string is thicker between two of the nodes, it will (try to) vibrate at a different frequency to the section of the string next to it. If this is the case, I could see one dampening the other and making the overtones diminished.

But saying that, it could be the best guitar invention yet, you just never know

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Unrelated to the engineering discussion you raise, but inspired by your post--

"Treated" pianos and Rhodes have been popular with keyboardists for years. Basically, a bunch of crap is thrown into the string/tine area, which messes crap up.

Haven't heard of anyone doing a "treated" guitar, but I don't see why you couldn't.

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ToneMonkey: I agree. I don't think it would be a good idea but consider this:

A wound string has different thicknesses along its length because the winding has a round cross-section. If you cut a section along the length of the string it would look like this (excuse the asci art):

0000000000 <- winding

-------------- <- core

0000000000 <- winding

So the mass is less between the "0s" than it is in the middle of the Os. Now this variation in mass is on a length scale very much smaller than the length of the string so it will only have an effect in higher order harmonics but I suppose it's partly responsible for the destinctive sound of wound strings.

Exam question: What length scale would a mass variation need to be over in order to significantly affect the fundamental frequency of the vibrating string?

GregP: I like you use of the highly technical phrases "bunch of crap" and "messes crap up"!!

I know can get treated strings but I'm not exactly sure what you mean by the string/tine area

Edited by dh7892
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In a piano there are strings. In a rhodes, there are tines. That's all.

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i actually had a set of strings once where two of the wound strings had extra windings in a mid fretboard location - god knows how they got through quality control. I didnt notice till they were on the guitar (just answered my own question to god) so tuned it up to pitch anyway, It produced unpleasant overtones and a hell of a lot of fretbuzz from the fact the string was suddenly thicker. the heavier section was about a cm long and seemed to act as a pivot (possibly not teh right word!!) for the vibration. it had a trangular vibration rather than a nice long oval - at least thats how it looked, could have been a visual illusion.

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Intonation:

We know that, as strings age, the rust and other deposits on the string cause the intonation to change. Would it be possible to take a virgin string and add mass to certain parts of it in order to compensate for the nomal intonation problems that you get with guitars?

You have to think about elasticity. Strings wear as they lose elasticity, get kinked(lose elasticity, and not longer vibrate evenly). Effecting overall density can't be looked at without looking at elasticity. Adding mass to an area of the string that has lost elasticity will simply make it more rigid(at least using current methods, ie winding a core with additional material). The wrapping method used to add density without increasing stiffness as you would with a larger solid core wire only is great method. It allows us to tune down and still have a good responce. If you can improve the density to flexability ratio you improve performance. If you hurt the density to flexability ratio you will decrease performance. Just a thought to add to your discussion.

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ToneMonkey: I agree. I don't think it would be a good idea but consider this:

A wound string has different thicknesses along its length because the winding has a round cross-section. If you cut a section along the length of the string it would look like this (excuse the asci art):

0000000000 <- winding

-------------- <- core

0000000000 <- winding

So the mass is less between the "0s" than it is in the middle of the Os. Now this variation in mass is on a length scale very much smaller than the length of the string so it will only have an effect in higher order harmonics but I suppose it's partly responsible for the destinctive sound of wound strings.

Exam question: What length scale would a mass variation need to be over in order to significantly affect the fundamental frequency of the vibrating string?

GregP: I like you use of the highly technical phrases "bunch of crap" and "messes crap up"!!

I know can get treated strings but I'm not exactly sure what you mean by the string/tine area

mmm, interesting. I think that the distance between to O's is so small compared to the length between nodes that it wouldn't make that much difference....... until you think about the winding acting in compression and tension at the very top of each anti-node. This would cause friction and dampen the vibration of the string.

As for the exam question, I've been fighting with how to cut through bridges all day (except for going for a lot of ciggie breaks and drinking way too much coffee), so I'll leave that for a better day

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@Fryovanni: Do you mean "strings wear as they lose elasticity" or do you mean "strings loose elasticisty as they wear"? What to you mean by loosing elasticity?

I'm not proposing to fix an old string by adding some more mass to it. I'm suggesting that one might be able to avoid using a compensated bridge by instead compensating the new strings.

I agree that winding things around a core will affect more than just the mass of the string but I doubt it would have very much effect on the strength of the string in the axial direction.

What do you mean by "performance of the strings"? Do you mean their intonation or their ability to vibrate?

@Wez: Interesting. I thought it would sound pretty bad if you had something like that!! Hoe much extra mass was there? You said about a cm's worth but how thick? was it just one extra wrap? That would be a lot more than the sort of extra thickness than I would propose to try.

Edited by dh7892
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@Wez: Interesting. I thought it would sound pretty bad if you had something like that!! Hoe much extra mass was there? You said about a cm's worth but how thick? was it just one extra wrap? That would be a lot more than the sort of extra thickness than I would propose to try.

it did sound awfull!!!, yeah it was like an extra layer of winding for a cm or so

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@Fryovanni: Do you mean "strings wear as they lose elasticity" or do you mean "strings loose elasticisty as they wear"? What to you mean by loosing elasticity?

I'm not proposing to fix an old string by adding some more mass to it. I'm suggesting that one might be able to avoid using a compensated bridge by instead compensating the new strings.

I agree that winding things around a core will affect more than just the mass of the string but I doubt it would have very much effect on the strength of the string in the axial direction.

What do you mean by "performance of the strings"? Do you mean their intonation or their ability to vibrate?

@Wez: Interesting. I thought it would sound pretty bad if you had something like that!! Hoe much extra mass was there? You said about a cm's worth but how thick? was it just one extra wrap? That would be a lot more than the sort of extra thickness than I would propose to try.

Do you mean "strings wear as they lose elasticity" or do you mean "strings loose elasticisty as they wear"? What to you mean by loosing elasticity?
I am saying string wear=loss of elasticity=string wear. I believe both of your statements say the same thing to me(they are the same thing).

What do you mean by "performance of the strings"? Do you mean their intonation or their ability to vibrate?
. Again my answer would be that it is not "or" it is "and". A strings ability to perform relates to its ability to vibrate and intonate(you could also say a strings ability to vibrate directly effects the way it intonates also).

Maybe I can try to be more clear;(I am not a very good communicator Sorry)

While strings are in service. They are subjected to streching, forced over saddles and the nut, and are pressed against frets. These effect the strings elasticity(both across the length, and in specific locations. This degrades the strings elasticity. This leads to a string "wearing out" or losing its ability to perform correctly(vibrate evenly or as freely). Build up of grime and junk on a wound string will also effect the strings elasticity, by clogging or filling up if you will the space between the windings(oils or grime will have little effect on the inductive relationship between the pickup and string).

As strings lose elasticity the simply do no operate as efficiently(move as well). If a string becomes kinked to some extent it loses elasticity(in a location), this effects the way the string vibrates and directly effects intonation as well as efficiency. If a string becomes kinked at say the saddle or nut(near the ends of the vibrating scale length) you will have very dramatic changes in both intonation and efficiency. So when I say "performance of the strings" that includes intonation and efficiency.

That is my take based on my understanding of how a string functions.

With regards to density. If you want to bring a string up to a given pitch at a given scale length. It will require a given amount of tension based on the density of the string. If the amount of tension desired is known(lets say 25lbs of tension). You can vary the density of your strings to allow for different string tuning at that tension. The problematic side to increasing the volume of a given material to increase density is that you lose elasticity. A solid wire is not a good choice, so string manufacturers develop wound strings that allow you to add more density(mass & volume), but maintain a higher ratio of flexability to density.

As far as trying to improve intonation. I think you have to one define what causes intonation issues, and start there. Then look at a properly intonated bridge to get clues as to the relationship between gauge and intonation(as long as tension on the two strings is the same, and you are keeping other variables in mind such as action). However elasticicity of the two strings is not going to be exactly the same(the larger string will not be as supple). It may also be worth looking close at the unwound vs wound, as they will have different flexability to density ratios.

Peace,Rich

Edited by fryovanni
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Right, we're getting into the nitty-gritty here so the posts are going to be long!

I'm not trying to be pedantic about the definitions of "elasticity" but when I get into science mode, I tend to try to be very precise about what I'm saying. Don't take it as a criticism, just me trying to clarify a few things.

I think the two statements are different because "strings wear as they lose elasticity" implies (to me) that loss of elasticity causes wear where "string loose elasticity as they wear" implies that the wear causes the loss in elasticity.

I'm not sure that I agree that strings "have" elasticity as a quantity that they can loose. It's late for me here so I'll try to explain a bit more in the morning.

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Here is an article that was posted on Doolins website-link. In article Seven he gives a bit of info on worn strings. Here is another link to a bit on the subject from Siminoff's "The Luthiers Handbook"-link

I believe Daddario also has a pretty good bit of information about strings.

Peace,Rich

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Here is an article that was posted on Doolins website-link. In article Seven he gives a bit of info on worn strings. Here is another link to a bit on the subject from Siminoff's "The Luthiers Handbook"-link

I believe Daddario also has a pretty good bit of information about strings.

Peace,Rich

Thanks for the links. The intonation articles are particularly interesting. I think there is another factor to intonation other than the fact that fretting a note causes it to stretch and hence rise in pitch. There is also the fact that the actual vibrating length of a fretted string is a little bit longer than the distance between the fret and the bridge because of the height of the bridge. So if you have a string of length L and height (action) d fretted at the 12th fret (L/2) the actual length of the vibrating string will be SQRT((L/2)^2 + d^2).

Imagine the following scenario:

Consider a string of mass M and length L. A small mass m is added near the bridge.

When a note is fretted, the vibrating length is l.

Let’s pretend for a moment (and I don’t believe this for one second) that the string vibrates at a fundamental frequency that is related l and the mass of the vibrating part (M/L * l) + m. Given that the effect of m becomes increasingly significant as l gets smaller, this would work to compensate for the fact that the intonation is increasingly “worse” the further up the neck you go. (Stands back and wait for the diatribe!)

As for the elasticity, the string obviously deforms when it is plucked. If this deformation is not elastic then it is plastic and hence the string will not return to its original shape. This would mean that every time you plucked the string, it would need re-tuning. I know that there is some degree of plastic deformation over time (I think it's known as creep in metals) but I don't see how a string can loose elasticity and still be able to vibrate at all.

I can see how the build-up of dirt and grease in the strings will affect the mass, mass distribution and flexibility of the strings. Also corrosion will affect the thickness and the action of the frets on the strings will also have an effect on the homogeneity of the strings.

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Here is an article that was posted on Doolins website-link. In article Seven he gives a bit of info on worn strings. Here is another link to a bit on the subject from Siminoff's "The Luthiers Handbook"-link

I believe Daddario also has a pretty good bit of information about strings.

Peace,Rich

Thanks for the links. The intonation articles are particularly interesting. I think there is another factor to intonation other than the fact that fretting a note causes it to stretch and hence rise in pitch. There is also the fact that the actual vibrating length of a fretted string is a little bit longer than the distance between the fret and the bridge because of the height of the bridge. So if you have a string of length L and height (action) d fretted at the 12th fret (L/2) the actual length of the vibrating string will be SQRT((L/2)^2 + d^2).

Imagine the following scenario:

Consider a string of mass M and length L. A small mass m is added near the bridge.

When a note is fretted, the vibrating length is l.

Let’s pretend for a moment (and I don’t believe this for one second) that the string vibrates at a fundamental frequency that is related l and the mass of the vibrating part (M/L * l) + m. Given that the effect of m becomes increasingly significant as l gets smaller, this would work to compensate for the fact that the intonation is increasingly “worse” the further up the neck you go. (Stands back and wait for the diatribe!)

As for the elasticity, the string obviously deforms when it is plucked. If this deformation is not elastic then it is plastic and hence the string will not return to its original shape. This would mean that every time you plucked the string, it would need re-tuning. I know that there is some degree of plastic deformation over time (I think it's known as creep in metals) but I don't see how a string can loose elasticity and still be able to vibrate at all.

I can see how the build-up of dirt and grease in the strings will affect the mass, mass distribution and flexibility of the strings. Also corrosion will affect the thickness and the action of the frets on the strings will also have an effect on the homogeneity of the strings.

When you consider action and stretch(I take that as to tighten, or increase tension) the pitch does rise. Point taken on the length as a factor(adjusting that length is how we currently attempt to correct for increased tension from fretting. The added length should drop the pitch to some extent, but the increase in tension from fretting will be raise the pitch more than the drop in pitch from the slight increase in length(assuming we have not modified the fret position in relation to the scale length by moving the saddle). This could also be observed when bending. You will increase the vibrating length of the string from the point it contacts the fret to the saddle, which should drop the pitch. However the act of stretching(again same usage as above, to tighten) will raise the pitch more than the drop in pitch from added length. Daddario has information on their string properties(unit weight, in particular), and provides a formula to establish frequency based on unit weight, scale length(vibrating length), and tension.

As for elasticity and plastcity(or creep?). I think you have the right idea. There is some, but obviously a string would not function well if it had a high degree of plasticity. Look at nylon strings. Different core material, they are still wound to add density. However the elastic and plastic charictoristics may be easier to buy into if you take steel out of the picture. If you look again at steel strings and think about what a string looks like when you remove it from a tuner you can see that it certainly does have plasticity(else it would just straighten right back out). As far as seeing how a string can vibrate at all if it looses elasticity. I think that is exactly what I am saying about worn out strings or loss of efficiency. Old strings that have lost some of their elastic properties, become less efficient and do not vibrate as well(thus they are wear out). Wear as it relates to the material being "worn off"(by fretting and such), and thus altering the density of the string. Is certainly a factor, but with the frequency of string changes, and the actual amount of material that would be removed during that time. It is hard to believe that it is nearly as significant as loss of elasticity.

A closer look at how a deflected string will act as it passes over a saddle or nut will also come into play as a factor to consider. Although we would like to think of a strings vibrating length as homogenous. The ends of the vibrating length are often distorted to some extent(be that fretted, over a saddle, nut or what have you). I think we would have to add this to the list of factors to consider.

I am still seeing the possibility in what you are saying with regards to altering the density of a string. By increasing density tward at one side of the scale length you(given all else is equal, elasticicity, tension, deflection) you will alter the ratio of length to density when you fret. The concept is really good at a glance. I am still right with you on this being the focus of the conversation. Even though our conversation seems to be focused on identifying factors or variables that will relate, the objective is still to explore altering density tward on side of the scale length.

Peace,Rich

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One last quick thought about elasticity (since it's not really the main point of our discussion): I think it's all a matter of timescales. I agree with you about the fact that the string holds its shape from the tuner. This plastic deformation happens over a much longer timescale than a vibration of a string. Even though the string may creep if deformed and held for a longer time, this plastic deformation will just provide a new "starting position" for the string. Any (small) movements away from this "neutral" position will result in elastic deformation. The string will still try to return and hence oscillate. What you've said previously about kinks in the string will no doubt affect the neutral point of the string and hence (implicitly) the shape of the vibrations on the string but I'm still not sure that the elastic response is less. When the string truly stops being elastic, I think it will break almost instantly. In other words, I don't see how it can gradually lose elasticity without reaching critical failure strain very quickly.

You also raise a good point about nylon strings. As an aside, did you know that some polymers (I'm not sure if it applies to nylon but it certainly does apply to elastic bands) behave contrary to most "normal" materials in their response to temperature. Most things get easier to stretch when you heat them up but polymers are harder to stretch when hotter. Not really relevant but interesting isn't it?

With regard the main topic of this thread. I invite someone to do a little experiment (I'll try it myself when I'm next re-stringing one of my guitars):

Try fitting some form of collar (a tight fit would be important) of some noticeable mass (perhaps wrap a bit of wire?) around a short section of string near the bridge and observe the following:

How does the string sound when plucked? Any nasty harmonics?

Is the intonation affected? In which direction and by how much?

What happens when you move the "mass" along the string?

What happens if you increase/decrease the mass?

How annoying is it to realize that you've just made your guitar sound terrible on the whim of some bloke on the internet and you now have to re-restring it?

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Interesting...

Well... If there is a distinct boundary where the mass per unit length changes, moving waves would (partially) reflect at that point... (how much would reflect would depend on how big the change in mass between the 2 sections was) so if you had a constant variation of string mass along the length then I guess they'd somehow reflect gradually along the length of the string as they moved (?) [i can picture that happening in my head]

I'd imagine that if there was a sudden change in mass/ unit length, you'd certainly get some weird harmonics. If it was more gradual, I'm not so sure. It would surely affect the sound but I'm not so sure how.

How does an impedence mismatch between amp/ speakers affect the sound? I've never actually tried that myself.

I'd imagine that the change in sound would bear some similarity with the amp/ speaker mismatch actually...

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