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The Reason For Compensation And Wound Strings

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I am currently researching topics that involve compensation, string gauge and so forth. There are two reasons we need compensation at the bridge but I found about 9 out of 10 web pages only mention one reason, stretching of the string when fretting a note

Here are three pages where the other reason is mentioned and it is also why thicker gauge strings are wound. Remember you can use the “Find On This Page” function if you want to quickly find the paragraph. Just search for the first 2 or 3 words


“The whole reason for compensation is to make up for the extra stiffness in thicker strings. This makes the endpoints at the nut and bridge less than perfect nodes or "pivot points" for a vibrating string. The result is the vibrational length of the string is effectively shorter (sharp) than the bridge-to-nut physical length would indicate

Note how the compensation makes the thicker strings longer ... except in one case: The reason there is a significant change in compensation at the G string of an acoustic, is that this is the first wound string, and it's core filament is actually smaller than the B string, making its endpoints more flexible than the B -- so the G actually requires less compensation than the B”

If you read page two of this discussion some guy has shown some calculus but I’m not sure if its on the topic


“The reason for compensation is a combination of the imperfect flexibility of the string (which you mention), and the action of fretting a note. First, as you fret a note, you stretch the string to some degree - this effect gets greater as you go up the FB, and the compensation also becomes a larger % of the total string length - which is fortunate.

Second, as the vibrating part of the string gets shorter, the imperfect flexibility has a larger practical effect on both the primary note and the inharmonicity caused by the imperfect flexibility. This second effect is a double whammy, AND is the "art" part of piano tuning and guitar intonation”

This last one talks about piano tuning but is not very long and has an interesting variation of the fret-spacing formula so it would be good to read the whole thing. The part I was most interested in is what I remember Ripthorn talking about

I think this is translated from Swedish so the wording is unusual


“Inharmonicity is caused by the fastening fault in the string endings. A string is fastened very hard in the nut and the bridge, and because of its stiffness it can't vibrate all the way to its ends. Close to the nut and bridge there are short parts of the string that does not vibrate properly. It is said that the effective length of a string is shorter than its geometrical lenght. The stiffer the string the longer the non vibrating parts”

The reason that the ends of a string do not vibrate is because they are nodal points and I have always understood this to be the primary reason for compensation. For example if you have very low action you still need compensation, it cannot be eliminated

I hope people will find this interesting and also I am not trying to shoot anyone down in flames. After finding 9 out of 10 websites that only talk about the one reason for compensation I can understand why some people think fretting is the only reason for it

Edited by Crusader
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no real arguments with any of that (for a change :D )

but i am not so sure about the first one:

The whole reason for compensation is to make up for the extra stiffness in thicker strings.

i think its just the way he has stated it that doesnt sit right with me and could be misleading, since we know compensation is to make up for the action of fretting a note, and we also know instruments like lapsteels do not need any compensation whatever the thickness of the string. its not a perfect analogy since lapsteels are not 'fretted' in the same way and players have to use thier ears more. even so - if the statement above was true then it would make sense to add compensation to lapsteels for more accurate 'fretting'. It simply isnt needed

but it makes more sense in the actual thread since i think he is actually talking about the different amount of compensation on each string rather than teh actual reasons behind compensating at all (i.e. the need for an angled or even two part acoustic saddle)

even so, he is off in his description of compensation (at least he was when he posted that in 2004)

Note how the compensation makes the thicker strings longer ... except in one case: The reason there is a significant change in compensation at the G string of an acoustic, is that this is the first wound string

he has not mentioned the fact that compensation has actually made all the strings longer - even the G. Sure it needs less due to thickness, construction and tension , but it still needs compensating because of the fretting action

there is a brand of strings i have been using that make custom sets - it may be something you want to look into. Not only do they offer a choice of round or hex core (changing the mass of the string quite a bit) they also offer different sized cores for wound strings. this makes quite a difference to the feel, and i can also tell you that the same gauge of string in the same tuning will need a different amount of compensation depending on the size of its core... supporting the points you have found

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Both of the reasons mentioned really trace back to the fact that all real materials have a modulus of elasticity, which causes a change in vibrational behavior as the string is deformed and the equation for an ideal stringwhich is that frequency is proportional to the square root of tension over length (just going off memory, so I don't remember the exact equation, theres a 2 in there somewhere like sqrt(t/2l) or something like that), which when considered in this context, makes perfect sense.

As far as compensation with wound strings, you are all of a sudden introducing two different vibrators (the core and the winding) so it gets complex fast, but still some great structural acoustics (which I love). A good topic to bring up as understanding why we do things is the first step to any innovation.

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Working 7 days lately sorry for late response

Yes I think in the first two quotes they could have used better words. But the second one is just pointing out that the thicker 4th string has less compensation than the thinner 3rd string. With an Accoustic guitar the 3rd string is usually the first wound and has less compensation than the second. Imagine if all your strings were plain. The compensation would be so great at the 6th string that it would be impossible to intonate

... A good topic to bring up as understanding why we do things is the first step to any innovation

Yes I'm trying to achieve improved intonation and here's something interesting. On one occasion I put a set of 52 to 11 gauge strings on one of my guitars and had to wind the 6th string saddle way back to get compensation. I put a 52 to 11 set on the LP recently and found quite the opposite! I had a hunch that the core wire on the 52 was not much thicker than the 46 and I was right. Perhaps it was a different brand, I can’t remember but its all relevant to my current project

The other reason I brought this up is I scratch my head and wonder why so many people say that stretching of the string when fretting is THE reason for compensation and this is what I have to say about it

If you talk to a Luthier I’m sure you will find he will be rather tight-lipped like any tradesman about his trade. On the other hand they might just want to keep things simple and not want to go into lengthy explanations. Like when I fix-up a door, it could be because the frame was out of parallel, the hinges were binding, it was scraping on the bottom and the striker-plate was too high. But when the owner comes along and asks what was wrong with it, I have learnt to give one or two simple reasons that the average person can understand. I don’t want to get caught up for 20 minutes explaining every detail – which they probably won’t understand anyway!

I believe perhaps this is why so many people only mention the one reason that you need compensation, to keep it simple and in any case the playing action is more relevant to the average person. But on this forum we are not the average person, we are interested in making guitars and I think it is an advantage to understand these finer details, even if we never make use of the knowledge, its good to know more than you need to

I found this web page last night and I picked out a few paragraphs that say things better than I can. It re-states things a couple of times which is quite annoying but it leads to what I want to say at the end. If you read the whole page the paragraphs are not in this order btw


InharmonicityIt is a common scientific approach to use simple models to explain the behaviour of physical systems, because it’s easier to understand basic behaviour when using simplified components. Factors that give rise to very complex behaviour, or only have a small effect, are often just ignored

Stiffness is quite a major factor that’s missing from the simplistic approach and is one of the major problems that string technology has had to minimise…strings don’t flex freely at the nut and saddle…their vibrating length is slightly shorter than their physical length. To complicate things further, stiffness has a gradually increasing effect on the higher harmonic modes of a vibrating string. Also, as the higher notes are played and the vibrating length of a string is shortened, because the stiffness is a constant, it becomes gradually more significant. This effect is known as inharmonicity

Scale LengthAlthough it is often described as vibrating length of the strings this isn’t really true, since string lengths are always slightly longer than the scale length to allow for intonation compensation... The most accurate way to determine the scale length of a (conventionally fretted) guitar is to measure from the nut to the twelfth fret then double the measurement…even this isn’t accurate for those very few instruments that have nut compensation

18 RuleThis method was in use in the 16th century…Although it isn’t as precise as calculating fret positions using the pure form of equal temperament based on the twelfth root of two, in practice, the error it produces results in some degree of intonation compensation, because the higher frets wind up further away from the saddle…

This is what I believe the Gibson 24 ¾ scale is all about; some degree of compensation built-into the fret spacing. I figure the SG I used to own had the frets calculated by 18.0077 (which is more than 18) The 12th fret lands 12 9/32” from the nut but because its not “conventionally fretted” it doesn’t mean its a 24 9/16” scale

(A point I’m trying to make here is that I don’t think Stewmac and other Luthiers are telling lies, its just another case of wanting to “keep it simple”)

Also to say that the 18 rule isn’t as precise as using the twelfth root of two – I don’t entirely agree. That SG I used to own intonated 'perfectly' on the 3rd and 4th strings and was very good over-all. My experience with Fenders and Epiphones is they intonate perfectly on the 1st string and gradually get worse up to the 6th string; depending what gauge strings you use

This was brought up by Kingfisher a few months ago and I've been doing the same types of experimenting and will post some of the results later

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I think you need to remember the forum is frequented by all sorts of skill levels. That doesnt mean higher level discussion does not happen - but as you point out, its often best to go with the simplest explanation and work upwards. if we get the question 'why does my bridge need compensation?' the answer is clearly 'because fretting the string bends it slightly and pushes it sharp'. 9 times out of 10 its a fully appropriate answer... i would even go so far as to say its 100% correct - that is THE reason for compensation

which is why:

about 9 out of 10 web pages only mention one reason, stretching of the string when fretting a note

now if the question was 'why do i need different amounts of compensation on different strings?' the answer obviously becomes a lot more complex - its no real secret, just a different (and more complex) answer to a very different question

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Wez, pretty much nailed my thoughts. I know how to work with wood and how to turn it into a very playable guitar. I understand string compensation for fretting a string. I have a basic knowledge of what nodes are. But that is basically where it ends. I like to read the in depth discussion getting into pickup placement and this topic that goes further into depth on compensation, but it usually does not take long for me to get lost in the topic and have to read it several times to understand (or at least I think I understand) what is being said. I have never taken very high maths nor anything beyond intro to physics. So a lot of what is being said goes right over my head. I am sure I am not the only person in this situation.

Not to say that these more scientific discussions are a bad thing, like I said I do enjoy reading them and I try to learn from them. But it is nice for a lot of people to see things said in laymans terms at times.

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