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Thread: String compensation question

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    Default String compensation question

    Does the string tension come into play for figuring compensation or is it just core wire diameter size and distance from the fretboard. The reason I am asking is I just put a set of EJ80's on my octave mandolin, and the typical mandolin compensation was off. The A string is wound, but the core is 0.012, the same as the E string. There is a difference in string tension according to the D'Addario package with the E at 18.59lbs and the A at 25.43 lbs.
    Bob Schmidt

  2. #2

    Default Re: String compensation question

    How far is it off? I just say this because I have chased compensation issues that were actually the result of the bridge being in the wrong place. Easy to do!

    Technically it includes pitch of the string, composition and size as well as construction of the string (and therefore the resulting tension), scale length, action height, and how hard the player is fretting.
    But generally you can move up or down one gauge of strings without a measurable change. It's usually when you switch tunings or switching a course from plain to wound that things need to be completely re-cut.

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    Default Re: String compensation question

    Marty,
    The A string was out with the E and G good. The D was also slightly out. I made a different saddle for the bridge that was stepped on an angle that would be similar to a guitar and it is pretty close, but since both the E and A have the same core diameter I was wondering if I should change it so the top 2 coarses have the same compensation. I want to make another saddle anyhow. It is functional but I am not happy with the appearence.
    Bob Schmidt

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    Default Re: String compensation question

    Quote Originally Posted by irishmando View Post
    Does the string tension come into play for figuring compensation or is it just core wire diameter size and distance from the fretboard. The reason I am asking is I just put a set of EJ80's on my octave mandolin, and the typical mandolin compensation was off. The A string is wound, but the core is 0.012, the same as the E string. There is a difference in string tension according to the D'Addario package with the E at 18.59lbs and the A at 25.43 lbs.

    The usual formula for the frequency of an ideal string, f, is given by this:

    f = (1/2L) * SQRT(T/mu)

    where L is the string length, T is the string tension, and mu is the linear mass density (i.e., mass per unit length) of the string. "SQRT( )" means to take the square root of the quantity in parentheses, and "*" means multiplication).

    First, as you can see from the formula, the tension matters, and so does the mass density.

    Second, with respect to compensation: When you depress a string to fret it, you add a small bit of tension to it, by deflecting the string sideways. Also, at both the nut and bridge, the string is held tightly, and it is unable to flex as freely near these positions as it is towards the middle of the string. A physicist would refer to these as "end effects." Both of these phenomena -- tension change and end effects -- contribute to small deviations from ideality. The end effects, in particular, tend to suppress higher harmonics, and they also tend to shorten the "effective length" of the vibrating string by a little bit, thereby raising its frequency (see the formula above) relative to an ideal string. You can compensate for this effect, at least a little, by lengthening the string.

    Compensation is a complex subject. Here are just some (of many) things to consider. It is not possible to compensate for all types of strings in the same way. Also, compensation will introduce frequencies inaccuracies that depend on where the string is being fretted, that is, there exists no compensation that works for a given string at all fretted positions. Compensation also depends on the height of the action.

    Since compensation is used, at least in part, to "compensate" for the limited flexibility of the string near the nut and bridge (i.e., end effects), it will change with (1) the scale length of the instrument (changing the relative amounts of "free" compared with "less flexible" string), (2) the flexibility of the string itself (a wound string being more flexible than a solid-core string of the same mass density), and (3) the core size (only the core affects the change in tension under fretting), and (4) the string diameter, including any possible winding, and its height above the fretboard (this affects the amount of deflection required for fretting).

    When you change from a solid-core string to a wound string of the same frequency, you usually have to adjust the compensation, as well, to get the best possible intonation. On a mandolin, a wound "A" string of the same mu value uses slightly different compensation from a solid one. The solid core will require greater compensation.

    Also, to answer your question in a word, YES, the string tension comes into play, in addition to all those other factors -- including variables like your preferred action height. Since this topic is so complex, it is not usually approached theoretically, but practically. Compensation is simply a compromise -- not all fretted notes get fixed by it -- and you just have to find the best compromise.

    The "standard" mandolin bridge saddle, like the one found on most Gibson F5-style bridges that use the thumbwheel design, typically has fairly strong compensation (larger offset) for the A and G strings, which are the two strings with the largest cores. These offsets work fairly well for most medium string gauges, like D'Addario J-74's and their ilk. On most F- and A-model mandolins, the A string is typically unwound, while the G is wound. It is not so unusual, however, to find folks with such bridge saddles looking to change the default compensation if they happen to switch to using wound A strings with thinner cores (like Thomastik strings), which changes the optimal compensation. You just have to find out what works. Since compensation is such a small effect, most luthiers just copy a given saddle design (like the Gibson one) and don't worry further about it. Others find a slightly different design that they like better, and stick with that.

    The "standard" bridge saddle on an octave mandolin has a different compensation from the regular mandolin saddle just discussed, because it has more wound strings (G,D,A) with larger core sizes and the scale length is much longer (which changes the end effects). The string tension is different, too. The largest compensation on an octave mandolin saddle is for the G and D strings, with the G being the largest. The typical compensation on SOME octave saddles is the same for the A and E strings, reflecting their similar core sizes. On some OTHER octave mandolin saddles, however, the A string has slightly greater compensation than the E, but not as much as the D (which, in turn, is less than the G). It very much depends on the instrument and the luthier who made it.

    The bottom line is that, in most cases, bridge saddle compensation is optimized for the given instrument, strung up with a given set of strings, and with a given action! If you change any of these things, i.e., adjust the action to be significantly different, or swap out other string sets with different physical properties (wound/unwound, change in tension, mass density, etc.), you will change the compensation. Assuming that compensation had been optimized before this change (not always a good assumption!), then the compensation will be off, afterwards. How much? Only you can tell; compensation is strictly empirical. If it's a big annoyance to you, then you might have to get another bridge saddle cut by an experienced luthier who understands these issues. Short of that, you might try re-positioning or even tilting the bridge just a little (which affects compensation on all 4 string pairs) to see if that helps. But remember that the best compensation will always be specific to certain classes of strings sets that have similar physical properties.

    Good luck!

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    Default Re: String compensation question

    sblock, thanks for the reply. What you describe as an octave mandolin is what I guessed at, and it is pretty close, at least at the 12th fret with the current action which is not bad. I did add a bit of compensation for the wound A but not as much as the D string. It is now close, but since I am going to make another saddle I was wondering if I should remove that. From what you said it looks like I should just confirm what I have is good and go with it.
    Bob Schmidt

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    Default Re: String compensation question

    Quote Originally Posted by irishmando View Post
    sblock, thanks for the reply. What you describe as an octave mandolin is what I guessed at, and it is pretty close, at least at the 12th fret with the current action which is not bad. I did add a bit of compensation for the wound A but not as much as the D string. It is now close, but since I am going to make another saddle I was wondering if I should remove that. From what you said it looks like I should just confirm what I have is good and go with it.

    It always pays to check the history of these things on the MC!

    There's an earlier MC thread on the subject of octave mandolin saddles that has everything you need: htTtps://www.mandolincafe.com/forum/threads/101455-Octave-bridge-compensation

    See especially Paul Hostetter's posts and his detailed PICTURE of two types of octave mando compensation, at: http://www.lutherie.net/saddle_angle.htm.

    Reproduced here:
    Click image for larger version. 

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    That should answer your inquiry. All the best.

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  10. #7

    Default Re: String compensation question

    Great answers by @sblock. He doesn't highlight it, but (at least IMHO) the biggest part of the difference in compensation when changing strings, or changing between wound & unwound, is the non-ideal part, due to inelasticity. The equations get you close but not close enough, and trial & error is really the best guide.

    Also, as he points out, it's a compromise and never perfect. To see what it takes to get as close to perfect as possible, search the webz for images of "true temperament frets." Those are the guitars with the squiggly frets. There's also an interesting youtube on it by Paul Davids, with Adam Neely (two heroes of mine):

    https://www.youtube.com/watch?v=-penQWPHJzI

    That's for guitars; I wonder how it'd sound for mandolin. Frankly, I love a perfectly tuned mando (like Chris Thile). Also, as a keyboard player, there are definitely times I wish the guitarist had one (but usually that really means that the arrangement is at fault.)

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  12. #8
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    Default Re: String compensation question

    Thanks a lot everyone. What I have now is the middle OM diagram. It is time to fine tune to see which of the 2 are better.
    Bob Schmidt

  13. #9

    Default Re: String compensation question

    For strings of the same diameter (or core diameter), higher tension requires less compensation. Tension change from fretting, which is the reason for different amounts of compensation, is the same (assumimg similar action). But higher initial tension means that that change is a smaller percentage of the total tension.
    John

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