MIMF

Mark:
I got an idea this morning that might help: remember that the string is being stretched at both ends when you push it down to fret it, and that's why you need to compensate at both ends.

Think of the string as being split into two lengths at the first fret: we'll call the length between the fret and the saddle the 'front string' and the length between the nut and the fret the 'back string'. Let's say you've attached them to a post that can pull them down to the fretboard surface. What happens to the tension in the two ends as you pull them down?

It goes up, of course. The length changes, as Pythagoras told us it would, and the tension rises. Because the back string is so much shorter than the front string it covers a larger angle, and the back string tension rises more than the front string. If you move the post to the second fret position, you'll find that the tension change is less for the back string, and greater for the front string, and it keeps going in the same way as you go up the fretboard.

Using this 'clamped' setup, you can see that compensating the saddle could be relatively straightforward. If you want the intonation to be right you need to add a little length between the fret and the saddle, and since the tension rises as you go up to higher frets, you need to add more length in proportion as you go up. I have not done the math, but I strongly suspect that whatever length change makes the intonation come out right for the first fret will be pretty close to right for every other fret as well. But that ignores the contribution of the back string.

With the back string you get the opposite effect in this clamped condition: the tension rise is highest at the first fret, and gets to be less and less as you go up. Of course, real strings are not clamped, and that tension rise is communicated to the front string, which would thus require more compensation in proportion at the first fret than it would at the 12th. That's backwards if all you can do is move is the saddle back, but if you can move the nut up toward the frets you can do it. Thus we see that to properly compensate the string, you really do need to move both the nut and the saddle.

Note that this is just talking about the fretted string. The string doesn't know if it's you doing the fretting, or a hydraulic cylinder, or a capo: it just makes the pitch it's going to make when you push it down. Thus the compensation that makes the open string play in tune should also make the guitar play in tune when it's capoed. Naturally, in the real world, it doesn't always work out that nicely, in part because the capo is likely to put more or less pressure on the string than you would use. Still, nut compensation does help the guitar to play in tune when it's capoed.

Does that help clear it up?

Alan Carruth / Luthier

Alan-

What does your rig for testing strings and compensation look like? Would you mind posting a photo with a little description?

And how do you add the compensation to your nuts? Do you construct an overhang to the nut over the fingerboard? Or you make the
distance to the first fret shorter and nibble the nut back? Both are functionally equivalent, but they will look different?

-Doug Shaker

Here's a photo of a peghead that I did with a compensated nut. I move the whole nut forward, and then using a small dremel router I cut back the groove to the point that I wanted.

This actually makes sense to me. I've noticed so many guitars that seem to be sharp coming right out of the first fret. It seems like so often that I have to tune the open E a bit flat to get the rest to play in tune/ and if I tune it true then every fret going up the way plays sharp. so I either have an open E that's flat or every note after that is sharp. Neither way is good. I'm going to seriously look into this.
Also, I've seen somewhere before where a guy showed how to fix this after the fact. He took a little sliver of bone and superglued it to the front face of the nut so the the 6th string makes contact a bit closer to the saddle than the rest of the strings. I remember that it seemed to fix the problem, but it was really ugly. How would any of you suggest fixing this and still look nice rather than looking like an add on or afterthought?

Well, I did post that photo and tell how I do it.
There are a few things in the Library about this, too. Here's one link- this is under "necks" in the Library. http://www.mimf.com/old-lib/compensate_nut.htm

Alan, thanks for your patience and considered explanations. I've read them several times, and while they make sense, I somehow feel that something is missing.


After some thought, I realized why we went with this solution. We were dealing with a guitar that had a tall bridge and steep string angles, and we had a certain unwillingness to tear the bridge off a $5k plus guitar and redo the bridge plate and saddle. (I'm speaking of the Martin we did here, BTW.) We moved the string back almost a quarter of an inch because it worked out mathematically, and because we couldn't move it any less! That is, we couldn't add some extra bone to the back of the saddle, the tension forward would have gotten very dramatic.

What surprised me was that the tone didn't change one bit. I expected to find that it would sound lousy, and we would have to go back to the old setup. Instead, it still sounds incredible.

So, I suspect that the problem that I was solving could not have been solved as easily or cheaply with the more nuanced solutions presented here. Most importantly, the thing is in tune, and my friend is still thrilled to have a guitar play truly in tune.

I wish you sharp tools, flat workbenches, and perfect intonation!

Mark Swanson wrote:Well, I did post that photo and tell how I do it.
There are a few things in the Library about this, too. Here's one link- this is under "necks" in the Library. http://www.mimf.com/old-lib/compensate_nut.htm

Mark, didn't mean to insult... In fact I know it wasn't you that I'm thinking of because it wasn't here that I saw it. It was a youtube video or something. I'm sure yours would be much nicer than this one.

This article is a good one. http://www.mimf.com/nutcomp/index.htm

Mark Swanson wrote:This article is a good one. http://www.mimf.com/nutcomp/index.htm

That picture of a compensated 12 string nut is awe-inspiring.

Here, this'll clear it all up: http://translate.google.com/translate?h ... CDMQ7gEwAA

Yeah, that clears it all up all right! <sarcasm>

Steve Senseney asked:
"Does anyone have a precision method, or is it all guess work and luck?"

I have recently built a quick-and-dirty setup (which I rather immodestly christened the GNASHER – the Garland Nut And Saddle Harmonicity Enhancement Rig – without realizing Alan and others had been working on the issue and building similar devices!) to measure nut and saddle compensation for a single string at a time, more or less exactly in the way Alan describes.

The basic mechanism is sliders which engage in the fret slots of a sawn fretboard mounted in the rig (the nut position is initially just another sawn fret). The sliders at the nut and saddle end have long frets mounted at an angle to the string, so that sliding back and forth alters the point of contact with the string. These are calibrated with a zero position, which can be used to set to the nominal scale length, up to 6mm back for the saddle, and 3mm forward for the nut. A third slider has a straight fret mounted directly above the fret slot – this slider can be placed in any of the sawn fret positions.

First the desired action is set at the 12th fret by shimming as necessary under the saddle slider and third slider placed at the 12th fret (Gnasher Mk 1 uses shims; Mark 2 will have a screw adjustment to set the height of these sliders). The nut and saddle sliders can be set to the '0mm' position and the string tuned to pitch if you wish to measure the degree of sharpness using no compensation (measurement is by placing the third slider in a fret slot and fretting a note, reading the pitch deviation via the tuner output jack).

Then the iterative process Alan describes begins. The saddle slider is moved to lengthen the string, the string retuned to pitch, and the pitch at the 12th fret (or some higher fret if desired) measured with the third slider. The nut slider is then adjusted accordingly, the string retuned etc. Once the saddle offset is correct, the nut slider is moved to shorten the string, measuring the pitch at the 1st, 2nd or 3rd fret position with the third slider in exactly the same way. Then the 12th fret intonation is rechecked and the saddle readjusted. Eventually the correct compensation at the nut and saddle end is arrived at. I have not yet had time to do multiple experiments to check the repeatablility as Alan has, but I suspect there would be some variation, as he describes.

Hi Mark,
One thing to remember is that nut compensation is for the "unstretched" string. Because the unfretted string has no additional tension added by fretting, it will sound flat at the mathematically correct position. Conversely, if it is tuned to pitch the fretted stings that have tension added by fretting will sound sharp. The nut compensation allows the open strings to sound it tune with the fretted (increased tension) strings.
Capoing at the first fret and putting the guitar in tune should show how much the open strings are off when the capo is removed.
Saddle compensation is still the main way to get things intonated, but your's seems a little extreme. <g>

I'd like to thank everyone who contributed to this thread.