Solving the 6th string intonation problem

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Mark Pollock
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Solving the 6th string intonation problem

Post by Mark Pollock »

Hi folks, first timer here.

I've been bothered by the difficulty of keeping that thick E string in tune as I play up the neck, and as I add a capo. Following the lead of some other folks, I calculated that I needed about 1/4" of extra length at the saddle to get the thing to intonate properly, and that put the saddle right on the bridge pin.

Solution? Get rid of the saddle at that point and just have the string come off the bridge pin.

Image

It worked incredibly well - perfect intonation, the tone is just as good as before, and the whole thing is reversible if I want to sell the guitar in the future.

Of course, this would be a lousy solution for anyone with an under saddle transducer, but it works for purely acoustic play.

I blogged the whole process as well, http://summergarageluthier.blogspot.com ... tring.html

The next step is to turn the pin so that is looks like a regular pin with a round head on top. That will be a little more difficult, but should be doable.

Hope this inspires somebody to come up with an even more elegant solution.

Mark

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Andrew Porter
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Re: Solving the 6th string intonation problem

Post by Andrew Porter »

Ingenious, simple and reversible!
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Bob Gramann
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Re: Solving the 6th string intonation problem

Post by Bob Gramann »

If it's just the fat E-string, I would check the nut and see if it has crumbled moving the contact point back towards the tuner. That seems way off for just one string if the nut is correct.

Alan Carruth
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Re: Solving the 6th string intonation problem

Post by Alan Carruth »

Have you checked the intonation at the first fret? Those fat strings can go really sharp on the low frets, and they just get worse as you go up. I've been using nut compensation lately, and find myself moving the nut up toward the first fret by two or three millimeters on a regular basis to get them to play in tune. One advantage; the more you compensate at the nut, the less you need at the bridge end.

Alan Carruth / Luthier

Mark Pollock
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Re: Solving the 6th string intonation problem

Post by Mark Pollock »

@Bob, the nut was just fine on both guitars we did this on. I had just made a new nut for the Guild D25M, and the D-41 has been set up just about perfectly within its limits.

@Alan, it was the same no matter where we capo'ed, the math worked out the same every time. These guitars are strung with lights, with a high action and often in drop tuning. Also, Ray, the owner of the D-41 on the blog, capos a lot, and once you capo, all the adjustments at the nut disappear. Thus the reason the Feitin system was not going to work for him, it doesn't hold up when a capo is introduced. This holds up perfectly, with no retuning needed no matter where the capo is moved.

Sadly, it only solves tuning problems at the 6th string. The 5th string, A, has a much more subtle problem, and we would probably just have to add a tiny sliver of bone in back of the saddle to get it dialed in perfectly. I'm not sure how much we would want to split hairs over perfect tuning after that - it seems to get kind of pointless. At least we solved the most audible and egregious problem!

Simon Magennis
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Re: Solving the 6th string intonation problem

Post by Simon Magennis »

Interesting. Looking at the photo, and of course the angle makes it difficult to be sure, the saddle looks to be almost parallel to the front of the bridge. How much compensation is built into the bridge?

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Mark Swanson
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Re: Solving the 6th string intonation problem

Post by Mark Swanson »

There's a better solution than that. If the guitar's intonation is really that bad, then something is wrong. I'd look further into the nut. I have had real eye opening experience when I worked with compensated nuts, they really make a big difference. I'd experiment with that before I went on. If this were my guitar, I imagine I'd end up with a new bridge, with more compensation (check to see if the stock bridge was in the right place- sometimes they are not) and a compensated nut.
A compensated nut does indeed make a difference, even when a capo is used. Nut compensation allows the guitar to play notes more in tune in the lower positions, right? So, what difference does it make if I fret a note at the 3rd fret, or if I capo there? The guitar doesn't "know" if I am using a finger or a capo to fret a note.
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Alan Carruth
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Re: Solving the 6th string intonation problem

Post by Alan Carruth »

Mark Pollack wrote:
"..once you capo, all the adjustments at the nut disappear. "

Not so. I used to think that too.

String pitch rises when you stretch it by fretting. It rises more than you might expect when you fret at the first fret, and the pitch rise becomes greater as you go to higher frets. If you plot out the pitch as a function of fret, you get a rising line that starts out somewhere sharp of 'right', and gets sharper.

Adding length at the bridge end by compensating the saddle changes the slope of the line. A given displacement of the saddle amounts to a larger proportion of string length as you go to higher frets, and flattens the note more in proportion. It hardly make any difference at the first fret, but you can add enough length so that the note is on pitch at the twelfth fret. This would give a _falling_ line; still a little sharp at the first fret, correct at the 12th, and probably somewhat flat in the higher positions.

The way to compensate for the sharping at the first fret is to move the fret closer to the nut. If the string is, say, 10 cents sharp at the first fret, then moving that fret toward the nut by about 1/8" will correct it. The second fret will still be out, but you can move that toward the nut too.But that's just the same as moving the nut toward the frets and re-tuning, so why not do that? It works out that a movement of the nut that flats the first fret note by ten cents will flat _all_ of the notes by about that amount. In terms of our 'sharpness' graph, that moves the whole line down toward 'correct' intonation, without altering the slope as you go up.

Thus it works out that moving both the nut and the saddle can alter the position and slope of the 'sharpness' line and get it very close to where it should be. Of course, the exact amount of offset needed at the nut and saddle will be different for each string, and will also depend on things like the scale length, action height and amount of relief. Also, the more the top moves the more likely you are to have single notes that are out of tune, due to coupling of the string and top resonances. In the end, you'll never get the intonation on an acoustic guitar 'perfect', but it's possible to get it pretty darn close. I'll also note that the more you compensate the nut, the less you need to compensate the saddle. Both things do, after all, tend to shift the pitch of the string flat, and you only need as much as you need.

I had to go through the reasoning a few times myself to get it, and may not have been wholly convinced until I tried it on a guitar. Now I'm convinced. The big problem I have now is that, as Trevor says, once you've heard one that's in tune, it's hard to listen to one that's not.

Alan Carruth / Luthier

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Mark Swanson
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Re: Solving the 6th string intonation problem

Post by Mark Swanson »

Right on, Al- that is my experience too but you explained it so much better than I could!
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Steven Smith
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Re: Solving the 6th string intonation problem

Post by Steven Smith »

I plan to look at nut compensation much more closely, especially after a recent experience. On my most recent build I cut more off of the nut end of the fret board than my usual 0.030" or so. I probably took about 0.070" or a bit more. I thought I would have to cut the nut back but after intonating just the saddle it turns out this fretboard is more in tune than any of the six or so I've done to date

Steve Senseney
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Re: Solving the 6th string intonation problem

Post by Steve Senseney »

I want to thank Al for explaining this clealy for me. I never really understood it nearly well enough until now.

But, what is the way to get the right amount of compensation at the nut?

Does anyone have a precision method, or is it all guess work and luck?

Mark Pollock
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Re: Solving the 6th string intonation problem

Post by Mark Pollock »

Simon Magennis wrote:Interesting. Looking at the photo, and of course the angle makes it difficult to be sure, the saddle looks to be almost parallel to the front of the bridge. How much compensation is built into the bridge?
It's pretty typical Guild compensation on the bridge, not a whole lot. It's a 1977 Guild D25M, dead stock, good action, new nut and saddle.

To reply to another point here -

I'm confused as to how a compensated nut can have any effect on intonation when a capo is used. Once the capo is on, the compensated nut is no longer in effect, and the intonation would continue to be off as one progresses up the neck, correct? That is, if you have a capo on the third fret, the 15th fret harmonic and fretted note will continue to play out of tune by the same ratio as they did before, correct? Correct compensation at the bridge stays in effect despite the presence of the capo.

I have no doubt that a well setup/compensated nut makes a tremendous difference in intonation when playing without a capo, but I don't see how it can effect intonation once a capo is placed. Also, do you have to vary the nut intonation depending on what tuning/type of string you use?

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Mark Swanson
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Re: Solving the 6th string intonation problem

Post by Mark Swanson »

Once the capo is on, the compensated nut is no longer in effect, and the intonation would continue to be off as one progresses up the neck, correct?
No. I addressed that, and Al did too but much better than I did. It isn't easy to see I know, but as I said, If you have a guitar with a compensated nut and you fret a note then the nut helps the guitar play in tune, right? What difference is there if it's the finger that frets the string or if it's the capo? The ONLY difference is that the capo frets all 6 strings at once, and that makes NO difference at all.
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Mark Pollock
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Re: Solving the 6th string intonation problem

Post by Mark Pollock »

Hmm - I don't see it. Here's what is bugging me -

First, the saddle is in the wrong place for the 6th string on these guitars. In fact, I would assert (probably without controversy) that it is in the wrong place on most traditionally constructed guitars. I think this point will stand most examination.

The saddle is out of place no matter what note I play or where I place the capo. It is always out of place, too close. We can determine that out-of-place-ness mathematically for a particular string or tuning, by comparing the percent difference between the 12th fret harmonic and 12th fret fretted notes. We can also get reading on this by capoing in different places and getting harmonics and fretted notes 12 frets from the capoed spot.

Now, let up compensate SOLELY at the nut. We put in a little shim. The intonation improves based on that open note tuning - that is, the unfretted low "E" note.

I then capo the string. It is now, for all intents and purposes, using that fret as the nut. All is fine, UNTIL I start playing notes further up the string. That is, if I capo at the third fret, and play a G shape chord, I am now fretting a non-compensated string at the 6th fret, and I am sharp again. It is the same as if I simply hack-sawed off the nut and fretboard to the first fret - the nut is out of the picture. The capo worked fine, the capoed note was fine, but now, as I play of the neck, the intonation is sharp again.

The difference is not the difference BETWEEN a finger and a capo, it is the introduction of the capo and then using the capoed fretboard and playing up the frets with fingers as well.

(I REALLY hope this isn't a case of simple miscommunication. I've really tried to read these replies several times, and I suspect one of us isn't getting what the other is saying. I readily admit that it could be me.)

Could someone with a compensated nut capo their guitar and check the fretted notes with a tuner for sharpness?

Mark Pollock
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Re: Solving the 6th string intonation problem

Post by Mark Pollock »

Ugh - That was one ugly chunk of brain-dead writing on my part just now - having a nasty cold seems to reduce my literary skills. I'll take another shot at this tomorrow.

Trevor Gore
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Re: Solving the 6th string intonation problem

Post by Trevor Gore »

OK, I'll have a go, Mark.

Lets suppose that we have a perfect imaginary guitar, and lets say the distance between the nut (in its normal position) and the first fret is 35mm (just to make the maths easy). Fretting at the first fret will change pitch by exactly a semitone on our perfect guitar, which equals exactly 100 cents pitch change. If we introduce a new fret, 3.5mm from the nut in the direction of the first fret (i.e. one tenth of the first fret distance) and fret there (with our perfect tiny fingers) we get a note that is ~10 cents sharper than the open strings and all the other frets play perfectly "in tune" as normal. Now, suppose we decide to call this new fret a zero fret, (or alternatively move the nut to that position) and retune the guitar flatter (by 10 cents) so that the open strings are now tuned true. Doing this now makes all notes on all the other frets 10 cents flatter than before. And no matter where you put a capo, all the strings on all the frets will still be 10 cents flatter than before relative to your accurately tuned open strings.

Now try reading Al's post again.

Mark Pollock
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Re: Solving the 6th string intonation problem

Post by Mark Pollock »

Trevor, did you just describe what a capo does? That is, render everything on the nut side of the capo moot, and establish it's own "zero fret" as it were?

Really, I'm not trying to be difficult here. :?:

I also suspect I posted this in the wrong place - it should have gone into "repairs", as I'm pretty dang sure that most people posting in this section make guitars that are a heck of a lot better intonated than most factory guitars.

Alan Carruth
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Re: Solving the 6th string intonation problem

Post by Alan Carruth »

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

There is a more or less precise way to establish both the nut and saddle compensation for a given string. Trevor shows it in his book, but it actually goes 'way back: Bartolini used the same setup in the 70s, and Byers describes a version in his article in 'American Lutherie'. Basically, you set up a stiff beam that you can mount a string on and get it up to pitch, arrange a way to be able to fret it at the first and 12th frets, and have a nut and saddle that can be adjusted to set the intonation based on the pitches of the fretted notes. If you're going to test more than one string length you'll need a way to adjust the position of the first fret, at least, as well. For the range of lengths I'm interested in, I figure the distance between the 11th and 12th frets doesn't change enough to matter. You need both of them to get a realistic string stretch when you fret at the 12th. Finally, some sort of pickup in the saddle makes it a lot easier plug in your tuner.

In use, I set mine up so that the first fret, nut, and saddle are at their correct 'theoretical' positions. The action is also set up to where I'll want it (on my rig, the 11th and 12th frets cam be moved up and down a little). The string is mounted, and brought up to pitch long enough to stay stable. Then I fret it at the 12th fret, and see how much sharp the intonation is from a true octave. Note that I don't use the 12th fret overtone: some strings are stiff enough to shift that several cents sharp. Based on how sharp the string is when fretted I move the saddle away from thew 12th fret, and keep going until I get the octave to be in tune. Then I go up and fret it at the first fret. This will also be sharp, so the nut gets shifted toward the first fret by enough to bring it into line.

At this point, you'll find that the 12th fret intonation has gone a bit flat, and you need to move the saddle back toward the nut a little. This, of course, effects the intonation at the first fret, so you adjust that accordingly, which shifts the 12th fret pitch again. Each iteration the adjustment becomes smaller, and at some point you can just declare victory and write the numbers down.

This is _supposed_ to give you a pair of unique numbers for the nut and saddle offsets that will be perfect and reproducible for any given string and setup. Somehow that never seems to happen for me. Trevor uses a mechanical setup to fret the strings which applies a uniform pressure at a known spot. Somehow the setup I cobbled together was no more uniform than fretting manually, so I just do that, and that certainly introduces some variation. I excuse this with the rationalization that, after all, players don't fret uniformly either. I know, lame.... At any rate, since I've developed a healthy respect for the workings of Murphy and his ilk, I run through each string set three times, mounting and dismounting each string for every reading, and then average the readings. There's always some variation in the offsets, even when the tuner tells me they're right on.

Even if there were no variations in the readings from the rig, I would not expect those numbers to yield exact intonation on a real guitar, if only because the bridge moves as the top vibrates. If you're careful to place the main resonances between scale pitches the changes will be minor, but still can be real.

There's a certain amount of work involved in this. On the bright side, you should only have to do it once for any given brand of string, scale length, and action setup. Also, as Trevor points out, some compensation of the nut is likely to be an improvement over none, even if it's not perfect. With all the uncertainties involved, I'm not sure if worrying about exactitude is going to be worthwhile, but, as I say, it does seem to be worth the effort to get at least reasonably close.

Alan Carruth / Luthier

Ron Belanger
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Re: Solving the 6th string intonation problem

Post by Ron Belanger »

Ah!!! The light goes on. Thanks Alan and Trevor for clarifying what has been a muddy issue for me.

Trevor Gore
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Re: Solving the 6th string intonation problem

Post by Trevor Gore »

Mark Pollock wrote:Trevor, did you just describe what a capo does? That is, render everything on the nut side of the capo moot, and establish it's own "zero fret" as it were?
What I described is what nut compensation does for a guitar and that if you put a capo on, nut compensation still has an effect.

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