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I have been cutting a little off the fingerboard to bring the nut forward for some time now. I do it because of good advice from some of the excellent buiders here. It does seem to work well when I intonnate the guitar.

But

The more I try to figure out what the correct nut/saddle intonnation is for a steel string the more baffled I get. I have read the research done by Gregory Byers for intonnating classical guitars. http://www.byersguitars.com/Research/Research.html It seems like a logical and straight forward approach. I have tried to translate it to SS, but the trouble is the math eludes me. Seems to be missing some expermential component that I don't have.

Then I look at the Earvanna Nut/Saddle. From what Brian Howard and others have said it works pretty well. How did Earvanna arrive at that design? Trial and error? Or Math?

So, how do you calculate the nut/saddle compensation for certain set of steel strings at a certain scale? I realize action height, and other factors play a role, but in general?

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Joe Beaver
Maker of Sawdust

Compensations at the nut will have a bigger effect on the first few frets due to the severe break angles formed when fretting those notes. I can't speak for Earvanna and how they arrived at their dimensions, but a mathematical approach makes the most sense. One cent on the tuner is 1% of a semitone, so by figuring an average shift in pitch needed, this can be converted to distance easily enough by multiplying the distance to the first fret ( one semitone) by this percentage and moving the edge of the nut that amount. Remember you must still lengthen or shorten as necessary so the adjustments at the nut moves in the opposite direction as those at the saddle. This of course will not be perfect due to the ever changing break angles and will require new compensations at the bridge. While there is no way to achieve perfect intonation on a fretted instrument, compensated nuts do play more in tune over more of the board. I use the same formula to get close when setting up Floyd Rose trems. But you need to have everything else set first, action, relief, string gauge, and have the instrument strung up. If you are asking how to calculate compensation before construction, I have found Stew Macs calculator to be pretty spot on.

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Brian

You never know what you are capable of until you actually try.

https://www.howardguitarsdelaware.com/

Thanks Brian, Yep, I use Stew Macs Calculator also. It is handy.

I was thinking along the lines of when Gregory Byer said something like 'imagine a fret board you could move back and forth between to fixed points. If you do it right you will find a spot where the nut will be closer to the first fret and the saddle will move back to bring it into close intonnation.

I would like to discover how to calculate those distances. Essentially that is what Earvanna has done. Or close to it.

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Joe Beaver
Maker of Sawdust

Joe, all the theory and mathematics for doing "proper" nut compensation is in "the book". Basically, it shows you how to do the calcs and how to make a nut like this:

Compensated nut

I didn't say it was simple, though! The book also has about half a dozen alternative "quick and dirty" methods of doing nut compensation, getting progressively more complicated and progressively more effective. Choose the method you're comfortable with.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

The problem is most people think of a compensated nut in the wrong fashion related to the frets and saddle placement. The nut is really a separate entity all together as much as it seems to be otherwise. Kind of a movable or adjustable fret. The only time the saddle length really plays directly into accurate unadjustable tone is when the guitar is fretted.

I think it's Stephen Delft that mentions the use of a capo at the 2nd fret and intonating at the 14th to isolate the nut from the saddle/fretboard relationship. After the saddle/string length is set to the fret positions then he removes the capo and adds shims one at a time to get proper tone in the open position. Not a big fan of this "shim approach".

I'm more in favor shortening the fret to nut position by taking 1.5 mm(.060 or 1/16th) off the nut end of the fretboard and cut back the nut to proper individual string length after the fret to saddle intonation has been set correctly. Mark Swanson did this, at one time, but now uses a zero nut, at last speaking.

This shortened fretboard will make the guitar play sharp in the open position, in relationship to the fretted positions, or play flat, fretted in relation to open tone, generally. This error is what happens naturally on a guitar that does not have a compensated nut only not to this degree or direction. As the string length is changed at the nut, by grinding back, the tone is checked against the fretted tone.

This corrects the problem of tuning, say by the fifth fret to open, then when one barres the two strings, they are off. If one tunes to fifths by barring, then its off when one frets the guitar one string to the other, open. Tuning by octaves at the seventh produces the same error as barring.

I have seen a few guitars that have compensated nuts and they are, for some reason different. Most follow a specific pattern but some do not....why?? I don't know.

As for Earvana, I think they can get to an improvement from a uncompensated nut but it's better to compensate the nut against a strob.

If you think about it the only time the nut comes into play is when the string is played in the open position. The other frets are set and cannot be adjusted, the nut can, and it can be for each individual string.

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Billy Dean Thomas
Covina, CA

"Multi famam, conscientiam, pauci verentur."
(Many fear their reputation, few their conscience)

Fascinating thread. Thanks for starting it off, Joe.

Trevor, on your site, I noticed that the linked page has a typo which you may want to fix. The last sentence currently reads as, "If I need to measure string properties (usually only for non-standard strings) it take me a little longer." That should be "takes" and not "take," right?

BTW, I like your website.

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George :-)

Trevor,
That gives me yet another reason to buy the book. I’m going to have to see if I can budget it in.

Brian and Billy,
You guys are way beyond me in your musical knowledge. I thank you for the feedback.

After studying your post I have tried to eke out a procedure based on what I think you are saying. Please look at it and let me know if it is even in the ball park.

Procedure:
On a new build shorten the fret board at the nut by about .06”

String it up, setting action height etc.

Put a capo at the 2nd fret. Intonate the saddle using the 14th fret harmonic with the fretted note.

Remove capo and intonate the nut using maybe the 12th fret harmonic with the fretted note, recording the cents it is out. Use the cents as Brian suggested to determine the distance to setback the nut.

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Joe Beaver
Maker of Sawdust

I think you want to compare the 2nd fret fretted note to the 14th fret (or other) fretted note rather than the harmonic. The idea is to get the fretted notes to play more in tune with each other, which is what the saddle compensation if for (fretted notes). The harmonic that is 12 frets above a fretted note is like playing the string open; the saddle compensation doesn't factor in. If the low E is dead-nuts in tune, the 12th fret harmonic will be, too - regardless of saddle comp.

As far as the nut goes, maybe compare the open string to the fretted note on (or around) the 3rd fret. You don't need to compare to harmonics (same as open notes) or fretted notes up high on the neck.

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Finally escaped The Peoples' Republik of Massachusetts; I can smell the freedom in the air!

I couldn't put it off any longer! Put in my order.

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Waddy

Photobucket Build Album Library

Sound Clips of most of my guitars

You were right first time!

If you move the nut toward the first fret (and don't re-tune) the open string note gets sharper. But we tend to tune the open strings so that the open string plays the "true" note. This means that the note on every other fret is flatter than it was before by an amount commensurate with how far the nut was moved (~3 cents per mm for typical guitar scale lengths, constant for notes played on all frets). This is generally beneficial, because if a guitar is saddle-only compensated the frets below the twelfth typically play sharp.

If the saddle is moved, the difference in length is applied to each fretted string length but is a different percentage of string length in each fretted position, so it changes the pitch of each fretted position by a different amount.

Thanks, Waddy.

Thanks, George. Should be fixed by the time you read this.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Hey Trevor,
By adjusting my nut height and intonation at the saddle I can get every note to read correctly on my tuner, which is an equal tempered tuner.

What other effects are we looking for? It seems to me that since the nut is basically a fret, it makes no sense to compensate the nut, since every bit you move the nut around affects all the other notes, and the purpose for compensating the saddle is to compensate for string tension.

If it's necessary to compensate the nut, it should also be necessary to compensate every fret in every string position, as well as the nut and saddle, but the only time I see anybody do that, they are trying to change the guitars temperment from equal tempered to whatever, and it doesn't seem you are trying to change the instruments temperment, you are basically trying to get the instrument to play well in equal temperment (which is admittedly an imperfect temper by design).

Changing the absolute temper of the instrument is what the Buzz Feiten tuning system as well as the Earvana nut compensation are trying to do (I believe they both fail).

I could see compensating the nut if the strings were high at the nut, as that is why the saddle is compensated, but I can slot the nut so that the string is not being stretched any more than playing the next fret up, and they don't fret sharp in the slightest, and no nut compensation can change the temperment of the entire instrument from equal tempered.

If I can tune up my guitar in equal temperment without compensating the nut, what else are we trying to accomplish?

BTW I set up my guitars as low as my technique will allow, so that the neck can be as straight as possible, as I believe that too much neck relief affects the fret to fret spacing on the relieved part of the neck.

Maybe compensating the nut would allow me to set the guitar up higher for hard strummers, somehow.

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Old growth, shmold growth!

Nothing! You're there. I'd want to know my tuner was accurate, though.

The problem with standard saddle-only compensation is that the guitar, when perfectly set up, is in tune on the open string and at the twelfth fret. It would be an enormously happy coincidence if the amount of compensation required to fix things at the twelfth fret for the chosen action and relief also fixed things on all the other frets. Of course, mostly, it doesn't. Why should it? The result is that the majority of guitars play sharp on the first few frets to the tune of 4-6 cents. Now this, in itself, would not be a problem for most people. But the equal temperament interval of a 3rd (or 10th) is already ~14 cents sharp of Just intonation, which most people like to hear. Add to that another 6 cents (if you were pretty well perfectly set up) and you're now ~20 cents from a Just 3rd and that sounds pretty rough. This is why it is often difficult to get all the open chords to play in tune and most players do a bit of tweaking and end up with some acceptable compromise for what they're playing.

Sure, the only sensible target to aim for is accurate equal temperament, and that's what I do. But most guitars won't play that. If you look at all the micro-tonal errors (by fret, by string) and figure out where the frets would have to be in order to play equal temperament accurately (for a given set-up) what you find is that the fret spacing doesn't change from standard on a per string basis. So if you consider a fretboard sliced into six slivers, one for each string, and then shuffle the slivers slightly relative to each other you can get a much closer approximation to true equal temperament. But that would entail building a fretboard with stepped mini-frets, which would be hard to build and hard to play on. However, you can achieve the same effect by re-aligning all the slivers so that the frets are in straight lines again and moving the strings relative to the fretboard. And that just happens to be the same as nut and saddle compensation.

The Buzz Feiten thing is basically about setting up a "private" temperament so that guitar-friendly keys are slightly closer to Just temperament, at the expense of other keys which are now further away from Just. You either like it or you don't. I think the Earvana thing is about trying to get more accurate equal temperament. But Earvana is a "one size fits all" nut solution and conveniently forgets about the saddle, so is wrong a lot of the time. Proper nut compensation has to be done on a case by case basis, depending on string properties, set-up, etc. etc.

Not so much that you'd hear it! What you're affecting is the action at those fret, which will obviously impact the intonation.

There are other sources of intonation error, but this post is already long enough! One thing's for sure, though. If you hear the intonation errors inherent in the basic design and it bothers you, once you've played a properly intonated guitar (however you achieved it) there is no going back.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

It seems to me that since the nut is basically a fret, it makes no sense to compensate the nut,

In very simple terms, the reason for compensating the nut is because, as you say, it is basically a fret, BUT, the frets are not sharply pointed, but gently rounded, and that places the string contact area over a relatively wide area of the fret top, such that the actual stopped length of the string is a wee bit shorter. So we compensate the nut for this, to make the nut act like a ---correct--- fret. About .020" will do just fine; no need to do any special math, buy books, pray to the guitar gods, or sell your soul to the devil. Just cut the nut end of the fretboard about .020" shorter than the theoretical ideal, and all will be golden. If you use wide, "fat" frets, consider perhaps .030"....

K.I.S.S.(keep it simple, s*****)

I'll repeat myself: This is good stuff, fellas!

I do have one question, though. Sometimes people write about frets above or below the 12th fret. In my mind "below" means frets 1 - 11 and "above" means frets 13 - 19 or 20. Is this how others see it as well? Sorry if this is obvious, but just about every time I think something is obvious I make a mistake.

Again, thanks for sharing. This is really interesting.

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George :-)

It depends on what we're correcting for. String stretch? Innaccuracy in the chosen temperment? Both?
I was raised listening to a lot of piano and classical music, and learned to play guitar on a classical guitar that sounded horribly out of tune to me at all times, no matter what I did, but I was always told by my choir and band directors that was "just how guitars sound".
Later I learned about temperament.
If indeed we are correcting for string stretch, then the first few frets on a guitar require the least compensation, and the higher frets require the most.
If guitars are indeed sharp on the lower frets, then the stretching of the string will be much less a noticeable factor, but the compensating length will be a factor.
So it seems we would have a situation whereby on the lower frets, the compensating length corrects for the sharpness on the lower frets, transitioning to compensating for the string stretch on the upper frets, if I understand your description correctly.
There's a small region of overlap.
In either case, it would still seem to me that the neck should be as straight as possible in order to maintain the correct fret spacing proportion.
Right now I can get my steel strings to sound about as good as a piano chordally, but not as good as the orchestra music.
I remember the instrument parts being tuned in the upper register differently than the lower register instruments (upper clarinet, lower clarinet etc..) so it must be the same on the guitar, lower and upper registers. Is that what you are describing when you say the first frets on a guitar are sharp?

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Old growth, shmold growth!

Yes! The only real relationship the nut deals with is that between fretted and open tones. One can compensate the saddle without the nut, again, but as the nut does not stretch the string in playing, it is different than all the other frets, therefore must be positionally treated differently.

Also, as "fretted string stretch" is different as one goes up the neck, the frets actually progressively get sharper the further they get up the neck, to about the 7th to 9th position, then progressively better, tonally, from there to the 12th, then, worse thereafter. The nut has nothing to do with that. This means math is not your friend here because the equation is a lot more complicated than than just a straight line. Some classical builders deal with this somewhat by changing fret positions somewhat in relation to this exponential rate but as string stretch rates are different between different strings there's compromise there too.



I use this same .020(.5mm) method, but also when the guitar is first strung the strings are relatively flat. As the guitar is played, the strings develop flats in contact with the frets even on a freshly dressed fret. The G string worse than others because the windings are smaller. The 6th string contacts on one winding throughout the whole life of the string. The G can have noticeable flats after a couple of hours of heavy play. The other strings somewhere in between the two. This effects tuning too, to a lesser degree. As the frets wear, this becomes more pronounced especially in the very beginning after a fresh fret dress.

All this makes tuning a constant changing compromise. Compensating the nut is kind of like a scope on a rifle ..it doesn't change the shot grouping one bit, it just takes sighting error out of consideration. One can tune a guitar well by compromising notes, on some guitars better than others but a comp nut take a little error out.

To give an idea where this can be a real advantage is in the case of Nick Drake. He, much like Micheal Hedges used a huge amount of altered tunings...just about every song was different. Nick Drake being relatively small market player didn't have the advantage of Hedges, who had numerous guitars setup for different tunings, at the end of his career. Nick would spend 10-15 minutes sometimes trying to tune his guitar ... in front of an audience. Sometimes, as he was quite stage shy, Nick would literally walk off stage. ...and not come back.

On some of Hedge's guitars, he has these thick saddles, one can see on some youtubes and his altered tunings are drastic. It's difficult to make out any work done at the nut, but I'm pretty sure whoever was doing the work on Hedge's guitars knew what he was doing. Hedge's altered tunings sound perfect.

Tuning a guitar without knowledge of the compromises involved can be quite frustrating sometimes. Nut-comp helps with this, even more so, in front of an audience.

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Billy Dean Thomas
Covina, CA

"Multi famam, conscientiam, pauci verentur."
(Many fear their reputation, few their conscience)

I too am a proponent of KISS.

It is so true that when you are presented with choses, the simplest one tends to be the right one. Didn’t Eisenstein say something like that? Maybe not but I’m sure he wanted to.

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Joe Beaver
Maker of Sawdust

Unfortunately, keeping it simple doesn't make it right, though it may make it easy.

Joe, lets go back to your original post:
The experimental component that Byers doesn't give in the original paper is the string stretch data for steel strings, which you have to measure yourself. (BTW, the original paper was downloadable off Byer's site once, but doesn't appear to be now. The summary that exists now is a rather mangled version of what is in the original paper).

Mike Doolin does a good plain language description of the intonation problem here: Mike Doolin on Intonation and I agree with most of what he says. He says he can get away without nut intonation if he minimises nut height, but I find it is still helpful.
That differs from what both Doolin and I find: things tend to get sharper toward the nut and moving the nut impacts all frets (~3 cents per mm nut shift)

The correction is for string stretch so that you can get accurate equal temperament. If you want another temperament, you're probably better off going fretless.

A criticism I occasionally hear about well intonated guitars is that they don't sound like guitars any more. Some people actually like the jangly out-of-tuneness of standard compensation as they say that is part of the unique character of the guitar. So in-tune guitars are not for everyone!

No, that's something different again. Pianos are generally stretch tuned. Because of the bending stiffness of strings, particularly the large diameter low ones, the high string partials play sharp and so do not match the frequencies of the fundamentals on the high notes if the high notes are tuned true. So the high strings are tuned sharp to match the sharp lower string partials and the result is an instrument that sounds a lot more in tune. You can do this on guitars too, but that is not what I was referring to. For guitars you only need a couple of cents stretch. I forget what it is on pianos, but they have more octaves and the stretch is a lot more. So in an orchestra with a piano, the high register instruments would have to tune to match the piano. An orchestra without a piano may well be playing in something that more resembles Just intonation, because most of the rest of the instruments aren't in a fixed temperament.

It's how I see it.

So, back to keeping things simple. As I mentioned, I explain about half a dozen different ways of compensating guitars. If you want to keep it simple, you can. But if you want really accurate string by string, fret by fret intonation, it's not simple. Because it isn't! Just read Byers' paper.

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

I think I'm getting away with it, simply because I'm minimizing nut height already, so that's good to know. I'm thinking that guys with high action would certainly benefit. I know a guy who has me set his strats up so high that I can't get his open chords as sweet as I'd like, in fact the intonation past the 12 fret is better than below it, due to the amount of relief he needs for his hard strumming and picking.

I'm fine with equal temperament, LOL! There's that guy on youtube with the microtonal guitar, this guy: http://www.youtube.com/watch?v=MYK_PF9WTRE
HE seems obsessed......

The director often accompanied us with the piano, and it was the instruments playing in the upper registers that were tuning, so that makes sense too.

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Old growth, shmold growth!

That depends on where you're coming from. If you are going from the nut the notes become progressively sharper, "in relation to the note from the nut" until the 7th to 9th. Then back to true harmonic at the 12th fret.

... provided you've intonated correctly!

This is an interesting thread.

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Billy Dean Thomas
Covina, CA

"Multi famam, conscientiam, pauci verentur."
(Many fear their reputation, few their conscience)

Unfortunately, keeping it simple doesn't make it right, though it may make it easy.

Ah, but over-complicating something doesn't necessarily make it better, either.

Genius is simplifying the complicated, not complicating the simple, after all.

I'm all for refining our intonation and understand thereof, but this is an area where it is very easy to over-think it, and get lost in the science behind it all.

But if you want really accurate string by string, fret by fret intonation, it's not simple. Because it isn't!

First, it needs to be mentioned that nobody, not even a magician, can ever attain perfect intonation at every string, every fret. Impossible. The only way that could happen is to have an individual fret for each note, and even then, it would only be perfect in one key. As such, everything we do is a compromise. And we must add the various string gauges, and wrap-to-core ratio, type of strings, player's style, players' preferences for certain keys, etc, etc, etc,.... There's no end to the possible scenarios. For example, I promise you that if you hand me your best intonated guitar, that you just tuned with a strobe tuner, I'll play a few things on it, and reach for the headstock and tweak a string or two. It's not that I don't like a perfectly tuned guitar, but rather it's that I am human, and as such, am not perfect, and my left hand's strength has a strange quirk in that my ring and pinky fingers are very strong, and despite years of trying to correct the "problem", I will always sharp certain notes in certain keys. So, depending on which key we're in, I have to tweak the guitar ever so slightly for it to play in perfect tune. Yes, the closer the intonation is to ideal, the less tweaking needs to be done, but fact remains that chasing perfect intonation, which is an impossible goal, is akin to chasing one's tail. As soon as you find an ideal intonation setup for a player who's favorite key is E, you'll have a guitar that will frustrate players whom play in the key of G more often the E, for example.

And then there's the fact that some musicians are more bothered by notes that intonate slightly flat than sharp. And vicey versey; some can't stand a note that plays a tad sharp, but will tolerate a note that is slightly flat. So, for very fussy ears, sometimes we need to move the intonation slight sharp or flat overall, so that it will be more pleasing to the player. Arguing with a seasoned professional musician that your setup is ideal and that he/she needs to get used to hearing "perfection" won't win you many friends, or sales!

And finally, I was much, much, MUCH more concerned with intonation in the first few years I was playing. As I became a better musician, I learned to tune correctly, and stopped blaming the guitar. Yes, it helps that by that time I had attained a very well intonated setup, but no matter if I am playing one of mine, or a client's early 70's Martin with the saddle 1/8" too far forward, I can get 'em to play in tune and just enjoy the music.

After all, making music is the goal of making instruments, right?

Okay.
I've read almost all of the replies,
and I will tell you what is going on here, IMO.
I have a very good ear for relative pitch .
I play lap steel only.
I noticed a long time ago,
that the bar, or steel was not over the fret marker on SOME frets, to be in tune.
I took a class with Steve Kimock, a very good player,
and he pointed out that SOME frets on the guitar played sharp.
These frets are 2, 4, and 10 or 11,
I can't remember.
When I play on those frets, on a lap steel,
the bar is about an 1/8" south of the fret marker!
On the 5th fret, it is right over the marker!
So, my conclusion is that this so called "compensated nut",
is actually just "splitting the difference",
so the guitar will play just a little more in tune across the board.
Nut compensation has nothing to do with "string stretch".
That is done at the saddle.
What Steve does to compensate this phenomenon,
is he actually pulls the string towards the saddle,
which flattens the note.
Blew me out of the water when he told us that!

That's the real end answer. That is why symphony string instruments (the viol family) do not have frets, and why you seldom see an acoustic guitar in an orchestra ( Archtops with intonated saddles being the main exception). The real problem is that the actual working length and tension of any given string will vary from fret to fret when played. Viol family instruments have no frets and instead the musician is trained ( hopefully) to finger correctly and play the proper pitch, much like a singer is taught pitch.

_________________
Brian

You never know what you are capable of until you actually try.

https://www.howardguitarsdelaware.com/

You could if you cut each fret into 6 pieces,
and placed them where the string fretted would be in tune.
Slightly impractical .

But it would only be good in one key - maybe two or three.

_________________
Waddy

Photobucket Build Album Library

Sound Clips of most of my guitars