The Compensated Nut

[Turnaround]

Every once in a while a discussion is started on TalkBass about compensated nuts. This thread is intended to become a repository of information about the compensated nut and its use on bass guitars.

At least one bass manufacturer puts a compensated nut on some (not all) of their production basses. It looks like this:

So what's going on and why?

It turns out that notes at the first fret are always a tiny bit sharp. So is the first fret in the wrong position? And the answer is "yes and no".

Frets are located on the fretboard at specific places based on a mathematical formula that is a function of the scale length of the string, dividing it up in semi-tone placements. But this does not account for one factor that is significant - the stretching of the string as it is pressed to the fret. That little bit of stretching drives the note sharp. That is the very reason that the saddles on the bridge have to be adjusted to intonate the bass - it compensates for the stretching of the string from fretting.

It doesn't seem like there's much stretching involved, but it is enough to be significant. You can demonstrate that for yourself. Look at the space between the E string and the last fret - that's how much bend you need to put into the string to fret it a that position. Now fret the note and listen to its pitch. Next bend the string (as a string bend playing guitar) the same amount as the space you noted and listen to the pitch again or check it with your tuner.

So we compensate for string stretch by moving the saddles away from the frets, effectively making all the frets play slightly flat (in theory), but compensating for the sharpness induced by fretting in reality. The amount of compensation needed for any string is related to three factors:

1. The frequency of the open string
2. The tension of the open string
3. The mass of the vibrating part of the string

All three factors are interlinked so that a change in any one affects the others. Since each string differs in at least two aspects (balanced tension sets try to negate differences in tension), we can expect a difference in the amount of compensation needed.

So if we need to compensate for string stretching by adjusting the saddles, why do we need to do the same at the nut? Supposedly we already compensated for string stretch. A little geometry might help us understand. To really see we need to use extreme examples. Here's a string (red) resting on a really high nut and bridge:

The string is 12 inches long and site 1 inch above the fretboard. Now if we depress the string in the middle (the 6 inch point) we can calculate the stretched string length:

Since we know the height and the midpoint between nut and bridge, we can calculate the hypotenuse (the string length from nut to depressed centre point), the square root of the sum of the squares on the other sides. That comes to 6.083 inches. And the other half of thee string will be the same length giving an overall stretched length of 12.166 inches, a gain of .166 inches.

If we press the string down one inch from the nut instead of in the middle it looks like this:

Using the same calculations we find the length of the string from nut to depression point is 1.414 inches, and the length from the depression point to the bridge is 11.045 inches. That means the stretched length of the entire string is now 12.459 inches, a gain of .459 inches. So clearly the amount of compensation that is needed is dependent upon where we are fretting.

That means in order to get even compensation all along the fretboard, we need to provide compensation for stretch at both ends of the fretboard, the bridge and the nut.

The two most common systems for compensation at the nut are the Buzz Feiten tuning system and that known as the Earvana system. Both attempt to correct intonation issues, slightly differently. The BF system involves slightly different compensation at the saddles, a compensated nut and a slight off-tuning of the strings. The Earvana system requires a compensated nut, but no other alteration.

So why don't we just buy a compensated nut and be done? Because there's theoretical stretch and real world stretch. The calculations above gave us the theoretical stretch, but in the real world there are some other factors that contribute to the real amount of stretch caused by fretting.

The theoretical model would be accurate if we precisely pressed the string to the top of the fret, but we don't. We press just behind the fret, like this:

You can see that we are adding additional stretch beyond what it took to make the string contact the fret. Granted, we generally don't push the string all the way down to contact the fretboard, but there will be some additional stretch depending on how hard you squeeze the string and where your finger is placed with respect to the fret. So if we need to compensate for string stretch, we need to account for this "extra" stretch. The Earvana system purports to address this particular concern.

And that's where the real problem lies. We all play differently. Some play with a lighter touch, some play closer to the fret, and indeed we are probably not consistent in either of these. And because of differing playing styles we may have more or less string height and thus more nut height. And we may use different string gauges. All of these are factors in determining how much compensated is needed on each string.

The consequence of all of this is that a properly compensated nut will be specific to a particular bass, it's scale length, the makeup of the string, the tuning used, the style of the player, the nut height, and the saddle positions, (and perhaps a host of other factors like ambient temperature).

So far I have avoided expressing my thoughts about the usefulness/effectiveness of compensated nuts. I will express my opinions as the discussion progresses.

 

[SteveCS]

@Turnaround. Thanks for starting this thread - I don't think I've spawned a pro-bench thread before! I pretty much stated my views in the other thread so I'll also just follow for now and see where it goes.

 

[Lesfunk]

Since we are talking about compensated nuts and my bass has one, I’ll ask a question here.
It may or may not have relevance ..
My Stingray is intonated using the standard method 12th fret method. I use a Peterson digital strobe tuner, so I trust it’s accuracy.
When I play in the “money area” of the fretboard (frets 3,4,5,6,7)I notice that my fingered notes noticeably and audibly ring flat although my bass is tuned and shows proper intonation. It seems to be the E string is the main offender. im thinking it may be the string itself and plan on changing strings and re-setting up the bass.
Would the compensated nut play into this phenomenon?
Is it better to intonate the instrument at the seventh fret fingered rather than the 12th?
Curious.

 

[James Collins]

Excellent write up. This makes me think of another issue: should players adjust their own setups? Honestly, i think it is fine to. But as the above post describes, the compensated nut is customized to a particular setup and is the last step in a setup. So if you are doing your own setup where you flatten the neck and lower the action from where the luthier set it, now the compensation will be wrong. Not sure how much it matters practically though.

My only compensated nut is on a classical guitar. It was setup by the original luthier. It plays well, and I wouldn't change the setup myself. It's funny because I setup all my basses myself, but my classical guitar if it needed the action lowered I would mail it somewhere to be setup.

 

[micahwc]

We need evertune to make a bass bridge. Intonation is very good with them and it compensates when you press the strings down or bend them.

As for doing your own setups, yes absolutely players should be doing this. It saves them money in the long run and makes your instruments much more enjoyable to play (if you can do it correctly).

 

[James Collins]

I agree with players needing to be able to do their own setups. I was more referring to the point where you have a compensated nut since a new setup would require changing the compensation. Also, if basses were setup well in the first place, not sure if it would be necessary, but most manufactured instruments have the setup outsourced to the end user.

 

[SteveCS]

Would the compensated nut play into this phenomenon?

Yes. The problem with the EBMM basses, as I experienced them, is they don't need them because they are one of the few factory instruments that has well cut nuts to begin with - the compensated nut actually over-compensates, leaving everything a little flat.

 

[Turnaround]

A few more facts before we get into the discussion further. I just measured one of my basses. it is well set up with lowish action, well intonated at the 12th fret and sporting fairly new strings. I didn't restring it with unused strings because I wanted the measurements to reflect real world conditions, and though I change my string probably more often than most, they're not super fresh every time I play. The nut is not compensated. Tuning is done with a highly accurate strobe tuner. Every effort has been made to keep margins of error within 1 cent (one one-hundredth of a semitone), but for anyone who has used a really accurate tuner knows, it is very difficult to actually tune to this level of accuracy. If I got a reading that was within 1 cent of my target I called it good enough. All tuning is measure with the bass in playing position (it makes a difference).

E string at the first fret is within .2 cents of being in tune (flat). That's 2 thousandths of a semitone. Since I have an open string error of less once cent (flat), and the first fret also reads flat, we have a real error at the first fret in the neighbourhood of less somewhere near half a cent (less than one 500th of a semitone).

A string reads around 0.5 cents flat open. At the first fret it reads about 2.2 cents sharp putting its tuning less than 2 cents sharp at the first fret

D string reads 0.3 cents flat open and 5.6 cents flat at the first. Net is 5.3 cents flat at the first.

G reads 0.2 cents flat open, 4.2 cents flat at the first fret. Net = 4 cents flat.

Interestingly all strings read slightly flat at the first fret. BUT and it's a big one, all those numbers go out the window if:

1. I squeeze the string a bit more tightly. I can drive the E string 12 cents sharp at the first fret just by squeezing harder. Same is true in differing degrees with the other strings.

2. I take the bass out of playing position. If I lay the bass with it's back on my knee, the open E string reads about 7 cents sharp. In playing position it was about 0.8 cents flat. This is the effect of gravity on the neck.

3. I don't remain still. As I move about both open and fretted notes shift their tuning by several cents.

4. I bend the neck. This one seems obvious, but it takes very little pressure on the neck to affect the pitch of the string, at least within the range of the differences we are seeing here. Try it for yourself if you have an accurate tuner.

5. I pluck harder or softer.

Remember these findings as we proceed into the discussion about the compensated nut.

 

[Turnaround]

Since we are talking about compensated nuts and my bass has one, I’ll ask a question here.
It may or may not have relevance ..
My Stingray is intonated using the standard method 12th fret method. I use a Peterson digital strobe tuner, so I trust it’s accuracy.
When I play in the “money area” of the fretboard (frets 3,4,5,6,7)I notice that my fingered notes noticeably and audibly ring flat although my bass is tuned and shows proper intonation. It seems to be the E string is the main offender. im thinking it may be the string itself and plan on changing strings and re-setting up the bass.
Would the compensated nut play into this phenomenon?
Is it better to intonate the instrument at the seventh fret fingered rather than the 12th?
Curious.

My best advice is to intonate in the area you play most. Who cares if the 12th fret is in tune if you never go there? And I will get into the vagaries of compensated nuts as this thread progresses.

 

[Turnaround]

One more fact that we need in this discussion.

It is a popular belief that the 12th fret harmonic of a string will be an exact octave above the open string. While this is true in theory, it's not so true in the real world. I managed to get my G string perfectly in tune at the 12th fret harmonic - it wavered by 0.2 cents either side of perfect. However the open string rings between about 4.2 cents flat. The other strings are off as well by varying amounts. If you check a taper wound string you are likely to find an even larger difference.

 

[Turnaround]

Apologies - in my first post I included a picture of a compensated nut on a guitar. It looks similar on a bass:

 

[Turnaround]

but most manufactured instruments have the setup outsourced to the end user.

A clever way of putting it!

 

[Lesfunk]

My best advice is to intonate in the area you play most. Who cares if the 12th fret is in tune if you never go there? And I will get into the vagaries of compensated nuts as this thread progresses.

yeah, I appreciate that. I was kind of thinking the same thing that it makes more sense to Set the intonation to the general area where I spend most of my time. However, that’s just the way I was taught. I’m sure many other people were taught the same way as well

 

[JRA]

following.....

 

[JKos]

It is a popular belief that the 12th fret harmonic of a string will be an exact octave above the open string.

This is, indeed, an extremely popular yet false belief. What I also think is a bit of a false belief is that setting the intonation at the 12th fret is the best you can do. No, for a given instrument, set of strings, and player, setting the intonation at a different fret or best compromise of a couple frets can be better.

 

[James Collins]

yeah, I appreciate that. I was kind of thinking the same thing that it makes more sense to Set the intonation to the general area where I spend most of my time. However, that’s just the way I was taught. I’m sure many other people were taught the same way as well

Also, tune to where you are playing. If you are playing a song that you play at the 7th position the entire time, make sure that is in tune. The open strings aren't always the most important thing to be in tune.

 

[gln1955]

What does this mean for the lowly zero fret, which some love and some hate?

 

[Turnaround]

What does this mean for the lowly zero fret, which some love and some hate?

It's a very good question. If a zero fret is the same height as the other frets, shouldn't the slot in the nut bring the string to that level? If not, why not? If the string clearance at the second fret is adequate when fretting at the first, why do you need more clearance at the first fret when the string is open? It is my opinion that you don't, and that any additional height only makes it harder to fret at the first fret and causes intonation issues.

 

[James Collins]

Are there any situations where you would think a compensated nut had a purpose or benefit?

 

[Turnaround]

Now back to the discussion about the compensated nut. The need for such a nut, according to Buzz Feiten creator of the Buzz Feiten Tuning System, is that without compensation at the nut the notes at the first few frets will be slightly sharp. This is the most often expressed need for a compensated nut - sharpness at the first few frets.

The real question is "why are the notes sharp?". And looking at the illustrations in my first post you can see that the string is being stretched when fretted and that drives the pitch sharp. And we can see that stretch increases as we get closer to the nut. But then how sharp does it get?

The obvious answer is that it depends how far you stretch the string. If the nut slots are too high you will need to stretch further than if they are lower. So before we look into intonation errors that need nut compensation, you need to ensure that the problem is not being caused by a nut that is too high to start with. As you can see from the measurements taken on my bass, it has no intonation issue at the first fret. And it doesn't have any nut compensation. But my bass is unusual in a few ways.

First let me tell you that the bass in question is nothing special - It's a Mexican Fender Jazz. But it's not exactly stock. I have recut the nut slots to my specs. I have done critical levelling of the frets. I have adjusted string height and relief to suit my playing. I don't like fret buzz so I have it dialed in to be free of buzz unless I really dig in, and when I do the amount of buzz is consistent all along the neck and on the open strings. So the bass has been finessed - in that sense it is far from "stock".

A BIG part of that is the work I did on the nut. It is significantly lower than stock and lower than the recommendations from many of the "experts". John Carruthers, a highly respected technician, recommends a nut height that puts the string .022" above the first fret. Mine is less than half that amount. Tony Hagy, writing for Premier Guitar, recommended that you should be able to slip a business card between the first fret and the string when the string is resting on the second fret, whereas others have said that distance should be about the thickness of a piece of paper. It is my contention that any of those heights will definitely contribute to sharpness at the first fret. My bass does not exhibit sharpness at the first fret because my string clearance over the first fret is the same as the clearance of the string over the second fret when fretting the first. In my case that's about 0.010". It's worth noting too that I have done the same to all of my basses and none are sharp at the first few frets. None have compensated nuts.

You can draw your own conclusion, but I maintain that you do not need a compensated nut to deal with intonation issues in the first few frets - you need a well set up bass with truly level frets and the right nut height. If you insist on having the nut higher then you probably will need a compensated nut to be in tune.

Next I will look at other intonation problems and see if the use of a compensated nut will correct them.