Zero Fret Nut position

As Prof Chris said, we are discussing very small "inaccuracies". Nowadays much closer tolerances can be achieved than a man could in the (say) eighteenth century, working with hand tools only, but that is not to say that the eighteenth century standards were not good enough. We have to strive for the highest level of accuracy and consistency, that's the way we are wired, but good enough will do.

I cut my fret slots by hand, to the rule of 18, using a very rudimentary jig. It works for me.

ukantor said:

Hi Pete, I have just typed out a long, detailed reply, only to be told I was not logged in. When I logged back on, my message had gone!

Using the rule of eighteen to determine the placement of the frets does give the required amount of compensation. It is "built in" to the calculation.

John Colter

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Hi John,

I have had the same problem with typing text and the system timing me out, it’s very frustrating. These days I go back a screen when that happens and then select and copy everything that I’ve written before re-logging in. I the select response and paste all that I previously wrote. I hope that that info is of some help.

Did you have a stand at the Cheltenham festival? My memory fades but someone looking similar to you and from the midlands too had a stand in one of the corridors - next or near to the Tin Guitars stand.

What’s the rule of eighteen?

Hi Graham, thanks for the posting suggestion - I'll try that. It wasn't me at Cheltenham, I went to a couple of the early fests, but haven't been recently.

The rule of eighteen simply means using 18 as the divisor to determine fret positions. The mathematically "perfect" number is 17.817 (choose as many decimal places as you like) but then you have to add some compensation to the saddle, to refine the intonation. If you use 18, you don't need to add any compensation, and it still puts the frets where you want them to be.

Some folk don't believe me, but it works. Try it!

Hello,

Funny to see how such a mundane matter can become so controversial...

From my own experience, and after a totally intuitive idea, I saved a cheap Mahilele soprano with terrible intonation issue just by putting a piece of metal cut off from a paperclip as a poor man's zero fret, which keeps in place only by the pressure of the strings. The intonation is still not spot-on, but really tolerable so, yes, I do think that zero fret affects strongly the intonation — for the better in my case.

just my 2 cents,
regards,

Gilles

The guitar I learned my first three chords on was a Hofner arch top with a zero fret. I think they make perfect sense, although I don't own any guitars with zero frets. If you play open chords on a guitar without a zero fret, the open strings will be vibrating off a bone or plastic or ebony. . . nut while the fretted strings will be vibrating off a metal fret. On a guitar with a zero fret, all strings, open and closed are vibrating off a metal fret, giving a more uniform, balanced sound, similar to what you'd get when using a capo.
My 5 string banjos have all been converted so that the fifth string comes off the 5th fret rather than having a bone pip.

gilles T said:

Hello,

Funny to see how such a mundane matter can become so controversial...

From my own experience, and after a totally intuitive idea, I saved a cheap Mahilele soprano with terrible intonation issue just by putting a piece of metal cut off from a paperclip as a poor man's zero fret, which keeps in place only by the pressure of the strings. The intonation is still not spot-on, but really tolerable so, yes, I do think that zero fret affects strongly the intonation — for the better in my case.

just my 2 cents,
regards,

Gilles

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I'm reading this as:
- you shortened the scale length overall
- you shortened the distance between the "nut" and the first fret
- the scale length for every string fretted stays the same

Unless I'm missing something?

Kekani said:

I'm reading this as:
- you shortened the scale length overall
- you shortened the distance between the "nut" and the first fret
- the scale length for every string fretted stays the same

Unless I'm missing something?

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I’m trying to get my head around this fix too. One thing not stated but implied is that the Uke is retuned to compensate for the now reduced scale length. As all the frets are now proportionally nearer the ‘nut’ the note produced at each of them will be slightly flatter than before; assuming my understanding is correct.

As nut positioning and slots are sometimes imperfect it can be worth tuning off of the second fret, obviously you’ll be up a full tone there and it’s just a tweak of the tuners to get things spot on. When doing that revised tuning you then at least have everything from the second fret on more in tune - that’s worked for me 'till I sorted the nut out, etc - and the bulk of chords will be nearer in tune. Well that's my experience but YMMV.

I’m not sure that this divergence from the OP is OK, but no doubt Pete will let us know if he's unhappy about it.

I dug up this old post I wrote a few years back. It's a comparison between three different ways to place frets. The measurements are i millimeters, sorry about that, but it does show that there are only minor differences.

The thing to remember is that "the rule of 18" is used on a known or already chosen string length and the other methods are used on a theoretical string length, the one we call scale length to which we then add compensation by moving the saddle to lengthen the strings. I show the scale length I use for my sopranos, 350 mm (13.77953 inches, or 13 25/32").

I understand Pete's question because I pondered it myself when I bought a scale template from Stewmac. Using a fret slot to cut off the fretboard at the nut end will place the front end of the nut half a slot width closer to the first fret, or to the bridge. It won't however be 1 or 2%, it would be 0.3 mm divided with 350 and that is a lot less. And when I asked about this I think it was Chuck who told me not to worry, and there are some builders who intentionally shortens the space between the nut and the first fret even more (Buzz Feiten theory comes to mind). Using a zero fret will most likely, as ProfChris points out, give a lower string height close at the first frets so that compensation because of string stretch isn't necessary. If I were to use a zero fret I would use the exact same slot position as the one I'm using now to cut off the board for a regular nut.

Old post from here:

Well I did run it through excel and I'm not very good at it. I compared a 352 mm string length with the rule of 18 applied, and then 350 mm scale length using both 17.817 and a more exact number wot i found on the internetz; 17.81715375. The numbers given below are fret-to-fret distances for 15 frets.

The minor discrepancies seem to be less minor at the first few frets.

Thank you for that, Sven. The rule of 18 seems to be widely regarded as the imperfect system that was used before the more accurate divisor of 17.817 was adopted. Your chart illustrates that the difference in fret placement is less than 1/10th of a millimeter.

I wouldn't advocate the use of one over the other - for all practical purposes they both give the same answer - but I always use 18 as a homage to the luthiers of old, who really did know what they were doing.

John Colter.

Using any constant divisor introduces a small bit of inaccuracy. Just for the record, the fret distance calculation (which puts the 12'th fret exactly 1/2 way) involves a fractional power of 2. ("^" in the formula below is 'to the power')


Calculating Fret Spacing for a Single Fret

d = s – (s / (2 ^ (n / 12)))

where:
d = distance from nut;
s = scale length;
n = fret number;

Graham Greenbag said:

If you know of one I’d be very interested to read a simple explanation of that, please.

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Graham asks about nut compensation theory. Here is my own sketchy grasp on it - the full maths is apparently in the Gore/Gilet books which I don't own.

1. A string is stiffer (technical term is compliance) near its ends than in the middle.

2. Thus fretting note 1 requires more force than fret 2, and so on.

3. As a result, notes on frets 1-11 play a fraction sharp, the amount decreasing as you approach fret 12.

4. Moving the nut towards the bridge a little while keeping the fret positions unchanged improves this.

5. Ideally each string gets different amounts as thicker strings are proportionally stiffer. But taking an average produces an improvement overall.

6. As a knock-on effect, the amount of compensation needed at the saddle decreases.

The reasoning seems plausible if 1 and 2 are true, and they certainly accord with my subjective experience of playing.

I've not tried this because I believe the improvement is likely to be small, though probably audible. On a soprano, which is what I mainly build, fretting techniques can change a note by a far greater amount, and my ukes are close enough that players are happy.

I gather that on a steel string guitar where more nearly perfect intonation is desired (ie not cowboy strumming) the effort might be worth it.

That's the simplest I can manage!

ProfChris said:

Graham asks about nut compensation theory. Here is my own sketchy grasp on it - the full maths is apparently in the Gore/Gilet books which I don't own................................................................... That's the simplest I can manage!

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Many thanks for the information, it’s much appreciated.

Sven said:

The thing to remember is that "the rule of 18" is used on a known or already chosen string length and the other methods are used on a theoretical string length, the one we call scale length to which we then add compensation by moving the saddle to lengthen the strings. I show the scale length I use for my sopranos, 350 mm (13.77953 inches, or 13 25/32").

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Yes, thank you Sven for that even if it is in millimeters. (who uses millimeters? Just most of the world!).... Always these discussions of scale length and compensation make my head throb. However, I've started building some pretty good looking and good playing ukes (in my opinion) and the intonation issues are starting to really bug me. I have a pretty good ear and I can hear the "beating" dissonances happening and I am not happy. Four out of five people can't hear it because four out of five people can't even hear when their instrument is out of tune.

What in my opinion is not addressed in these discussions is the difference in string diameter. The uke is reentrant tuning in that the strings are not arranged in a ascending order of string diameter like a guitar which is non-reentrant. https://en.wikipedia.org/wiki/Reentrant_tuning

Thus, moving the nut in or out or the saddle in or out is not going to do much to compensate for intonation issues. It might for some strings but not all. Thus any truly compensated uke will require a separate scale length for each string and that is just the physics of the situation.

The part about making the distance from the nut (or zero fret) slightly shorter to the second fret just blew my mind. That distance has always been a sacred distance in my mind, but I think I can see how it might solve some intonation issues when playing notes close to the nut, but doesn't do anything for a fretted note past the second fret and beyond. Great for playing a C7, but otherwise not a fix. What am I missing? Anyway, thanks for the post. I now am developing a headache.

sequoia said:

The part about making the distance from the nut (or zero fret) slightly shorter to the second fret just blew my mind. That distance has always been a sacred distance in my mind, but I think I can see how it might solve some intonation issues when playing notes close to the nut, but doesn't do anything for a fretted note past the second fret and beyond. Great for playing a C7, but otherwise not a fix. What am I missing? Anyway, thanks for the post. I now am developing a headache.

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What you're missing is that it affects *every* note (except the 12th fret), because the saddle is also adjusted to suit the revised scale (and yes, it took me ages to get that into my head as well!). If you use a spreadsheet with Sven's numbers for a 350mm scale, and assume 2mm compensation at the saddle, then applying 1mm nut compensation and reducing the saddle compensation to 0.865 gives you (after scaling to allow for the slightly different scale length) speaking lengths which are 0.89mm longer at fret 1, 0.47mm longer at fret 5, and the same at fret 12.

The changes are very small - the 1st fret speaking distance is only 0.27% longer, the 5th fret 0.18% longer. Mind you, my 1mm nut compensation was just a guess, maybe more is needed.

Unintuitive, but the maths doesn't lie!

But as I wrote, I don't bother. Sounds like you should experiment as your ear is offended by the normal system.

Really, wouldn't the center of the zero fret be further back than the front edge of a nut by exactly half the thickness of the tang?
Boy, that's a really, really small distance.

Also, is it normal for the zero fret to be taller than the rest? I understand that it would make string buzz less likely, but doesn't that run counter to one of the main reasons you would want a zero fret in the first place?

I use a zero fret the same size as the rest, no problems if you level the frets accurately.

ProfChris said:

I use a zero fret the same size as the rest, no problems if you level the frets accurately.

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Thank you, ProfChris. That's what I was thinking too.
I hope I don't derail the thread, but are you one of the people that associate a zero fret instrument with a low quality one? It seems to me like a good idea, so I wanted to make my new series of ukes with them. But I am also hoping to sell a few of these , so am I shooting myself in the foot by adding a zero fret?

This thread needs some photos

I'm motivated by the customer who has gone over an instrument with a Peterson tuner and complains about how many cents the intonation is out by...

Here's a photo of how you make sure every string is properly intonated (to the extreme) by working on the nut position..



I just don't think half a fret slot is the answer. Even though it might help for one set of strings, it's unlikely to work the same for another set of different material/composition.