Unfinished Antique - Nut/Scale Questions

[MrOldschool]

Hello everybody. A while back I picked up three ukuleles from eBay that needed a little TLC. Two of them just needed their tuners sorted out and to be strung, but one is proving more of a challenge than I realized at first. It is a "Victor Brand Hawaiian Ukulele" that appears to have never been finished assembling. It had no nut and no tuners. It also had no finish on the body, and had some pencil marks on the neck that look like it may have been the price at some point. It had very narrow holes for the tuners, which tells me it was supposed to have friction pegs. I had to improvise to get my Grover tuners to work on it by putting different collars in place that had small enough shoulders to settle in the holes. I found an ebony saddle to use as a nut because Victors used a narrow wood nut originally (I have another Victor that is all original to compare to), which I had to cut and sand to make fit, then I notched it in the right spots for the strings. The frets were all raw and not dressed or leveled, so I did quite a bit of work on dressing and prepping the frets. Then when I put it all together, I find that something is off in the scale. When I tune the strings to their correct open tuning, no notes ring true at any frets. Going with the assumption that it would most likely be something I did wrong, is this the placement of the nut? How do I determine where to make corrections or how do I go about them? I will put up some pictures to help illustrate what I'm working with.

 

[MrOldschool]

 

[sequoia]

What I would suspect is that it is nothing you did, but that the scale length is incorrect. In other words, the space between the frets is wrong for the scale length. Here is an idea: measure the scale length from the front of the nut to the front of the saddle (2x scale length), then use a scale calculator to see what the proper fret intervals distances should be. Measure the distance between frets and see if it matches what the calculator tells you they should be. Here is a fret calculator from Steward MacDonald. Be sure and use the drop down button and select ukulele.

Fret position calculator - StewMac

www.stewmac.com

 

[John Colter]

The distance from the nut to the saddle is the scale length - it should be double the distance from the nut to the twelfth fret plus an eighth of an inch.

Judging from the photos, the height of the strings over the first fret is excessive. Pressing the strings down behind the frets will stretch the strings out of tune. Try setting the nut right down in its groove and see if that is an improvement.

 

[anthonyg]

Is the intonation going sharp or flat and by how much?
Is the intonation better in the open position and getting worse up the neck or is it worse in the open position and getting better up the neck?

The nominal scale length of an instrument should be the distance from inside the nut to the centre of the 12th fret x 2.
The actual scale length is the nominal scale length + saddle compensation.
Instruments are fretted based on their nominal scale length, yet the actual measurable scale length from inside nut to saddle contact point should be a fraction longer.

 

[Moore Bettah Ukuleles]

Yeah, measure from the leading edge of the nut to the 12th fret and see if it’s the same to the bridge (+ a little).
What I find interesting though is that the neck seems to made from coconut palm. The grain pattern is very similar.

 

[MrOldschool]

Okay, here is some of the data I've been able to collect so far:
Measurement from Inside of nut to break point on bridge 12.938"
Nut to 12th fret = 6.406" Scale then calculates as 12.813" so that differs from above and from the 12.889" recommended bridge placement from the calculator
1st fret is at .6875" but should be .719" - A string intonation is 481.6Hz, flat of B
2nd fret is 1.404" but shout be 1.398" - A String intonation is 506.6Hz, sharp of B

Skipping down to the 12th fret, strangely, its A String intonation is 878.5Hz which is fairly close to A, where I believe it is supposed to be.
I checked the intonation of the A string the whole way down, but I didn't bother with measuring all of the fret positions yet. Also, the nut height is set at 1/16". In order to get the nut to settle further down into its groove, I will have to sand it narrower, as that was as far down as I could get it at the time.

 

[anthonyg]

Okay, here is some of the data I've been able to collect so far:
Measurement from Inside of nut to break point on bridge 12.938"
Nut to 12th fret = 6.406" Scale then calculates as 12.813" so that differs from above and from the 12.889" recommended bridge placement from the calculator
1st fret is at .6875" but should be .719" - A string intonation is 481.6Hz, flat of B
2nd fret is 1.404" but shout be 1.398" - A String intonation is 506.6Hz, sharp of B

Skipping down to the 12th fret, strangely, its A String intonation is 878.5Hz which is fairly close to A, where I believe it is supposed to be.
I checked the intonation of the A string the whole way down, but I didn't bother with measuring all of the fret positions yet. Also, the nut height is set at 1/16". In order to get the nut to settle further down into its groove, I will have to sand it narrower, as that was as far down as I could get it at the time.

OK, that's start.
Never discount the fact that BOTH the nut and saddle are incorrectly placed, and I strongly suspect that this is your case.
I also suspect that this is a hand fretted instrument so machine fretted accuracy is completely off the table.
I believe that perfection is not an option for this instrument.

When I eyeballed it, I suspected that the nut to first fret distance was too far. 12.813" just isn't a scale distance that anyone is coming up with.
My guesstimate is that this has a nominal scale length of 12 3/4" (12.75 inches). Inside nut to centre 12th fret should be 6 3/8" (6.375 inches).
That's my educated guess.
So, run those numbers through a calculator, calculate the first fret to 12th fret distance, and see how right or wrong it is and compare it to the other scale lengths you have guessed.

That's enough for now.

 

[rmmottola]

There is a calculator on my website that will help to identify scale lengths of mystery instruments and also help to identify misplaced frets and misplaced nuts. I ran it with some of the info you provided but there is not enough data to come up with reliable numbers. That generally means there are multiple errors. Check out the calculator here:

Liutaio Mottola Lutherie Information Website

Information for builders of stringed musical instruments.

liutaiomottola.com

 

[sequoia]

There is a calculator on my website that will help to identify scale lengths of mystery instruments and also help to identify misplaced frets and misplaced nuts. I ran it with some of the info you provided but there is not enough data to come up with reliable numbers. That generally means there are multiple errors. Check out the calculator here:

Liutaio Mottola Lutherie Information Website

Information for builders of stringed musical instruments.

liutaiomottola.com

Your site is such a great resource for luthiers, both professional and amatuer. I encourage everyone who isn't familiar with it to check it out.

 

[rmmottola]

Your site is such a great resource for luthiers, both professional and amatuer. I encourage everyone who isn't familiar with it to check it out.

Thanks so much for your kind words about my site!

The whole scale length / fret placement / saddle placement problem for an unknown instrument is amazingly complex. I got into this while doing a series of restorations and each time coming up against measurements that didn't make sense. Anyone that is interested can read the text before that calculator on my site, but here is just one example. As a number of posters have asserted, the distance between nut and the crown of the 12th fret is 1/2 the scale length. This is indeed true, but only under ALL of the following conditions:

1. The nut was accurately placed;
2. The 12th fret was accurately placed;
3. Frets were laid out using the 12th root of 2 (NOT the Rule of 18!).

If any of these conditions are not met, then that measured distance will not be 1/2 the scale length. Note that older instruments where the fret slots were cut by hand and which used the Rule of 18 for fret layout probably don't meet any of these conditions.

 

[John Colter]

Thanks so much for your kind words about my site!

The whole scale length / fret placement / saddle placement problem for an unknown instrument is amazingly complex. I got into this while doing a series of restorations and each time coming up against measurements that didn't make sense. Anyone that is interested can read the text before that calculator on my site, but here is just one example. As a number of posters have asserted, the distance between nut and the crown of the 12th fret is 1/2 the scale length. This is indeed true, but only under ALL of the following conditions:

1. The nut was accurately placed;
2. The 12th fret was accurately placed;
3. Frets were laid out using the 12th root of 2 (NOT the Rule of 18!).

If any of these conditions are not met, then that measured distance will not be 1/2 the scale length. Note that older instruments where the fret slots were cut by hand and which used the Rule of 18 for fret layout probably don't meet any of these conditions.

Why do you exclude the rule of eighteen and hand cut fret slots so dismissively? Used properly they give perfectly acceptable results.

 

[anthonyg]

Why do you exclude the rule of eighteen and hand cut fret slots so dismissively? Used properly they give perfectly acceptable results.

I didn't think he was dismissing rule of 18 and hand cut frets out of hand.
What I thought he was saying is that if you are looking at unknown frets from the perspective of modern calculations, CNC cut frets, then what you would measure, would not match your expectations of what the measurements should be, if they were instead rule of 18, hand cut frets.

Its a matter of looking at the issue through the right lens.

 

[rmmottola]

Hi John,
Yes, what anthonyg said.
For the purposes of construction of musical instruments there is absolutely nothing wrong with the Rule of 18 and hand cut fret slots. In American Lutherie articles written by both Jim Buckland and myself, we have demonstrated that the Rule of 18 can yield overall intonation as good as or in some cases better than the modern 12th root of two system. It is also possible to express fret location errors in terms of intonation and demonstrate that, with reasonable care, hand cut fret slots will result in no audible intonation differences compared with CNC cut slots.

But the context of this discussion is figuring out what you got when you are looking at an instrument which you didn't build and which has poor intonation. How does MrOldschool figure out if his nut is in the right place? It is easy to do if you know the scale length of course, but he needs to know where the nut is to figure out what the scale length is.

 

[John Colter]

"How does MrOldschool figure out if his nut is in the right place? It is easy to do if you know the scale length of course, but he needs to know where the nut is to figure out what the scale length is"

For this purpose, I would take a very simple approach. If the distance from the nut to the 1st fret is not greater than the first to the second, then it is wrong. If it is much more than 1 or 2mm greater, then it is wrong. If it meets these requirements I would look elsewhere.

How do we know the 1st to 2nd gap is correct? Well, if the first five fret gaps are all diminishing by about 1mm, that should be OK. This is all very approximate but close enough for the purpose of elimination.

The problem can be solved to umpteen decimal places, using mathematical formulae, if necessary.

 

[anthonyg]

"How does MrOldschool figure out if his nut is in the right place? It is easy to do if you know the scale length of course, but he needs to know where the nut is to figure out what the scale length is"

With all due respect John, we need to be a little more accurate than 0.5mm.
I advised on how to work out an unknown scale length.
You take an educated guess to start with. Run the numbers through a calculator and work out some fret to fret distances (fret 1 to 12), and then take that measurement to the instrument to see if its correct.
Not correct?
Guess another number, run it through the calculator, work out some fret to fret distances and try again.

Since posting this, rmmottola provided a link to a very good calculator that he created.

Now my experience say's that the nominal scale length will be in increments no less than 1/4 "(meh, maybe there are examples of 1/8" increments), unless its in metric. Given its an old American instrument it will be in inches and my educated guess was a (SUPPOSED) scale length of 12 3/4". Either that or 12 1/2" or 13".
Now this is not taking into account errors, and I wasn't thinking rule of 18 at the time I made this guess.
Thank you rmmottola for bring that up.

I'm still guessing a nominal scale length of 12 3/4", yet if you use a modern calculator rather than a rule of 18 calculator it will give you a bum steer.
Who knows how accurate the ruler used in the first place was?
There are going to be errors, and compensations may need to be made to correct for some errors. Maybe it will work out, maybe it won't.

 

[John Colter]

"With all due respect John, we need to be a little more accurate than 0.5mm"

I did say, "For this purpose", the purpose being to try to identify why the uke is so hopelessly out of kilter. The OP says, "I find that something is off in the scale. When I tune the strings to their correct open tuning, no notes ring true at any frets".

If somebody handed me this uke and asked me to identify the cause of the problem, I wouldn't start by measuring precisely the positions of the nut, frets and saddle. I would expect to find the probable cause just by running the rule over it in a cursory manner. A nut misplaced by 0.5mm will not cause the degree of chaos described by the OP.

 

[MrOldschool]

I'm still looking at this as time permits... I pulled the nut back out to work on sanding it thinner in an attempt to get it to sit lower in the slot. With the strings and nut removed, I'm back to just looking things over and taking measurements.

Taking my ruler and setting 12 3/4" aligned with where the inside of the nut should be, the other end of the ruler just meets the base of the saddle component of the bridge (all one piece of wood). The problem is two things I see right away for meeting that scale: one, that is the base, not the break, so that's about an eighth of an inch, and two, the scale on the ruler stops about an eighth of an inch from the physical end of the ruler. So this instrument varies from that scale length by nearly a quarter of an inch. Using the mindset of standard measurements being likely, the distance from nut to saddle is 12 15/16".
So it seems like I should probably look at the placement of the frets to see if they align with a scale length somewhere as they sit. If so, I figure out where the bridge should be and move it there. If they are just haphazardly placed, I am guessing the solution would be to remove the frets, glue down an entirely new fingerboard, and start from scratch? If that's the case, I don't think this thing is worth the effort.

Edit: plugging in the fret measurements for 1-2 in the calculator and using the older method of rule of 18, the scale should be 13.103", so we are way off!

Edit #2:
Plugging in all of the numbers, I get a scale length of 12.722"

The fret to fret measurements are all within tolerance except the 0 to 1 measurement, which shows a variance of 0.043. So that looks like I need to reduce the distance from nut to F1, and then reposition the bridge to the appropriate spot, yes?

 

[MrOldschool]

Here is the calculator readout:

 

[MrOldschool]

I did take all of my measurements from centerline to centerline of each fret, so if that is not correct, I would need to redo all of this. I wasn't clear on that point from the directions.