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ukantor
04-08-2011, 08:10 AM
Some years ago, I read in a book that luthiers of old used something called "The Rule of Eighteen" to work out their fret spacings. The book went on to say that eighteen had been found to be inaccurate, and we now use a figure of 17.81715 (or somesuch) as the divisor in determining fret positions. This left me with the impression that luthiers had been making instruments with faulty intonation for hundreds of years, until fairly recent times.

Just recently, I "did the math" and discovered that The Rule of Eighteen actually works perfectly well. It is an odd quirky fact that it places the frets just were they should be, AND it provides a useful amount of compensation for the way a string will stretch when pressed down.

I have made a soprano uke, using eighteen as my fret position divisor, and it plays as well as any other uke I've ever tried.

Using the modern divisor will put the frets in the correct theoretical positions, and the twelfth fret will end up exactly at the half way point of the scale length, but if you leave it like that, with no compensation for string stretch, the uke will play progressively sharp as you move up the fretboard. So we get round this by moving the bridge/saddle away from the nut by about 3mm. This increases the scale length, of course.

Consider a uke with a scale length of 350mm. The Rule of Eighteen will place the first fret at 19.44mm (19.47); the 7th fret at 115.40mm (115.39); the twelfth at 173.72 (173.49) - the figures in brackets are for a scale length of 347mm using the modern divisor. Once you have added 3mm compensation, your scale length of 347 has become 350, so it is a valid comparison.

I think those good old boys of days gone by deserve a bit of respect. They DID know what they were doing, after all!

jonesjimbo
04-08-2011, 08:23 AM
Oh man, that is the second time that I tried to reply to a thread and messed up! I think I hit Reply to thread instead of post quick reply.

Anyhow, I find this very interesting ukantor. Do you have any good resources on uke building?

I always thought that the 12th fret was exactly in the middle of the string, but it looks like it isn't quite exact!

DaveVisi
04-09-2011, 07:23 AM
It would be in the exact middle if we didn't have to press the string down to the fret. A 12th fret harmonic would theoretically be the exact center.

ukantor
04-10-2011, 03:03 AM
Yes, that's the interesting thing, Dave. Today, we start with the theory, and then modify the way we apply it, so that it gives the results we want. In ancient times, they placed the frets where they gave the desired result, and worked out a formula to repeat it.

It would be misleading to suggest that the rule of eighteen was discarded because it was inaccurate. In fact it works very well indeed.

realityguy
04-10-2011, 05:46 AM
So far on the ukes I've made,the fretboards and compensation have been based on a Kamaka Soprano and Gibson Tenor I own..but I'm interested in making a concert size and will be using a different scale than what I have available to copy.Can you post(and kind of explain) the formula of the "eighteen rule" so I can plug in the scale I want and calculate them myself?..rather than me going to Stew-Mac and using their calculator.I'd much rather use and understand the fret layout the old fashioned way...Thanx..

ukantor
04-10-2011, 08:47 PM
Hi Realityguy,

The Stewart MacDonald calculator works by taking the scale length and dividing it by 17.81715. This gives the distance from the nut to the first fret. The distance from the first fret to the saddle is then divided, to give the measurement from the first to the second fret - and so on. The Rule of Eighteen does the same, but using 18 as the divisor. At first glance, you would think that the two different divisors would give significantly different results, but the modern method does not allow for compensation, and the older one does, so you end up with practically the same result.

I am not saying that one method is better than the other - they both work well - so there is no reason not to use the StewMac calculator. I have made one uke using the Rule of Eighteen, just for the heck of it, and it works just fine, but in future I'll stick with modern practice.

The point of my original post was to dispell the impression that old time luthiers were using an inaccurate method of fret calculation.

John Colter.

thistle3585
04-11-2011, 08:12 AM
Doesn't the rule of eighteen assume a zero fret is used and the modern rule is that a nut is used?

ukantor
04-11-2011, 10:12 AM
What's the difference? It's just another way of determining one end of the scale length.

thistle3585
04-11-2011, 11:32 AM
What's the difference? It's just another way of determining one end of the scale length.

The difference is that on a zero fret the string rests on the center of the slot and on the edge of the slot for a nut. In otherwords, for a zero fret the scale starts at the center of the slot whereas when using a nut it starts at the edge of the slot. I am wondering if the shift from the rule of eighteen some how had to do with the decrease in use of the zero fret. They needed to take that lost .0115 into consideration. As I see it, if you start the scale by being short .0115, which is half the width of a standard fret slot of .023, then by the time you get to the 12 fret then you are off by .138. This is more of a question than it is a statement of fact.

ukantor
04-11-2011, 12:08 PM
Hi Thistle,

Interesting point. I am considering these calculations purely mathematically. How accurately you apply the figures when you make your instrument, will, of couse, have a bearing on how good is its intonation. When using a nut, I measure from the face of the nut; when using a zero fret, I measure from the centre of that fret - for both systems.

The amount of compensation provided by the rule of eighteen, cannot be relied upon exactly, but it is pretty darn close to what we use in practice.

realityguy
04-11-2011, 04:29 PM
Ukantor..thanks..I'll probably use the Stew/mac calculator then...I have used it to check some cheap ukes to see how far off they are and reset things so they at least aren't total wallhangers if the frets are pretty close for a certain scale length.I've seen/reset some off as much as 1" or better,especially from China.

Moore Bettah Ukuleles
04-11-2011, 04:53 PM
Ukantor..thanks..I'll probably use the Stew/mac calculator then...I have used it to check some cheap ukes to see how far off they are and reset things so they at least aren't total wallhangers if the frets are pretty close for a certain scale length.I've seen/reset some off as much as 1" or better,especially from China.

Since you are on the luthiers part of this forum, just know there is no such thing as "pretty close" when it comes to correct fret spacing!

Vic D
04-11-2011, 06:28 PM
Couldn't live without my fret slot templates... first two fretboards I tried to hand slot were firewood... though they were pretty close to being accurate... well the 2nd one was. didn't use them... couldn't... wouldn't be prudent.

ukantor
04-11-2011, 09:36 PM
About ten of my ukes (of a total of around thirty) have had fret slots entirely marked out and cut by hand. It is time consuming and exacting work, but very satisfying. Only one was scrapped, and that was for a cosmetic problem, not one of accuracy.

I used the words "pretty darn close" in relation to compensation, which is adjustable. I wouldn't apply that thinking to fret placement.