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!

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!