From: dam@dcs.glasgow.ac.uk (David Morning)
Newsgroups: alt.guitar
Subject: Re: Scale Length and Fret layout
Date: 8 Sep 92 10:22:54 GMT
Organization: Glasgow University Computing Science Dept.

till@acid-rain.lucid.com (Don Tillman) writes:

Hello Don,

>   From: dahe@cl.cam.ac.uk (David Elworthy)

>   I went to a workshop on building stringed instruments at this year's
>   Sidmouth festival. As I recall the procedure is to place the first fret
>   so that it divided the scale length in the ratio 1:n, where n was
>   something like 17.85. Then place the second fret to divide the length
>   from the *first fret* to the bridge in the same ratio. The the thrid
>   fret to divide the distance from the second fret to the bridge in the
>   same ratio. And so on. Don't trust the figure I've give. 

>This method is bogus for two reasons:

>                                 1
>  1. The number is really  ----------------  
>                           1 - 1 / 2^(1/12)
>     which is roughly 17.817153745105778.

>  2. Any error will accumulate, and the worst error will be where it hurts  
>     most, at the higher frets.


I think what he is referring to is something called "The Rule of 17" although,
as you point out, it's not 17 at all. I believe it's still used in the
construction of traditional acoustic instruments such as mandolines and
classical guitar where going above the 12th fret is rare. The number is tweaked
to give the 12th fret in tune and any cumulative errors are distributed lower
down. A high degree of precision isn't essential since, in the case of a hand
made instrument, your liable to introduce far larger errors relating to the
thickness of the fret saw blade and trying to find its centre line. The
percentage error introduced by the saw blade will become relatively worse the
higher up the scale you go, so unless you 'jig' saw it (not the same as a
jig-saw, construct a steel jig to enable the saw to cut accurately) your errors
from trying to cut a fret with a hang-over are liable to be *much* worse.

I made a mandoline in 197*hurumph* using this method when I did a 2 year stint
at a college who offered an option of musical instrument making. It sounded
fine and had no tuning problems. I then made an electric guitar - didn't
sound too great, intonation was out above the 12th fret, particularly when you
got up to the 17th fret. I couldn't make up my mind if I'd bodged the sawing,
marking or the calculations so I redid the calculations using the tweaked 17
rule, rechecked the sizes and couldn't find any errors. A couple of people in
the same class as me made classical guitars using the same rule and they 
sounded fine so I just put it down to 'one of those things'.
Interestingly, the following year, when I had moved on to other things, a 
couple of people who'd moved into the instrument class made stell strung
acoustic guitars, one a 12th fret join traditional, the other a 15th fret
Martin type. The guy who made the Martin type complained about intonation
problems too while the guy who made the 12th fret join guitar was quite happy.


I'd guess the method Don suggests is probably far better than the Rule of 17
method for instruments which are going to be used often above the 12th fret
i.e. electric guitars.


Dave

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