innovative fretboards

Since the medieval times, the "rule of 18" has been used to locate
the fret positions on a plucked stringed instrument. According to
this procedure, each succesive half-step is obtained by positioning a
fret at one-eighteenth of the remaining length of the string. This
produced a ratio of frequencies of 1.0588, which is a reasonable
approx. to the equal-tempered half-step, 1.0595. More accurately,
guitar builders today have used to string length divided by 17.835 to
locate a proper half-step. This is fine if you are satisfied with the
12 tone equal tempered system. I seek to cut a fretboard that will
play exact harmonies. This will limit the instruments ability to play
in one key, but extremely well. I have frequencies on paper, but I
need to know where to place my frets. For example, the first fret
ratio would be 1.05. I need to know what I must divide my string
length by in order to obtain this ratio. The ratio's along the neck
will differ. If anyone has information, or leads on where I could
read information on this topic, I would be happy. I'm in dire straits
here.

In-Reply-To: <8gi3jh+8bca@eGroups.com>
The Venus wrote:

> Since I'm taking the time to cut a fretboard to play pure just
> harmonies, my dilemna now is intonation. Before I go ahead, purchase
> a blank fretboard, and bring out the hacksaw ...

I suggest you buy a fretsaw as well. I'm not sure exactly what they are
or how much they cost, but cutting the slots with a standard carpentry saw
did give me trouble. The frets slid in easily enough, but then had to be
glued in place, and didn't all stick the same way, amongst other problems.

Graham