Re: Re[2]: [HG] Key placement calculator

[Patrick Brown]

Long time ago, at least as far back as fretted instruments conforming  
to the newer than fretted instruments 'tempered scale,' which  
tempered scale goes back to the ca 1600's(?) and placed in our laps  
by a fellow appropriately named Werckmeister(sp), (and fretted  
instruments going back to the 1400's or earlier, depending on where  
you were),,,derived, as Alden says, from using the 12th root of  
2,,was known as the 'Rule of 18,' which means that each successive  
distance for each next fret, or tangent, closer to the bridge one  
goes, in order to find its placement, you divide that distance by 18,  
and that resulting  distance by 18, and so on ad infinitum 
(literally,,like the frog jumping halfway across the pond,,then  
halfway again). The actual number is generally agreed among luthiers  
to be 17.817, if memory serves, though I've read 17.835, but that's  
an obscure and only one or two source memory,,but 17.817 is the  
divisor, if that's the right word. The number you use to divide, at  
any rate. This is, of course, assuming you are after a tempered  
scale. If you want just temperament,,then you'd use fractions of the  
fundamental. The swinging tangent should allow either choice.

Pat