From: till@acid-rain.lucid.com (Don Tillman)
Subject: Re: Scale Length and Fret layout
Reply-To: till@lucid.com
Organization: Lucid, Inc.
	<Bu2CMp.HBn@watdragon.uwaterloo.ca>
Date: 4 Sep 92 18:00:28

   Date: 3 Sep 92 14:27:33 GMT
   From: schouten@sp1.csrd.uiuc.edu (Dale Schouten)
   Organization: Center for Supercomputing R & D

   Does anyone know a (the?) formula for determining fret positions based
   on the scale length?  

Zimple:

              scale-length
note-length = ------------
                2^(n/12)			 

Where n is the fret number (0 is the nut, 1 is the first fret, and so
forth) and note-length is the length from the effective bridge point to the
fret.  Obviously the units for note-length is the same as the units for
scale-length.

This equation might not be too practical because it's not always clear
where the effective bridge point is (compensation is added to this point,
moving the real bridge points back a bit), and additionally, the bridge
might be on a different piece of wood.  No matter, we just whip the
equation around:
                                            1
inverse-note-length = scale-length ( 1 - -------- )
                                         2^(n/12)

Where inverse-note-length is the distance between the nut and fret N.

This is the third time this question has been asked in recent memory; to
the FAQ!

   Does it vary for nylon vs. steel strings?

Nope, although the amount of bridge compensation certainly varies with
string material and gauge.

   Also, on a steel string, with a slanted bridge, do you measure scale
   length for the high string, low string, or somewhere in the middle?

Neither.  You measure from that effective bridge point I mentioned earlier,
which should be twice the length from the nut to the 12th fret.

   Date: 4 Sep 92 11:20:13 GMT
   From: dahe@cl.cam.ac.uk (David Elworthy)
   Organization: U of Cambridge Computer Lab, UK

   In article <SCHOUTEN.92Sep3102733@sp1.csrd.uiuc.edu>,
   schouten@sp1.csrd.uiuc.edu (Dale Schouten) writes:
   |> Does anyone know a (the?) formula for determining fret positions based
   |> on the scale length?

   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.


   |> Also, on a steel string, with a slanted bridge, do you measure scale
   |> length for the high string, low string, or somewhere in the middle?

   The theory would suggest you do it separately for each string and place
   the frets at an angle. But an approximation may be sufficient.

Incorrect.  The slanted bridge is for string compensation purposes.  

   Date: Fri, 4 Sep 1992 17:01:37 GMT
   From: rblander@watdragon.uwaterloo.ca (Robyn Landers)
   Organization: University of Waterloo

   In article <1992Sep4.112013.7029@cl.cam.ac.uk> dahe@cl.cam.ac.uk (David Elworthy) writes:

   >The theory would suggest you do it separately for each string and place
   >the frets at an angle. But an approximation may be sufficient.

	   Such designs exist.  I think a company even sells replacement
   necks done this way.  I've seen the occasional photo and write-up
   in Guitar Player, although not for over a year or so now as I recall.

The slanted frets neck (at least the one I remember) was actually a hack so
that the higher strings could have a 24.75-inch scale while the lower
strings could have a 25.5-inch scale.  Slanted frets are otherwise
unnecessary.

This is not to be confused with the Rickenbacker slanted frets feature
which was an experiment to make fingering easier.  The nut, frets, and
bridge were all tilted from the norm by an equal amount.

   I remember one design with slanted frets, and another with fragmented
   frets.  Not sure how well one could bend on the latter.

The fragmented frets was yet another hack to do different (non-equal
tempered) scale tunings.

  -- Don