(edited - removed extraneous information, and added more detail)
In a cone section, the radius is proportional to the distance from the apex (the pointed end).
The radius is also proportional to the distance between two lines on the surface that extend
from the apex. These lines represent the fingerboard path beneath the strings. If you extend
these lines beyond the nut, they will converge at the apex of the cone.
At the nut, the strings are very close to the fingerboard, and the distance between the lines
is very close to the distance between the E and G (center to center). At the bridge end of the
fingerboard, the E and G need to be pressed down to the board to find this distance because
we need this measurement at the radius of the fingerboard, not at the radius of the strings.
At the nut, the bottom of the strings are already at the fingerboard radius.
These two measurements are basically the E to G string spacing, with the strings lying flat
on the fingerboard. One measurement at the nut, and one at the bridge end of the board.
The ratio of these two measurements is also the ratio of the radius at the two ends of the
fingerboard for a matching cone.
Note - these are not actual radius of that particular board; they are the radius for a cone that
would fit perfectly beneath the strings.
On my bass, E to G at nut is about 1.25". E to G at bridge end of fingerboard is about 2.75".
So the ratio is 2.2, which is a nut radius that's 45 percent of the fingerboard end radius.
Based on the string spacing on my bass, a matching cone would have a radius ratio of 2.2.
The nut end would be about 45 percent of the bridge end. The board is 34". So I'm getting
similar numbers to yours for a matching cone.
My fingerboard also measures close to 3" radius at the bridge end, but it's close to 2" radius
at the nut. So it has a conical surface, but does not match the string paths. The actual radius
at nut is 67 percent instead of 45.
The positive scoop that you mentioned, caused by angled strings on a cylindrical surface, is
typically less than 0.001" for an electric guitar. Very surprising! I expected it to be more and
modeled it with a PC program a couple years ago. Someone in another forum also became
interested and modeled it with a CAD program. He got the same results. I dusted off my program
and ran it again with upright bass parameters. These are the results:
scale 42"
string spacing at nut 1.25"
string spacing at bridge 3.12"
radius 3.0"
height at nut 0.0000
height at midpoint 0.0265
height at fretboard end 0.0000
The midpoint value shows the height of the positive scoop, or "hump" along the fingerboard
path beneath the E or G string. A straight edge placed parallel to the string would rock on a
hump that was 0.0265" high. The height at the ends are the reference points.
And that is for a cylindrical (constant radius) board. A conical board would have less to none,
depending on the match to string spacing.
Also a cone is not the only shape that has straight fingerboard paths beneath each string.
You can modify a cylindrical surface by simply "scooping" the outer strings slightly more than
the inner strings. You get something that sort of resembles an hourglass shape.
Whether or not a matching cone is best for a neck is a whole 'nother matter, as JoeyNaeger
suggested.
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