a graphical representation

Here's one way to visualize this shape.  I used find_circle.c to make 25 pairs of y-value, radius numbers.  Then I made a simple PostScript program to plot circles of the right radiuses at the specified offsets, in a staggered manner so that the resulting figure kind of resembles a 3-D representation (although the perspective isn't actually correct, the circles should be ellipses).  The fingerboard would be a narrow strip cut out of the top, relatively flat, portion of this shape.  (Maybe I'll put that into the diagram, too.)


...OK, try this:


The curved lines can cause a bit of an optical illusion; but if you check with a straightedge, you can verify that each of the four rows of dots representing the path of a string, follows a straight line over the surface of the shape.  You can also see that my guesswork values for the string positions are not as realistic as I might have hoped: down at the bridge, the two middle strings are clearly too close together, compared with the spacing of the outer strings.

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