how the pros do it (?)

I found this article online, which addresses some of the same concerns as I have been investigating:
https://joeynaegerbasses.com/resources/fingerboard-geometry/

However, the author does not seem to fully understand the geometry of the situation.  There is no clear diagram showing what happens "in the middle", between the two defined radiuses at the nut and bridge.  This, of course, is the key issue!  But this author, with so many others, just digresses into a discussion of "scoop", which seems to be something that is just iteratively added until things play correctly.

I found an even more clear confirmation of my suspicions about how the pros may handle this problem, reading some of the online discussion forums dedicated to the upright bass.  One maker said that his approach was to simply plane away the fingerboard until it followed the "lie of the strings".  This is conceptually brilliant, and should result in the same figure that I have created mathematically, through a simple and "blind" procedure.

As a practical matter, I'm not sure how he accomplishes this: surely, it's not convenient to plane the fingerboard while it's installed on the bass, with the strings in place.  My guess is, he has made some kind of fixture or jig for planing fingerboards, with some way to stretch wires over the top representing the strings.

I also found this page:
https://hazeguitars.com/blog/compound-radius-setup

This one refers mainly to electric guitar, where "compound radius" exists but is a little different.  On a guitar, the radius starts small at the nut, and then widens out towards the bridge.  Thus, it is basically conical in shape, and the "non-conical" effects which I've discussed do not come into play.  Consequently, it's a bit dangerous: people think they know about compound radiusing from guitar, try to apply this to upright bass -- and disaster ensues!

However, the notable thing about this page, is that it also uses the terminology of planing the board to fit the "lie of the strings".

See also:
http://www.mccarthystringedinstruments.com/page41/page42/page42.html
https://www.talkbass.com/threads/fingerboard-radius.495545/




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