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The below article is an paraphrase from a Dan Erelewine article on fingerboard radius.
There's a difference in the fingerboard radius of different guitars. Understanding this difference is important to a guitar player and a technician.
Radius fret boards exist to compliment the natural curve of a human finger. In choosing a guitar a player should consider a fingerboard radius. The most heavily radius fingerboards are Rickenbacker and Fender.
Guitars that have a 7 1/4 radius (ala' Fender) feels good, but when bending a high "E" or "B" these notes will usually "note out." The solution is to raise the string height. If one doesn't bend notes then no problem.
A flatter fingerboard of 12" is good for blues players, but the flatter a fingerboard the harder to chord the guitar. Thus, an in-between radius of 9" or 10" may be the right fit.
Factory production guitars usually cuts fingerboards into a "cylindrical" shape. Thus the fingerboard is more narrow at the nut. Imagine a drinking glass as a Cylindrical fingerboard. Its easy to wrap your finger around the glass even as it gets narrow. Great for chording and single note playing, but probable "note out" when bending strings as the string will touch the top or crown of the fret.
To avoid this a "cone shape" fingerboard comes into play. Simply, its a compound board meaning its has one radius in the top half of the board (1st - 7th position usually) and another radius in the higher register. Meaning the fingerboard will flatten out. Thus, bending strings at the high register will negate: Note out!
These days Warmoth, Jackson, Collings, Taylor, and Martin make a compound fingerboard. Also, Fender offers a 9" and 12" radius fingerboards keeping the 7 1/4 radius on their vintage type models.
In the end, knowing the radius of the guitar/s fingerboard is significant to the playing style of the guitarist and is a must know.